MODULE FOR
MICROECONOMICS I (ECON 111)
BY:
WODAJO WOLDEGIORGIS (PHD)
WONDAFERAHU MULUGETA (MSC)
TSEGA WONDIMAGEGNEHU (MA)
HASSEN ABDA (MSC)
ORGANIZED BY:
FACULTY OF BUSINESS AND ECONOMICS
JIMMA UNIVERSITY
SEPTEMBER, 2008
JIMMA
Table of Contents Page
CHAPTER ONE: INTRODUCTION ............................................................................. 1
1.1 Introduction............................................................................................................... 1
1.2 Chapter Objectives.................................................................................................... 2
1.3 Definitions, Scope and Nature of Economics ........................................................... 2
1.4 The Fundamental Economic Problems and the Alternative Economic Systems...... 7
1.5 Scarcity, Opportunity Cost and Efficiency ............................................................. 13
1.6 Decision Making Units and the Circular Flow of Economic Activities ................. 15
1.7 The Concept of Market Structure ........................................................................... 18
1.8 Microeconomic Theory and the Price System........................................................ 18
1.9 Lesson Summary..................................................................................................... 19
1.10 Review Questions ................................................................................................. 21
CHAPTER TWO: THE THEORY OF CONSUMER BEHAVIOR ......................... 24
2.1 Introduction............................................................................................................. 24
2.2 Chapter Objectives.................................................................................................. 26
2.3 What Is the Theory of Consumer Behavior? .......................................................... 27
2.4 The Rational for the Theory of Consumer Behavior .............................................. 27
2.5 Methods of Comparing Utility................................................................................ 28
2.5.1 The Cardinal Utility Theory......................................................................... 28
2.5.2 The Ordinal Utility Theory .......................................................................... 35
2.6 The Market Demand for a Commodity................................................................... 71
2.7 Elasticity of Demand............................................................................................... 75
2.8 Choice under Uncertainty ....................................................................................... 89
2.9 Lesson Summary..................................................................................................... 96
2.10 Review Questions ................................................................................................. 97
CHAPTER THREE: THEORY OF PRODUCTION ............................................... 103
3.1 Introduction........................................................................................................... 103
3.2 Chapter Objectives................................................................................................ 103
3.3 The Production Function....................................................................................... 104
3.4 The Short Run Production Function and Stages of Production ............................ 109
3.5 Laws of Production............................................................................................... 121
3.6 Returns to Scale and Homogeneity of the Production Function........................... 123
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3.7 Equilibrium of the Firm: Choice of Optimal Combination of
Factors of Production.......................................................................................... 125
3.8 Lesson Summary................................................................................................... 133
3.9 Review Questions ................................................................................................. 134
CHAPTER FOUR: THE THEORY OF COST ......................................................... 137
4.1 Introduction........................................................................................................... 137
4.2 Chapter Objectives................................................................................................ 138
4.3 Short-Run Costs .................................................................................................... 138
4.4 The Relationship between Product Curves and Cost Curves in the Short Run .... 149
4. 5 Long-Run Costs ................................................................................................... 152
4.6 The Relationship between Short-Run and Long-Run
Average and Marginal Costs............................................................................... 154
4.7 Derivation of Cost Function from Production Function ....................................... 158
4.8 Dynamic Changes in Costs – The Learning Curve............................................... 161
4.9 Lesson Summary................................................................................................... 163
4.10 Review Questions ............................................................................................... 164
CHAPTER FIVE: PERFECT COMPETITION ....................................................... 168
5.1 Introduction........................................................................................................... 168
5.2 Chapter Objectives................................................................................................ 169
5.3 Characteristics of Pure and Perfect Competition .................................................. 169
5.4 Market Equilibrium............................................................................................... 173
5.4.1 The Market Period Equilibrium................................................................. 173
5.4.2 The Short Run Equilibrium of a Firm and Industry/Market ...................... 174
5.4.3 The Long Run Equilibrium........................................................................ 184
5.5 Perfect Competition and Consumers' Welfare...................................................... 187
5.6 Lesson Summary................................................................................................... 188
5.7 Review Questions ................................................................................................. 189
CHAPTER SIX: PURE MONOPOLY ....................................................................... 192
6.1 Introduction........................................................................................................... 192
6.2 Chapter Objectives................................................................................................ 193
6.3 The Characteristic Features of Pure Monopoly .................................................... 193
6.4 Origins of Monopoly Power ................................................................................. 196
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6.5 Short Run Equilibrium of a Pure Monopolist ....................................................... 199
6.6 The Long Run Equilibrium of a Pure Monopolist ................................................ 207
6.7 Price Discrimination ............................................................................................. 213
6.7.1 Definition and Necessary Conditions ........................................................ 213
6.7.2 Types of Price Discrimination ................................................................... 214
6.8 A Multi-Plant Monopolist..................................................................................... 221
6.9 The Social Cost of Monopoly ............................................................................... 226
6.10 Lesson Summary................................................................................................. 234
6.11 Review Questions ............................................................................................... 236
References …………………………………………………………………………..…239
Answers to Selected Review Questions ……………………………………….……..240
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CHAPTER ONE
INTRODUCTION
LESSON STRUCTURE
1.1 Introduction
1.2 Chapter Objectives
1.3 Definitions, Scope and Nature of Economics
1.4 The Fundamental Economic Problems and the Alternative Economic Systems
1.5 Scarcity, Opportunity Cost and Efficiency
1.6 Decision Making Units and the Circular Flow of Economic Activities
1.7 The Concept of Market Structure
1.8 Microeconomic Theory and the Price System
1.9 Lesson Summary
1.10 Review Questions
1.1 INTRODUCTION
This lesson tries to acquaint students with basic economic concepts and terminologies,
which are necessary to understand any subject of economics (particularly this one –
microeconomics). It attempts to present some reasons why you as a student learn
economics. The two fundamental facts, limited resources and unlimited wants, which
provide a reason for the existence of the subject of economics, are also briefly explained.
The lesson will present the fundamental economic problems, which are common to all
countries, and how they are solved in different economic systems in some detail. The
lesson will also provide an illumination of some basic concepts like scarcity of economic
resources, opportunity cost and efficiency. The circular flow of economic activities
presents how decision-making units interact in the market economy system. Towards its
end, the chapter describes the concern of microeconomics.
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1.2 CHAPTER OBJECTIVES
After working through this lesson, you should be able to:
• Define economics;
• Explain the nature and scope of economics in general and microeconomics in
particular;
• Understand different methods of economic analysis;
• Explain what economic resources are, and the issue of scarcity;
• Understand the different economic systems and how each of them answer the
basic economic problems;
• Understand the concept of opportunity cost and efficiency;
• Have an overview of the different types of market structure;
1.3 DEFINITIONS, SCOPE AND NATURE OF ECONOMICS
Why Do You Study Economics?
Economics is a word commonly used in our daily conversation. What is economics and
why do you need to learn economics? Before defining economics first let us try to see the
reasons why people want to study economics. Many people study economics for various
reasons. Some people want to study economics because they hope to make money. Some,
on the other hand, need to study economics because they feel illiterate if they cannot
know and understand the law of demand and supply. Many want to learn economics
because they want to know and understand how inflation and budget deficit will affect
their future life.
Generally, knowledge about economics is important because each one of us faces
economic problems at different levels and makes economic decision throughout his/her
life knowingly or unknowingly. For instance, on a personal level, we often make some
personal decisions on issues like: Which job should we take? How can we best spend our
income? Shall we buy or rent a house? And so on.
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If someone enters into business, he/she will face many economic decisions like: what to
produce or what type of service to provide? How and in what quantity to produce? And
so on. Also in politics, we face many economic decisions like how much the nation
should spend on defense, on health care and environment, on education and on different
physical infrastructure? Even as a voter, we evaluate candidates partly on the basis of
their economic view. That is, on the basis of their view on unemployment, on inflation
and over all on their socio-economic programs.
In short, economic literacy is important because economic issues facing government and
individuals shape the future of the nation and affect the well being of its citizens.
Therefore, for these and the like reasons, it is essential that economics be made accessible
to everyone.
What is Economics?
Before defining economics, again, we better first introduce some terminologies which are
necessary for better understanding of the definition of economics.
A. Resources
Resource is anything that can be used to produce goods and services. Resources are also
called inputs or factors of production. Resources (factors or inputs of production) are
divided into four categories, namely:
i. Land
ii. Labor
iii. Capital
iv. Entrepreneurship
i. Land: is a natural gift, which includes all natural resources which are found inside and
on the surface of the land. These are like:
• Different minerals
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• Soil, river, lake pond
• Timber or forest resources and other natural materials necessary to produce goods
and services.
ii. Labor: is mental and physical human effort (ability) used in the production process.
The skill and amount of labor will be important in determining level and quality of
production.
iii. Capital: capital is a man-made means of production used in the production process.
Here belong resources like:
• Machineries, equipments, tools used in the production process.
• Buildings and materials attached to it, and
• Financial capital
iv. Entrepreneurship: it is managerial skill of organizing and combining the above three
resources for production purposes. The above resources cannot be productive and be
changed into goods and services without the creative effort of entrepreneur.
Entrepreneur is an individual who organizes resources for production, introduces new
products or techniques of production.
The principal role of entrepreneur includes:
• Introducing new product and new methods of production
• Setting the overall direction of the firm
• Being a risk taker
Factors of production are combined differently by entrepreneur in the production process
and will be converted into goods and services.
Inputs (Resources) Output
Land, Labor, Capital, (production process) (Goods and Services)
Entrepreneurship
4B. Goods versus Services
The distinction between goods and services is based on whether the output (product) is
tangible or intangible. Tangible Outputs (Goods) are those like clothes, shoes, beverage,
automobile and the like. These goods are feasible and their existence can be sensed.
Intangibles Outputs (Services) are those like haircut, computer repairs, teaching and
consultation, and so on.
C. The Fundamental Economic Facts
There are two fundamental facts, which constitute the economizing problems and provide
foundation for the subject economics. These are unlimited wants and limited economic
resources.
Society's wants for material goods and services are unlimited: Our needs for goods and
services are insatiable or can not be fully satisfied because,
i. Wants are multiplicative. Introduction of a new commodity creates need for
many other commodities. For example, purchasing of a car creates needs for
parking place, fuel, oil and so on.
ii. Wants are recurrent. Even if a specific want is satisfied at a particular time, it
may recur. Take for instance food consumption. Need for food may reoccur
several times a day. The same thing is true for clothing. In short, people will
consume most of the commodity many times throughout their life.
iii. Wants multiply endlessly. If one want is satisfied, the need for another arises. If
we satisfy our need for food in a particular period of time, need for cloth arises and
if we satisfy our need for it, need for shelter comes. In such manner, human wants
multiply continuously.
iv. Human nature is accumulative. People accumulate things beyond their present
need. Even if all needs were satisfied at a particular period of time, people would
like to keep it more for consumption sometimes in the future.
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In general, people have insatiable desires for goods and services to raise their standard of
living.
Limited economic resources: Economic resources like various types of labor, natural
resources, capital and entrepreneurial ability we use to produce goods and services are
limited.
If economic resources are not sufficient to produce all goods and services needed by a
society, then we have to make choice as to which good to produce first.
Thus, unlimited wants and limited resources will give us the problem of scarcity.
Because of scarcity, economic resources must be allocated efficiently. Scarcity implies
that resources are insufficient to produce all goods and services desired by consumers or
society as a whole. To solve this and related issues we have a discipline called
Economics. Therefore, economics is the study of how scarce resources are allocated
among alternative and competing ends or uses in order to maximize the consumption of
material goods and services.
In addition to the above concepts, there are others which are very important in
understanding this course. Some of them are given below.
I. Microeconomics versus Macroeconomics
Economics is typically divided into two parts: microeconomics and macroeconomics.
Microeconomics is the part of economics which studies the decision making process by
individuals (households) and by firms. It studies the behavior of individual components
of the economy like households and business firms.
Macroeconomics, on the other hand, is the part of economics which studies the behavior
of the economy taken as a whole. It deals with phenomenon at overall economy level
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like: unemployment, inflation and national income. It studies the function of the economy
taken as a whole.
II. Positive Economics versus Normative Economics
Positive Economics is that part of economic science which deals with specific statements
that are capable of verification, by reference to the facts about economic behavior. That
is, it is concerned with describing and analyzing the economy as it is. It is an economic
analysis strictly limited to make purely descriptive statements of scientific prediction. For
example, if the price of oil increases relative to all other prices, then the amount that
people will buy will fall. Here economics will tell us what will happen if some action is
taken.
Normative Economics, on the other hand, is analysis involving value judgment. It is that
part of economic science which involves someone’s value judgments about what the
economy should be like or what particular policy action should be recommended to solve
economic problems based on a given economic generalization or relationship. Here the
economics will tell us what should be done. For example, if the price of oil goes up,
people will buy less of it, therefore, we should not allow the price to go up. Such
statement is a normative economic statement.
1.4 THE FUNDAMENTAL ECONOMIC PROBLEMS AND THE
ALTERNATIVE ECONOMIC SYSTEM
Economic system is the set of organizational arrangement and institutions established to
solve the fundamental economic problems, what, how and for whom to produce.
Economic systems are different from each other on the basis of the ownership of
economic resources and the method by which economic activities are coordinated.
Economic system is a basic means of achieving economic goals that are inherent in the
economic structure of a society.
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The fundamental role of an economic system in any society is to provide a set of rules for
allocating resources and/or consumption among individuals who can't satisfy their wants,
given limited resources. The rules that each economic system provides function within a
framework of formal institutions (e.g., laws) and informal institutions (e.g., customs).
As we have mentioned earlier, because of scarcity, there must be a choice in the use of
economic resources. The important characteristics of economic resources are that they
can be put into alternative uses. Society, therefore, must choose the best ways of using
scarce resources. Nations, be it rich or poor, developed or underdeveloped, will all face
the problem of choice.
In every nation, no matter what the form of government, what the type of economic
system, who controls the government, or how rich or poor the country is, three basic
economic questions must be answered. They are:
i. What to produce?
ii. How to produce?
iii. For whom to produce?
What and how much will be produced? Literally, billions of different outputs could be
produced with society's scarce resources. Some mechanism must exist that differentiates
between products to be produced and others that remain as either unexploited inventions
or as individuals' unfulfilled desires.
How will it be produced? There are many ways to produce a desired item. It may be
possible to use more labor and less capital, or vice versa. It may be possible to use more
unskilled labor to substitute for fewer units of skilled labor. Choices must be made about
the particular input mix, the way the inputs should be organized, how they are brought
together, and where the production is to take place.
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For whom will it be produced? Once a commodity is produced, some mechanism must
exist that distributes finished products to the ultimate consumers of the product. The
mechanism of distribution for these commodities differs by economic system.
Historically, four different types of economic systems are observed. These are:
1. Pure Capitalism (Free Market Economy)
2. Pure Socialism (Command Economy)
3. Mixed Economy (Hybrid Economy)
4. Traditional Economy (Customary Economy)
Market versus Command Economic Systems
One way to define economic systems is to classify them according to whether they are
market systems or command systems. In a market system, individuals own the factors of
production and individually decide how to use them. The cumulative decisions of these
individuals are reflected in constantly changing prices, which result from the supply and
demand for different commodities and, in turn, impact that supply and demand. The
prices of those commodities are signals to everyone within the system indicating relative
scarcity and abundance. Indeed, it is the signaling aspect of the price system that provides
the information to buyers and sellers about what should be bought and what should be
produced.
In a market system the interaction of supply and demand for each good determines what
and how much to produce. For example, if the highest price that consumers are willing to
pay is less than the lowest cost at which a good can be produced, output will be zero.
That doesn't mean that the market system has failed. It merely implies that the demand is
not high enough in relation to supply to create a market; however, it might be someday.
In a market economy the efficient use of scarce inputs determines how output will be
produced. Specifically, in a market system, the least-cost production method will have to
be used. If any other method was used, firms would be sacrificing potential profit. Any
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firm that fails to employ the least-cost technique will find that other firms can undercut
its price. That is, other firms can choose the least-cost or any lower-cost production
method and be able to offer the product at a lower price, while still making a profit. This
lower price will induce consumers to shift purchases from the higher-priced firm to the
lower-priced firm, and inefficient firms will be forced out of business.
In a market system, individuals make the choice about what is purchased; however,
ability to pay, as well as the consumer's willingness to purchase the good or service,
determine that choice. Who gets what is determined by the distribution of money income.
In a market system, a consumer's ability to pay for consumer products is based on the
consumer's money income. Money income in turn depends on the quantities, qualities,
and types of the various human and non-human resources that the individual owns and
supplies to the resource market. It also depends on the prices, or payments, for those
resources. When you are selling your human resources as labor services, your money
income is based on the wages you can earn in the labor market. If you own non-human
resources – capital and land, for example – the level of interest and rents that you are paid
for your resources will influence the size of your money income, and thus your ability to
buy consumer products.
Critics commonly argue that in a market system the rich, who begin with a
disproportionately large share of resources, tend to become richer while the poor, who
begin with a disproportionately small share of resources, tend to become poorer. They
further argue that a government, which is designed to protect private-property rights, will
tend to be exploited by those in power, which tends to be the economically wealthy.
These critics argue that a market economy leads to selfish behavior rather than socially
desirable outcomes.
In contrast, a command system is one in which decision making is centralized. In a
command system, the government controls the factors of production and makes all
decisions about their use and about the consumption of output. The central planning unit
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takes the inputs of the economy and directs them into outputs in a socially desirable
manner. This requires a careful balancing between output goals and available resources.
In a command system the central planners determine what and how much will be
produced by first forecasting an optimal level of consumption for a future period and then
specifically allocating resources projected to be sufficient to support that level of
production. The "optimal" level of production in a command economy is determined by
the central planners and is consistent with government objectives rather than being a
function of consumer desires.
As a part of the resource allocation process, the central planners also determine how
production will take place. This process could focus on low-cost production or high
quality production or full-employment of relatively inefficient resources or any number
of other governmental objectives.
Finally, the command system will determine for whom the product is produced. Again,
the focus is on socially-desirable objectives. The product can be allocated based on class,
on a queuing process, on a reward system for outstanding or loyal performance, or on any
other socially-desirable basis for the economy.
Critics commonly argue that because planned economies cannot effectively process as
much relevant information as a market does, command economic systems cannot
coordinate economic activity or satisfy consumer demand as well as market forces do.
For example, consider an economic planning board of twenty people that must decide
how many coats, apartment buildings, cars, trains, museums, jets, grocery stores, and so
forth should be built in the next five years. Where should these planners begin? How
would they forecast the future need for each of these?
Critics argue that, at best, planners would make a guess about what goods and services
would be needed. If they guess wrong, resources would be misallocated and too much or
too little production would take place. These critics argue that private individuals, guided
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by rising and falling prices and by the desire to earn profits, are better at satisfying
consumer demand.
The Mixed Economic System
In practice, most economies blend some elements of both market and command
economies in answering the three fundamental economic questions: What and how much
will be produced? How will it be produced? For whom will it be produced? Furthermore,
within any economy, the degree of the mix will vary.
The economy of the United States is generally considered to be a free market or capitalist
economic system. However, even in the United States the government has determined a
"minimum wage", has set rules and regulations for environmental protection, has
provided price supports for agricultural products, restricts the imports of items that might
compete with local production, restricts the exports of sensitive output, provides for
public goods such as a park system, and provides health and retirement services through
Medicaid and Medicare. All of these detract/depart from the essential nature of a
capitalist economy. However, most decisions continue to be left to free markets, leaving
the United States as a mixed economy that leans heavily toward the capitalist economic
system.
In contrast, the economy of the former Soviet Union is generally considered to be
communist. However, the strict controls of the central planning unit of the country tended
to be more intensely focused on heavy industry, including the defense and aerospace
industries, than on agricultural industries. Farmers often had significant freedom to
produce and sell (or barter) what they wished. The former Soviet Union is thus an
example of a mixed economy that leans heavily toward the socialist economic system.
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1.5 SCARCITY, OPPORTUNITY COST AND EFFICIENCY
If human desire were fully satisfied, we don't need to worry about the efficient use of
resources. Because all of us could have as much as we please and no one would care
about the distribution of income among people. But, the reality is somewhat different.
Because, we cannot have all we want from nature with out sacrifices. The law of scarcity
states that goods are scarce because there are no enough resources to produce all the
goods that people want to consume. This implies that there is always a tradeoff between
alternative choices.
As we have mentioned it earlier, because of scarcity, there must be a choice in the use of
economic resources. The important characteristics of economic resources are that they
can be put into alternative uses. Societies or individuals, therefore, must choose the best
ways of using scarce resources. Nations be it rich or poor, developed or under developed,
will all face the problem of choice. Tradeoff here implies the economy can only produce
more of one item if it gives up the production of some other good(s). The value of trade
off is called opportunity cost. Opportunity Cost is the value (amount) that must be
sacrificed to attend something.
That is,
goodother of obtainedamount the good one of sacrificedamount theCost y Opportunit =
Although opportunity cost can be hard to quantify, the effect of opportunity cost is
universal and very real on the individual level. In fact, this principle applies to all
decisions, not just economic ones. Since the work of the Austrian economist Friedrich
von Wieser, opportunity cost has been seen as the foundation of the marginal theory of
value.
Opportunity cost is one way to measure the cost of something. Rather than merely
identifying and adding the costs of a project, one may also identify the next best
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alternative way to spend the same amount of money. The forgone profit of this next best
alternative is the opportunity cost of the original choice. A common example is a farmer
that chooses to farm his land rather than rent it to neighbors, wherein the opportunity cost
is the forgone profit from renting. In this case, the farmer may expect to generate more
profit himself. Similarly, the opportunity cost of attending university is the lost wages a
student could have earned in the workforce, rather than the cost of tuition, books, and
other requisite items (whose sum makes up the total cost of attendance).
Note that opportunity cost is not the sum of the available alternatives, but rather the
benefit of the single, best alternative. Possible opportunity costs of the city's decision to
build the hospital on its vacant land are the loss of the land for a sporting center, or the
inability to use the land for a parking lot, or the money that could have been made from
selling the land, or the loss of any of the various other possible uses—but not all of these
in aggregate. The true opportunity cost would be the forgone profit of the most lucrative
of those listed.
One question that arises here is how to assess the benefit of dissimilar alternatives. We
must determine a dollar value associated with each alternative to facilitate comparison
and assess opportunity cost, which may be more or less difficult depending on the things
we are trying to compare. For example, many decisions involve environmental impacts
whose dollar value is difficult to assess because of scientific uncertainty. Valuing a
human life or the economic impact of an Arctic oil spill involves making subjective
choices with ethical implications.
Efficiency occurs when the economy is using its resources so well that producing more of
one good results in less of other goods, i.e., no resources are being wasted. Note that the
employment of all available resources is insufficient to achieve efficiency. Full
production must also be realized. Full production implies two kinds of efficiency:
allocative efficiency and productive efficiency. Allocative efficiency means that
resources are being devoted to those combinations of goods and services most wanted by
society. In addition, productive efficiency is realized when the desired goods and services
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are produced in the least costly ways. Thus, full production means producing the “right
goods” (allocative efficiency) in the “right way” (productive efficiency).
Check Your Progress
1. What are resources? Explain how resources are classified?
2. What are the principal roles of Entrepreneur?
3. Society’s want for material goods and services is unlimited. Explain!
4. What are the two fundamental facts of economics? How do these fundamental
facts lay ground for the foundation of economics?
5. Compare and contrast microeconomics and macroeconomics?
6. What are fundamental (basic) problems of economics? And how are these
problems solved under the alternative economic systems?
1.6 DECISION MAKING UNITS AND THE CIRCULAR FLOW OF
ECONOMIC ACTIVITIES
What are the major decision making units in the economy?
The major decision-making units in the economy are households, business firms and
government.
Households: Households are consumers of final goods and services produced in the
economy. Consumers are the owners of economic resources (land, labor, and capital and
entrepreneurship). They earn income from their labor and from the property they own.
Households are generally assumed to maximize their well-being or what economists call
"utility”.
Business Firms: Business firms are the producing unit in the economy. They hire
workers and pay for the use of various property owned by households. They use
economic resources to produce goods and services needed by households and other firms.
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Firms come in all size and forms. However, regardless of their size all firms share
common objective, i.e. profit maximization.
Government: The term government used to broadly include all government and quasi-
government bodies at the federal, state and local levels. Unlike the households and
business firms, government is not assumed to have a single goal. In a pure market
economy, the role of the government is limited to such activities as law entertainment.
Generally, how the market economic system functions can be shown using the simple
model called circular flow diagram depicted in Figure 1.1 below.
The Circular Flow of Economic Activities
The circular flow diagram tries to illustrate how an economic system works and how
solutions to the basic economic problems are made. It also captures the interrelationship
between resource markets and product markets. Households need goods and services on
which they spend their income. Business firms need economic resources (owned by
households) to produce goods and services needed by households.
To buy goods and services, households will sell their economic resources (labor, capital,
land and entrepreneur skill) and generate income which will be spent on goods and
services produced by business firms as shown in Figure 1.1 below.
Business firms will pay for the resources in the resource market in the form of wage (for
the labor resource), interest rate (for capital) and rent (for land), and use these resources
to produce goods and services demanded by households. There are two different markets
in the diagram: resource market and product market.
In the resource market economic resources are traded. From the resource market, money
in the form of consumers' income flow to households and economic resources flow to
business firms. Similarly in the product market, money income in the form of revenue
flow to business firms and goods and services flow to households. Generally, both
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households and firms participate in both markets but on different side of each, once as a
demander then as a supplier. Households are suppliers in the resource market and
demanders in the product market; firms are demanders in the resource market and
suppliers in the product market.
Firms’ Expenditure on
Economic Resources Income to Resource Owners
Flow of Resources Flow of Resources
Resource Market
Business
Firms Households
Product
Markets
Flow of Goods and Services
Revenue of Firms Consumption Expenditure
Flow of Goods and Services
Figure 1.1: The Circular Flow Model
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1.7 THE CONCEPT OF MARKET STRUCTURE
Market is a place or condition in which buyers and sellers meet to exchange goods and
services for the price they agree on. In the theory of the firm we are concerned with the
question: “How are prices of commodities determined in the market?” The determination
of price of a commodity depends on the number of sellers and buyer in the market. The
number of buyers and sellers determine the nature and degree of competition in the
market.
The nature and degree of competition makes or creates the structure of the market. Thus,
the market structure is determined or defined by the nature and degree of competition in
market.
Depending on the number of sellers and the degree of competition, the market structure is
broadly classified as follows.
1. Perfect competition (competitive market), and
2. Imperfect markets (noncompetitive markets). Here belong market structures of:
a. Monopoly,
b. Monopolistic competition, and
c. Oligopoly.
This particular course gives focus only to the perfectly competitive and monopoly
markets and how prices of goods and services are determined in these market structures.
1.8 MICROECONOMIC THEORY AND THE PRICE SYSTEM
Microeconomics (or price theory) is a branch of economics that studies how individuals,
households, and firms make decisions to allocate limited resources in consumption and/or
production.
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One of the goals of microeconomics is to analyze the market mechanisms that establish
relative prices amongst goods and services, and the allocation of limited resources
amongst many alternative uses. Microeconomics also analyzes market failure, where
markets fail to produce efficient results, as well as describing the theoretical conditions
needed for perfect competition. Significant fields of study in microeconomics include
general equilibrium, markets under asymmetric information, choice under uncertainty
and economic applications of game theory. Also considered is the elasticity of products
within the market system.
This course (Microeconomics I) deals with the price theory, where the price system plays
the fundamental role of determining what to produce, how to produce, and for whom to
produce. In the chapters to follow, we will analyze the behaviors of consumers (chapter
two) and firms (chapters three and four) separately. Chapters five and six bring the two
economic units, consumers and producers, in perfectly competitive and purely
monopolistic market structures.
Check Your Progress
1. What do you understand by opportunity cost?
2. What are the decision-making units in an economy and what are their objectives?
3. Explain the difference between product market and resources market.
4. What are payments for labor, land, capital and entrepreneurial skill?
1.9 LESSON SUMMARY
Though different people have different motives to study economics, knowledge
about economics in general is essential because everyone faces economic problems
at different levels, and makes economic decision throughout his/her life knowingly
or unknowingly. Therefore, economic literacy is important because economic
issues facing government and individuals shape the future of the nation and affect
the well being of its citizens.
19
Limited economic resources and unlimited societal wants for material goods and
services are the two fundamental facts, which lay foundation for the economizing
problem and economics as discipline. Economic resources like, different types of
labor, land, capital and entrepreneurial skill are limited. Whereas society’s need for
goods and services are unlimited as wants are multiplicative, recurrent and as
human nature is accumulative. The limited availability of resources and the
unlimited wants give rise to the problem of scarcity. Scarcity forces us to make
choices. Making a choice, in turn, implies the need for the efficient utilization of
resources.
Economics is, therefore, the study of how scarce resources are allocated among
alternative and competing ends in order to maximize the consumption of goods and
services.
The basic divisions in economics are microeconomics and macroeconomics.
Microeconomics studies the behavior of individual components of the economy:
households and business firms. Macroeconomics, on the other hand, deals with
issues at the overall economic level like unemployment, inflation and national
income. Economics can be positive or normative. Positive economics is limited to
making purely descriptive statements of scientific prediction. Normative economics
involves value judgments and it tells us what should be done.
The three major or fundamental problems of economics are what to produce, how to
produce, and for whom to produce. These problems are universal to all countries
regardless of their level of development. However, different countries having
different economic system use different approach to solve them. Economic systems
are different from each other on the basis of the ownership of economic resources
and the method by which economic activities are coordinated. The four economic
systems are free market economy, command economy, mixed economy and
traditional economy system.
Opportunity cost is the amount of one product, which must be given up to obtain
additional unit of another product. Efficiency occurs when the economy is using its
resources so well that producing more of one good results in less of other goods,
i.e., no resources are being wasted. But full production must also be realized. Full
20
production means producing the “right goods” (allocative efficiency) in the “right
way” (productive efficiency).
Households, business and government are the major decision-making units of an
economy. While households attempt to maximize their utility, firms seek to
maximize their profits. The link between them is shown by the circular flow
diagram.
1.10 REVIEW QUESTIONS
I. Multiple Choice Questions
1. Which of the following is addressed by microeconomics?
a. How tax and price controls affect consumers and producers
b. The extent to which the economy’s resources are employed
c. Overseas trade
d. ‘a’ and ‘b’
2. Ceteris paribus means,
a. Other things positively sloped
b. Supply is positively sloped
c. Demand is positively sloped
d. Other things remaining constant
e. None of the above
3. In a free market economy, the fundamental problems of the economy are solved by:
a. The agreement among economists
b. Individuals who make price in a market
c. The planning committee of the country
d. Intervention of the government in every aspect of the economy
e. the price mechanism
4. Economic resources are also called
a. Capital goods
b. Consumption goods
21
c. Free goods
d. Factors of production
e. None
5. The dual role of firms comprises of:
a. providing resources and using goods and services
b. providing resources and producing goods and services
c. employing resources and producing goods and services
d. All of the above
e. None of the above
6. Which of the following is not true about the roles of entrepreneur?
a. Determines the price of the commodity
b. Takes risk
c. Introduces new technology
d. Introduces new product
e. None
7. If the amount of a commodity available at zero price could fully satisfy the human
need, then this good is a/an:
a. Free good
b. Economic good
c. Scarce good
d. Efficient good
e. None
8. Macroeconomics is a branch of economics which deals with:
a. Price determination of the individual sellers/firms
b. The level of total output in the economy as a whole
c. Movements in the overall price level (inflation)
d. ‘b’ and ‘c’
e. ‘a’ and ‘b’
22
II. True or False Questions
1. Scarcity is ever present because every economy faces the problem of not having
enough resources to produce all the goods and services that people want.
2. A market system always produces the combination and amounts of goods that are
best for society.
III. Discussion Questions
1. What are the fundamental (basic) problems of economies? How are these problems
solved?
2. How do you relate the concepts of scarcity, opportunity cost and efficiency to one
another and to the discipline of economics?
23
CHAPTER TWO
THE THEORY OF CONSUMER BEHAVIOR
LESSON STRUCTURE
2.1 Introduction
2.2 Chapter Objectives
2.3 What is the Theory of Consumer Behavior?
2.4 The Rational for the Theory of Consumer Behavior
2.5 Methods of Comparing Utility
2.5.1 The Cardinal Utility Theory
2.5.2 The Ordinal Utility Theory
2.6 Market Demand
2.7 Elasticity of Demand
2.8 Choice under Uncertainty
2.9 Lesson Summary
2.10 Review Questions
2.1 INTRODUCTION As it has been mentioned in the first chapter, there are three decision making units in
economics and they are households (the primary consuming units), firms (the primary
producing units) and government. As you recall from the topic “Alternative Economic
Systems” of chapter one, the decision making units in a pure market economy are
households and firms. Hence, in order to understand the pure market system it is better to
analyze the behavior of households and firms. Thus, in this chapter we will study the
behavior of households (consumers) under the “Theory of Consumer Behavior “and in
the next two chapters we will be concerned with the behavior of firms under “The
Theories of Production and Costs”.
24
In a given economy it is a must to find a market for a commodity. And in any market we
find the demanders as well as the suppliers. Hence, there is a need to study about the
markets so as to know the behavior of the economy; and, in order to know about the
market, it is necessary to deal with the components of the market i.e. demanders and
suppliers.
The analysis of the demand side and the supply side of the market involves the study of
the behaviors of households (demanders of final goods and services in the product
market) and firms (suppliers of final goods and services in the product market). Thus, the
rational for studying the theory of consumer behavior is the fact that it is the basis for the
theory of demand. This is because the market demand is assumed to be the horizontal
summation of the demand of the individual consumers. That means, we first analyze the
behavior of a consumer to determine the individual demand, and then stepping on the
demand of an individual consumer we will develop the market demand.
However, in our attempt to study the behavior of the consumer, we deal with the
traditional demand theory which has the following important features.
The traditional theory of demand examines only the final consumer’s demand for
durables and non- durables. It deals only with consumers’ demand, i.e., it does not
deal with the demand for investment good, nor with the demand for intermediate
products.
It examines the demand in one market in isolation without considering the
conditions of demand in other markets (what is referred to as partial equilibrium
analysis).
It also assumes that firms sell their product directly to the final consumers.
In order to determine the various factors that affect demand we need to deal with the
theory of demand. As demand is a multivariate relationship determined by many factors
simultaneously, we need to go beyond the law of demand which states that there is
negative relationship between market demand and price under the assumption of ceteris
25
paribus (other things remaining constant). All those important determinants of demand
are related with the behavior of the consumer. Thus, the traditional theory of demand
starts with the behavior of a consumer.
Under the theory of consumer behavior, the following important assumptions are made:
1. The consumer is assumed to be rational. Given his/her income and the market
prices of the commodities, he/she spends his/her income on the basket of goods and
services that give the highest possible satisfaction or utility. This is the
axiom/postulate of utility maximization.
2. It is also assumed that the consumer has all relevant information important for
his/her decision. This means that the consumer has perfect knowledge about his/her
income, complete knowledge of the available commodities in the market, and exact
knowledge of the prices of all available commodities in the market.
At this point it is important to mention that the theory of consumer behavior in this
chapter will be dealt with in two parts. The first part is in line with the second assumption
which considers that the consumer has full knowledge of all the information relevant to
his/her decision. The second part relaxes this assumption and tries to involve the
possibility of the existence of uncertainties in the market. In short, the first part deals with
the behavior of the consumer under the condition of certain information (Choice under
certainty), while the second part is concerned with choice under uncertainty.
2.2 CHAPTER OBJECTIVES
This chapter has a general objective of enabling the students know how consumers decide
on baskets of goods and services to maximize their satisfaction. The specific objectives of
the chapter are:
Help students know the basis of the theory of demand;
Enable students derive a consumer’s demand under some alternative sets of
information;
Enable students know the concepts of utility and preferences;
26
Help students understand different types of utility functions;
Help students understand the determinants of individual and market demands, and
the concept of elasticity.
2.3 WHAT IS THE THEORY OF CONSUMER BEHAVIOR?
Before looking at what the theory of consumer behavior is all about, let’s first see what a
consumer is.
A consumer is an individual or a household who uses/consumes final goods and services
with a primary objective of maximizing utility.
The theory of consumer behavior is a description of how consumers allocate income
among different goods and services to maximize their well-being. It answers the
question: “How can a consumer with a limited income decide which goods and services
to buy with the objective of maximizing their utility?” It deals with how consumers
allocate their income across various goods and services and explain how these allocation
decisions determine the demands for the various goods and services.
2.4 THE RATIONAL FOR THE THEORY OF CONSUMER
BEHAVIOR
Understanding the consumers’ purchasing decisions will help us understand how changes
in income and prices affect demands for goods and services, and why the demands for
some products are more sensitive than others to changes in prices and income. In general,
as it has been mentioned above, we study the theory of consumer behavior since it is the
basis for the theory of demand.
We have said that consumers are the primary consuming units with an objective of
maximizing their utility/satisfaction. In order to attain this objective, the consumer must
27
be able to compare the utility/satisfaction of the various baskets of goods and services
which he/she can buy with his/her income.
2.5 METHODS OF COMPARING UTILITY
Utility is the level of satisfaction/pleasure that the consumer can derive from
consumption of goods and services or by undertaking a certain activity. It is the power of
a good or service to satisfy a certain human need.
There are two basic approaches to the problem of comparison of utilities. These
approaches are:
1. The Cardinalist Approach, and
2. The Ordinalist Approach.
In the next section, we will examine the two approaches one by one. In each case, we first
state the assumptions underlying the approach, and then derive the equilibrium of the
consumer.
From this equilibrium of the consumer, we will determine the demand for individual
products which will help us establish the market demand for the commodity.
Finally, we will point out the critics of each approach. Let’s first see the Cardinalist
Approach.
2.5.1 The Cardinal Utility Theory
There are some theories of utility that attach significance to the magnitude of utility.
These are known as Cardinal Utility Theories.
The cardinalist school postulates that utility can be measured. The advocates of this
school have given various suggestions for the measurement of utility. With the
28
assumption of complete knowledge of market conditions and income levels over the
planning period i.e. under certainty, some economists have suggested that utility can be
measured in monetary units, say, by the amount of money the consumer is willing to
sacrifice for another unit of a commodity. And others suggested the measurement of
utility in subjective units, called Utils.
Thus, in a theory of cardinal utility, the size of the utility difference between two bundles
of goods and services is supposed to have some sort of significance.
In its attempt to reach at the equilibrium of the consumer, the cardinal utility approach
makes the following assumptions.
Assumptions of the Cardinal Utility Theory
1. Rationality: The consumer is rational. He/she aims at the maximization of his/her
utility subject to the constraint imposed by his/her given income. This means that
the consumer is able to allocate his/her limited income first on the good that gives
him/her the highest possible level of satisfaction, and then move to the next best,
and so on.
2. Cardinal Utility: The utility of each commodity is measurable. It is assumed that
utility is a cardinal concept. The most convenient measure of utility is money: the
utility is measured by the monetary units that the consumer is willing to pay for
another unit of the commodity.
3. Constant Marginal Utility of Money: This assumption is necessary if the monetary
unit is used as the measure of utility. The essential feature of a standard unit of
measurement is that it is constant. If the marginal utility of money changes as
income changes (increase or decrease) the measuring rod for utility becomes, like
an elastic ruler, inappropriate for measurement.
4. Diminishing Marginal Utility of Commodities: The utility gained from successive
units of a commodity diminishes. In other words, the marginal utility of a
29
commodity diminishes as the consumer consumes larger quantities of it. This is
what is referred to as the axiom of diminishing marginal utility.
5. The Total Utility of a Basket of Goods and Services Depends on the Quantities of
the Individual Commodities. For example , if there are n commodities in the bundle
with quantities x1, x2,…………,xn, the total utility is given by:
U = f(x1, x2,…………,xn)
6. Additivity of Utility: In very early version of the theory of consumer behavior, it
was assumed that the total utility is additive. This means, if there are n commodities
in the bundle with quantities x1, x2,…………,xn, the total utility is:
U = u1(x1) + u2(x2) + ………+un (xn)
However, the additivity assumption is dropped in later versions of the cardinal
utility theory because additivity implies independent utilities of the various
commodities in the bundle, and this is an assumption which is clearly unrealistic
and unnecessary for the cardinal utility theory.
Equilibrium of the Consumer under the Cardinal Utility Theory
Let’s begin our analysis of the equilibrium of the consumer with a simple model of a
single commodity, X. The consumer has two alternatives for the use of his/her income:
either to buy X or retain the money income, Y. Under this condition, the consumer is in
equilibrium (at the highest possible level of satisfaction) when the marginal utility of X is
equal to its market price (Px). Marginal utility of a commodity is the extra satisfaction
that one can derive from one additional unit of the commodity.
Symbolically, the equilibrium of the consumer can be represented as:
MUx = Px
Where: MUx is the marginal utility of the commodity (X), and
Px is the price of the commodity (X)
If the marginal utility of X is greater than its price (MUx > Px), the consumer can
increase his/her welfare by purchasing more units of the commodity X. Similarly, if the
30
marginal utility of the commodity is less than its price, the consumer can increase his/her
total satisfaction by cutting down the quantity of the commodity X and keeping more of
his/her income unspent. Therefore, the consumer attains the maximum level of
satisfaction (utility) when MUx = Px.
So far, for the sake of simplicity we have been assuming that there is only one
commodity. However, in reality, since the consumer may consume more than one
commodity, we can extend our analysis of the consumer into the case of many
commodities. If there are more commodities, the condition for the equilibrium of the
consumer is the equality of the ratios of the marginal utilities for the individual
commodities to their prices.
Symbolically, assuming that there are N commodities: X, Y, Z, ………..N, the
equilibrium is attained when:
= Y
Y
PMU
= Z
Z
PMU
= … = N
N
PMU
X
X
PMU
Mathematically, we can derive the equilibrium of the consumer as follows:
Suppose the utility function in a simple model of single commodity X is given by:
U= f (Qx) where U is total utility measured in monetary units and Qx is quantity of the
commodity X.
If price of the commodity is Px and the consumer buys Qx units of commodity X, the
expenditure of the consumer will be the product, PxQx. Hence, the consumer wants to
maximize the difference between his/her utility and his/her expenditure.
i.e, Maximize (U- PxQx)
In order to maximize the above mentioned difference there is necessary condition as well
as sufficient condition. The necessary condition is that the partial derivative of the
function with respect to Qx be equal to zero.
31
Thus,
XQU
∂∂ –
X
XX
QQP
∂∂ )(
= 0
By rearranging the above expression we obtain:
XQU
∂∂ =
X
XX
QQP
∂∂ )(
, but since price is constant we can factor it out and find
XQU
∂∂ =
X
XX
QQP
∂∂ 1
XQU
∂∂ = XP
XMU = XP
In the case of several commodities, the utility derived from spending an additional unit of
money must be the same for all commodities. If the consumer derives greater utility from
any one commodity, he/she can increase his/her welfare by spending more on that
commodity and less on the others, until the above equilibrium condition is fulfilled.
Derivation of the Demand of the Consumer
The derivation of demand is based on the axiom of diminishing marginal utility. As it has
been mentioned above, the marginal utility of a commodity (MUx) is the slope of the
total utility of the commodity (U=f(Qx)). Total utility is the total amount of satisfaction
that one can derive from the use of a certain bundle of goods and services or by
undertaking a certain activity.
Total utility of a commodity (X), TUx, increases, but at a decreasing rate initially up to a
certain level of quantity, let’s say X1, and then starts declining. Thus, this implies that
TUx is at its maximum point at X1 units of quantity (See Figure 2.1). Accordingly, the
1
X
X
QQ∂∂ = 1 and only Px will be remaining on the right hand side, and
XQU
∂∂ is marginal
utility of the commodity (X) which is the slope of total utility.
32
marginal utility of the commodity (MUx) declines continuously when TUx increases at a
decreasing rate, and becomes negative beyond quantity X1 i.e MUx is zero at the
maximum point of TUx. Thus, the marginal utility of a commodity is depicted by a
negatively sloped line (See Figure 2.2).
Geometrically, marginal utility of a commodity is the slope of the total utility function
U = f (X). That means, marginal utility of a commodity is an extra satisfaction as a result
of one unit increase in the consumption of the commodity.
Mathematically, given total utility function U = f (X), Marginal utility of the function is
given by:
)(
)(Xd
TUd X=MU Where: MUx is the marginal utility of commodity
X, d(TUx) is change in the total utility of commodity X, and d(X) is change in the
quantity of X consumed.
MUx
TUx
X1
Figure 2.1: Total Utility Function
TUx
X
MUx
X1 X
Figure 2.2: Marginal Utility Function
33
NB. The slope of a tangent line to total utility function gives marginal utility of the
commodity at that point. Hence, as can be seen on Figure 2.1 above the tangent lines on
the total utility function are becoming flatter and flatter with increase in consumption of
X. This implies that the slopes of the tangent lines, which are the slope of the total utility
function, are declining with increase in consumption of the commodity.
If the marginal utility is measured in monetary units the demand curve for commodity X
is identical to the positive segment of the marginal utility curve since marginal utility of
the commodity is equal to price of the commodity (MUx = Px). As depicted in Figure
2.3a below, at quantity level X1 the marginal utility is MU1 which is equal to the price
level P1 by definition. Hence, at the price level P1 the consumer demands X1 units of he
commodity (Figure 2.3b). Similarly, at X2 the marginal utility of the commodity is MU2,
which is equal to P2. Hence, at P2 the consumer will buy X2 units of the commodity, and
so on. Thus, we can observe that Figure 2.3b shows the demand curve which is derived
from the marginal utility function of a commodity (Figure 2.3a)
MUX1
MUX2 MUX3
X
P1
P2
P3
Demand Curve
P
O X1 X2 X3O X1 X2 X3
X
MUx
MUx
Figure 2.3a: Marginal Utility of X Figure 2.3b: Demand Curve for X
34
NB. The negative section of the MUx curve does not form part of the demand curve since
negative prices do not make sense in economics.
Critiques of the Cardinal Utility Approach
There are three basic weaknesses in the cardinal utility approach.
a) The assumption of cardinal utility is extremely doubtful. This is because the
satisfaction derived from various commodities can not be measured objectively.
The attempt by Walras to use subjective units (Utils) for the measurement of utility
does not provide any satisfactory solution.
b) The assumption of constant utility of money is also unrealistic. As income increases
the marginal utility of money changes. Thus, money can not be used as a measuring
rod for utility since its own utility changes.
c) The additivivty of utility is questionable since there is no objective measure of
utility.
Check Your Progress
1. Explain why we study the theory of consumer behaviour.
2. What does it mean by: the marginal utility of a commodity is diminishing?
3. Explain the meaning of MUx = 4.
4. Derive the demand curve using the approach you studied above.
2.5.2 The Ordinal Utility Theory
The ordinalist school postulates that utility is not measurable, but is an ordinal
magnitude. The consumer need not know in specific the utility of various commodities to
make his/her choice. Under this approach, it suffices for the consumer to be able to rank
the various baskets of goods and services according to the satisfaction that each bundle
35
gives him/her. The consumer must be able to determine his/her order of preference
among the different bundles of goods and services.
There are two main ordinal utility theories, which are:
1. The Indifference Curves Theory
2. The Revealed Preference Hypothesis
1. The Indifference Curves Theory
The indifference curves theory is one of the theories which argues that utility is not
cardinally measured rather it is ordinally measured. This theory tries to show the
equilibrium of the consumer using the concept of indifference curves as the name
suggests.
Assumptions of the Indifference Curves Theory
1) Rationality: The consumer is assumed to be rational – he/she aims at the
maximization of his/her utility, given his/her income and the market prices. It is
also assumed that the consumer has full knowledge (certainty) of relevant
information.
2) Utility is Ordinal. It is taken as axiomatically true that the consumer can rank
his/her preferences (orders the various baskets of goods and services) according to
the satisfaction of each basket. Unlike the cardinal utility theory, he/she need not
know perfectly the amount of satisfaction. It suffices that he/she expresses his/her
preference for the various bundles of commodities. That means it is not necessary to
assume that utility is cardinally measurable, but only ordinal measurement is
required.
3) Diminishing Marginal Rate of Substitution: Preferences are ranked in terms of
indifference curves which are assumed to be convex to the origin. This implies that
the slope of the indifference curves decreases with increase in consumption of the
commodity. The slope of the indifference curves is called the marginal rate of
36
substitution of the commodities. Thus, the indifference curve theory is based on the
axiom of diminishing marginal rate of substitution. (More will be said on marginal
rate of substitution later in the chapter.)
4) The Total Utility of the Consumer Depends on the Quantities of the Commodity
Consumed:
U = f(X1, X2, …, Xn)
5) Consistency and Transitivity of Choice: It is assumed that the consumer is
consistent in his/her choice, that is, if he/she chooses bundle A over B in one
period, he/she will not use B over A in another period if both bundle are available to
him/her, under exactly the same conditions. The consistency assumption may be
symbolically written as follows:
If A > B, then B ≯A.
Similarly, it is assumed that consumer’s choices are characterized by transitivity: if
bundle A is preferred to B and B is preferred to C, then bundle A is preferred to C.
Symbolically, we may write the transitivity assumption as follows:
If A > B and B > C, then A > C.
Equilibrium of the Consumer under the Indifference Curves Theory
To define the equilibrium of the consumer (that is his/her choice of the bundle that
maximises his/her utility) we must introduce two concepts:
the indifference curve and its slope which is the marginal rate of substitution, and
the budget line.
These are the basic tools of the indifference curves theory.
The Indifference Curve
An Indifference Curve is a curve representing all combinations of market baskets that
provide a consumer with the same level of satisfaction. Hence, all points along the same
indifference curve give the consumer the same level of satisfaction. The consumer is,
37
therefore, indifferent among different combinations of goods represented by the points
graphed on a curve.
Y
Indifference
Curve
X O
Figure 2.4: An Indifference Curve
An Indifference Map shows a set of indifference curves which rank the preferences of
the consumer. Combinations of goods situated on an indifference curve yield the same
level of satisfaction for the consumer.
However, combinations of goods lying on a higher indifference curve yield higher level
of satisfaction and are preferred. Combinations of goods on a lower (close to the origin)
indifference curve yield lower level of satisfaction.
I3
I2
I1
Y
X
Figure 2.5: An Indifference Map
O
38
An indifference curve is shown in Figure 2.4 and an indifference map is depicted in
Figure 2.5. It is assumed that the commodities Y and X are can substitute one another to a
certain extent but are not perfect substitutes.
Symbolically, an indifference curve is given by the equation:
U = f(X1, X2……..Xn) = K Where K is a constant.
Given the above utility function, an indifference map can be derived by assigning every
possible value to K in such a way that as we move away from the origin the level of
satisfaction increases (Higher K).
The negative of the slope of indifference curve at any one point measures the rate of
change of commodity Y as a result of change in commodity X, and is called the marginal
rate of substitution of the two commodities.
Geometrically, the marginal rate of substitution is given by the slope of the tangent line at
that point:
Curve ceIndifferen theof Slope , −=−=dXdYMRS YX
The marginal rate of substitution of X for Y is defined as the number of units of
commodity Y that must be given up in exchange for an extra unit of commodity X so that
the consumer maintains the same level of satisfaction.
For example, MRSX,Y = 5 can be interpreted as: five units of Y must be sacrificed in
order to increase the consumption of X by one unit and leave the consumer on the same
level of satisfaction. Similarly, MRSY,X = 3 can be interpreted as: three units of
commodity X must be sacrificed in order to increase the consumption of commodity Y by
one unit and leave the consumer on the same level of satisfaction. With this definition,
the proponents of the indifference curves approach thought that they could avoid the non-
operational concept of marginal utility.
39
Marginal Utility (MU) and Marginal Rate of Substitution (MRS)
The concept of marginal utility (MU) is implicit in the definition of the marginal rate of
substitution (MRS), since it can be proved that the marginal rate of substitution (the slope
of the indifference curve) is equal to the ratio of the marginal utilities of the commodities
involved in the utility function:
Symbolically:
Y
XYX MU
MUMRS =,X
YXY MU
MUMRS =, or
Where, MRSx,y is marginal rate of substitution of x for y
MRSy,x is marginal rate of substitution of y for x
MUx is marginal utility of commodity x
MUy is marginal utility of commodity y
We can prove the above relationship between MRS and MU
Proof:
The slope of any curve at any one point is measured by the slope of the tangent line at
that point. For example the slope of the curve f(x) at point a in the figure below (figure
2.6) is the slope of line one (L1) and the slope of the curve at point b is the slope of line
two (L2). The equation of a tangent line is given by the total derivative2, which shows the
total change of the function as its determinant changes.
2 The total derivative of a function is change in the dependent variable as a result of change in the
independent variable. For example, if the function is given by Y= f(X), Y being the dependent variable
and X the independent variable, then the total derivative of the function is dXdY
, where dY is change in Y
and dX is change in X.
40
X O
b
a
f(x)
L2
L1
Y
Figure 2.6: Slope of a Curve
The total utility function in the case of two commodities x and y (assuming that the
consumer is consuming only two commodities x and y) is: U = f(x,y).
The equation of an indifference curve is: U = f (x,y) = K, where K is a constant.
The total differential of the utility function is measured by dU. dU shows the total
change in utility as the quantities of both commodities change.
dYYUdX
XUdU
∂∂
+∂∂
=
YX MUYUMU
XU
=∂∂
=∂∂ and [ ]
l utility
nsumer derives the same level of satisfaction
ndifference curve.
dYMUdXMUdU YX )()( +=
In words, the total change in utility (dU) caused by changes in X and Y is
approximately equal to the change in X (dX) multiplied by its margina
(MUx) plus the change in Y (dY) multiplied by its marginal utility (MUy).
By definition, along any particular indifference, the total change (differential) in
utility is equal to zero since the co
along the same i
41
Hence, dU = 0
By rearranging the above equation we obtain:
()( += = 0
dYMUdXMUdU YX )()( += = 0
)dYMUdXMUdU YX
dYMUdXMU YX )()( −=
MUYMUXdY
=− . dX
[But, recall that MRSX,YdXdY
−= ]
Y
XYX MU
MUdXdYMRS =−=,
Similarly, X
YXY MU
MUdYdXMRS =−=, .
The indifference curves theorists substitute the assumption of diminishing marginal
tility of commodities with the assumption of diminishing MRS of commodities since the
indifference curves solute value from
left to right, i.e., declining MRSx,y).
u
are convex to the origin (with declining slope in ab
Properties of Well-Behaved Indifference Curves
a) Well-behaved indifference curves are negatively sloped. This denotes that if the
quantity of one commodity (X) decreases, the quantity of the other commodity (Y)
must increase, if the consumer is to stay on the same level of satisfaction.
b) The further away from the origin an indifference curve lies, the higher the level of
utility it denotes. Bundles of goods on a higher indifference curve are preferred by
the rational consumer.
42
c) h other. If they did, the point of their
intersection would imply two different levels of satisfaction, which is impossible.
That means if indifference curves intersect to each other, they will violate the
assumption of transitivity and consistency.
I1
I2
I3
Y
O X
I3 > I2 > I1
Figure 2.7: A Higher Indifference Curves Denote Higher Level of Utility
Indifference curves do not intersect to eac
X
Y
O
I
I2
1
Figure 2.8: Intersecting Indifference Curves, Which Is Not Possible
43
d)
ng the curve from the left downwards to
t along
the indifference curve. The case of convex indifference curves implies that the
nds of
difference curves which violate some of the above mentioned behaviors of an
ing different types of indifference curves.
goods which can serve similar needs of the consumer. For example,
oca Cola and Pepsi, Tea and coffee, Bread and ‘Injera’ may be considered as examples
to substitute one good for the other at a constant rate. The simplest
ase of perfect substitutes occurs when the consumer is willing to substitute the goods on
Indifference curves are convex to the origin: The slope of the indifference curves
decline (in absolute terms) as we move alo
the right. This implies that the marginal rate of substitution of the commodity X for
commodity Y (= MRSx,y) is diminishing.
The axiom of decreasing marginal rate of substitution expresses the observed
behavioral rule that the number of units of X that the consumer is willing to sacrifice
in order to obtain an additional unit of Y increases as the quantity of Y decreases. It
becomes increasingly difficult to substitute X for Y as we move to the righ
commodities are substitutes for one another, but are not perfect substitutes.
However, depending on the type of the commodities there are different ki
in
indifference curve. Consider the follow
1. The Case of Perfect Substitutes
Substitute goods are
C
of substitute goods.
If the two goods X and Y are perfect substitutes to each other, the indifference curves
will be downward sloping straight line. Hence, the marginal rate of substitution between
the two goods will be constant. In other words, two goods are perfect substitutes if the
consumer is willing
c
a one-to-one basis.
For example, let us consider a choice between red pencil and blue pencil, and the
consumer involved like pencils, but doesn’t care about colours at all. Pick a consumption
bundle, say (10, 10). Then for this consumer, any other consumption bundle that has 20
44
pencils in it is just as good as (10, 10). Mathematically speaking, any consumption
bundle (X, Y) such that X + Y = 20 will be on the consumer’s indifference curves.
Hence, the indifference curves for this consumer are parallel downward sloping straight
lines.
ed with fixed proportions.
hus if the two goods are perfect complements to each other, the indifference curves will
X O
Figure 2.9: Indifference Curves for Perfectly Substitute Goods
Y
2. The Case of Perfect Complements
Complement goods are goods which are consumed together to serve a single need of the
consumer. Perfect complements are goods that are always consumed together in fixed
proportions. For instance, Sugar and Tea, Photo camera and Film, Car and Fuel can be
considered as examples of perfect complementary goods. This means that one good
cannot be consumed without the other as the goods are consum
T
be L-Shaped (right angled) as depicted in Figure 2.10 below.
A good example of perfect complements is the case of right shoe and left shoe. The
consumer likes shoes but always wear right shoe with left shoe together. Having many of
left shoes and one right shoe doest allow the consumer to wear more than one pair of
shoes, meaning, having only one out of a pair of shoes does not do a consumer a bit of
45
good. The consumption bundle (10, 10), i.e., 10 units of left and 10 units right shoes,
gives the consumer the same level of satisfaction for the consumer as a bundle which is
composed of (11, 10) or (10, 11). Hence, the consumer always consume at the vertex of
e ference curves where the number of the two goods are the same or the proportion
of the two perfectly complementary goods are the same.
creasing both the number of left shoes and right shoes at the same time will move the
e curves will still be L shaped. In
is case the corners of the indifference curves will occur at (2 teaspoons of sugar, 1 cup
on.
th indif
X
Y
O
Figure 2.10: Indifference Curve for Perfect Complements
In
consumer to a higher indifference curve, or to a more preferred position.
The important thing about perfect complement goods is that the consumer consumes the
goods in fixed proportions, not necessarily that the proportion is one-to-one. For
example, if the consumer always uses two teaspoons of sugar in his/her cup of tea and
doesn’t use sugar for anything else, then the indifferenc
th
of tea), (4 teaspoons of sugar, 2 cup of tea), and so
3. The Case of ‘bad’ and ‘good’ Commodities
If one of the two commodities is ‘good’ and the other is ‘bad’ (for example, alcohol
(‘bad’) and milk (‘good’)), the consumer needs some compensation for every unit of the
46
‘bad’ commodity he consumes. A bad is a commodity that the consumer doesn’t like to
consume. And this compensation is by extra unit consumption of the ‘good’ commodity.
This implies that the consumer increases his consumption of the ‘good’ commodity for
increase in consumption of the ‘bad’ commodity. In such a case, the indifference curve
will be upward sloping. The level of satisfaction increases as we move closer to the axis
of the ‘good’ commodity.
doesn’t care about it one way or another. Let’s
say that the consumer is neutral about good Y and likes good X. Then in this case, the
diff ves will be vertical lines.
4. The Case of Neutrals
A good is a neutral good if the consumer
X (Good)
Y (Bad)
O
Figure 2.11: Indifference Curves for ‘good’ and ‘bad’ Commodities
in erence cur
Y
(Neutral)
O
X
Figure 2.12: Indifference Curves for a Neutral Good
47
The Budget Constraint of the Consumer
Economists assume that consumers choose the best bundle of goods and services they can
afford. Suppose that there is some set of goods from which the consumer can choose. In
real life there are many goods to consume, but for the sake of simplicity it is enough to
consider the case of only two goods X and Y so that we can depict the consumer’s choice
behavior graphically. Consider that the prices of the two commodities are given by Px
en the budget
X
Qy is the quantity of commodity Y, and
/ her income. In
ther words, the consumer has a given income which sets limits to his/her maximizing
nd Y
xQx + PyQy) is equal to I (Income of the consumer) as it is assumed that the consumer
commodity
and Py, and that the amount of money the consumer has to spend is I. Th
constraint of the consumer can be written as:
Px Qx + PyQy ≤ I where: Px is the price of commodity X
Py is the price of commodity Y
Qx is the quantity of commodity
I is the income of the consumer
The consumer maximizes his/her satisfaction given his/her income. That means the
consumer’s utility maximization objective is constrained or limited by his
o
behavior. Income acts as a constraint for utility maximization.
In the above equation which shows the budget constraint of the consumer, PxQx gives
the total amount of income that the consumer spends on commodity X and PyQy gives
the total amount of income that the consumer spends on commodity Y. Hence, the total
amount of spending of the consumer on the two goods, X and Y, is PxQx + PyQy. It is
considered that this total amount of spending of the consumer on commodities X a
(P
spends all of his/her income on the consumption of the two commodities X and Y.
Thus, if the consumer spends all of his/her income on the consumption of the two
commodities, X and Y, the proportion of income spent on commodity X and
48
Y is determined by dividing the total spending o n X (= PxQx) by total income (I) and
er, respectively.
total spending on Y (= PyQy) by total income of the consum
Proportion of income spent on commodity X = I
Proportion of income spent on commodity Y =
QP XX
IQP YY
The budget constraint of the consumer requires that the amount of money spent on the
o goods be no more than the total amount of the consumer’s income. Hence, the
consumer’s affordable consu o not cost any more than I.
he set of all affordable consumption bundles at prices Px and Py, and income I is called
get Line
tw
mption bundles are those that d
T
the budget set of the consumer.
Properties of the Bud
f goods that just exhaust the consumer’s income.
PxQx + PyQy = I --------------------------------------------------- Budget Line
y solving for Qy from the general
budget equation. From the general budget equation we know that PxQx + PyQy = I.
PyQy = I – PxQx Bringing PxQx to the right
The budget line can be defined as the locus of points of all the combinations of the two
commodities that cost exactly the consumer income. The budget line includes the bundles
o
In the case of two commodities the general budget line equation can be given by:
We can present the income constraint graphically b
By solving for Qy we obtain:
Y
YY
PQP
= Y
XX
Y PQP
PI− Dividing both the right hand side and the left hand side by Py
49
Qy = Y
XX
Y PQP
PI− …………………………………………………….. Budget line
Given the prices of the two commodities, Px and Py, and income of the consumer, I, we
may find the corresponding values of Qy by assuming various values of Qx.
hus, if Qx = 0 (that is, if the consumer spends all his/her income on commodity Y), the T
consumer can buy YPI units of Y. Mathematically, this will give us the vertical intercept
of t
on commodity X), the consumer can buy
he budget line. Similarly, if Qy = 0 (that is, if the consumer spends all his/her income
XPI units of X, and this will give us the
Let’s consider that we measure commodity Y on the y-axis and commodity X on the x-
axi
et line: when the consumer consumes commodity Y
horizontal intercept of the budget line.
s. Hence:
Vertical intercept of the budg
Y
XX
Y PQP
PI− only (0, Y) Qy =
Qy = )0XPI− , Since Qx = 0 (
YY PP
YPI Qy =
Horizontal intercept of the budget line: when the consumer consumes commodity
X only (X, 0) Qy = Y
XX
Y PQP
PI−
Y
XX
Y PQP
PI− 0 = , since Qy = 0
YY PP
, bringing XX QPI=
YPI to the left hand side to solve for Qx
50
XPI , multiplying both sides by
X
Y
PP
Qx = to solve for Qx
we join the vertical and the horizontal intercepts on the X–Y set of axis, then we will
btain the budget line shown Figure 2.13.
If
o
The area below the budget line is the budget set, which includes all affordable bundles by
the consumer.
Geometrically, the slope of the budget line is
I/Py
O
Y
X
Budget Line A
B
Budget set
I/Px
Figure 2.13: Budget Line and Budget Set of the Consumer
Y
XY PPIOA−=−=− .
X PPIOB
athematically, the slope of the budget line is the derivativeY
X
X
Y
PP
−=∂∂
. M
The slope of the budget line has a nice economic interpretation. It measures the rate at
which the market is willing to substitute commodity X for commodity Y. The negative
sign is there since the change in X and change in Y must always have opposite signs. If
ou consume more of commodity X, you have to consume less of commodity Y and vice
omists sometimes say that the
lope of the budget line measures the opportunity cost of consuming commodity X. This
y
versa if you continue to satisfy the budget constraint. Econ
s
51
is because in order to consume more of commodity X you have to give up some
consumption of commodity Y.
Changes in the Budget Line
is because in order to consume more of commodity X you have to give up some
consumption of commodity Y.
Changes in the Budget Line
W
I2/Py
I1/Py
I2/Py
I1/Py
hen prices and/or income change, the set of goods that a consumer can afford changes
s well. How do these changes affect the budg et? Let us first consider changes in
. The Effect of Change in Income on the B dget Line
n increase in income, assuming that Px and Py are constant, will increase the vertical
tercept and the horizontal intercept, and does not affect the slope of the budget line.
hus, an increase in income will result in a parallel outward shift of the budget line.
imilarly, a decrease in income will reduce both the vertical and the horizontal intercepts
nd as a result it will cause a parallel inward hift of the bud
a et s
inc . ome
a u
A
in
T
S
a s get line.
X
Figure 2.14a: Effect of Increase in
Income from I1 to I2 on the Budget Line
Y
O X I1/Px I2/Px
Y
I /P
I /P
1 y
I2/Px I1/Px
Figure 2.14b: Effect of Decrease in
Income from I to I on the Budget Line 1 2
2 y
52
b. The Effect of Changes in Price on the Budget Line
Let us first consider an increase in price of X while holding price of Y and income
constant.
Accor to the budge line equation, increase in Px will not change the vertical intercept
/Py), since I and Py are constant. But it will make the budget line steeper since Px/Py
h of the budget line in absolute terms) will become larger. That means, increase
Px shifts the horizontal intercept inward, a lt the budget line rotates inward with
constant vertical intercept and a steeper slope.
imilarly, if we consider the effect of decline in Px while holding Py and I constant, the
ertical intercept remains constant but the slope becomes flatter and the horizontal
tercept increases and shift outward, as a result the budget line rotates outward with a
onstant vertical intercept and a flatter slop
ding
(I
(t e slope
in s a resu
a
S
v
in
c e.
Figure 2.15a: Effect of Increase in Px from Px1 to Px2 on the Budget Line
Figure 2.15b: Effect of Decrease in Px from Px1 to Px2 on theBudget Line
Y
X
I/Px2 I/Px1
Y
I/Py
O O
I/Py
I/Px1 I/Px2
X
53
Not
1.
2.
oice of the consumer from the budget set doesn’t change
either.
3. T es in
market conditions (demand and/or supply conditions) or because of government
is good increases
from PX to PX + 0.05PX = (1 + 0.05)PX = 1.05PX. If the price of the other commodity
e:
If both prices Px and Py increase in the same proportion, both the vertical and the
horizontal intercepts shift inward by half of increase in prices. Thus, the budget line
will shift inward. The opposite is true for proportionate decline in price of X and Y.
The budget set does not change when we multiply all prices and income by a positive
number, the optimal ch
he changes in commodities prices could be either the result of natural chang
policies (because of taxes imposed on or subsidies granted for the consumption of a
particular commodity). For instance, if government imposes a value (an ad valorem),
tax on the consumption of good X, at a rate of 5%, then the price th
(PY) and income (I) are kept constant, the effect of this tax on the budget line will be
similar to the one shown in Figure 2.15a. Similarly, if a value subsidy of 10% is
granted on the consumption of X, the budget line is affected in a way similar to that
shown in Figure 2.15b.
The Equilibrium of the Consumer under the Indifference Curves Theory
Th er is at equilibrium when he/she maximizes his/her utility his/her
income and the market pri
e consum , given
ces of the commodities. Under the indifference curves theory,
o conditions must be fulfilled for the consumer to be in equilibrium.
he first condition is that the marginal rate of substitution be equal to the ratio of
ommodity prices.
tw
T
Y
X
Y
XXY P
PMUMUMRS == . This is a necessary but not sufficient
ondition for equilibrium. The second condition is that the indifference curves be convex
the origin. This is the sufficient condition for equilib um.
c
c
to ri
54
This means that at equilibrium the consumer’s budget line is tangent to the highest
ossible indifference curve and at the tangency point the slope of the indifference curve (
) is equal to the slope of the budget line (=
p
XYMRS−Y
X
PP
− ). That is, = XYMRSY
X
PP
= at
quilibrium.
The e
and t of commodity Y and X* units of
c
indiff
not c sume more given his/her
in
e
quilibrium of the consumer is attained at the tangency point of the budget line (BL)
he indifference curve (I2), consuming Y* units
ommodity X (Figure 2.16). This is because, the consumer cannot consume on the third
erence I3 curve as it is not attainable given his/her income. And, the consumer does
onsume on the first indifference curve (I1) as he/she can con
come.
Check Your Progress
1. Explain the difference between the equilibrium conditions of the consumer under
cardinal utility approach and ordinal utility (indifference curves) approach.
Figure 2.16: Equilibrium of the Consumer
Y
E I3
I2
B
O X
Y*
I1
X* L
55
2. Suppose the total utility function of a consumer is given by TU(x) = 2x2. What is
the marginal utility
3. Assuming the income of the consumer to be constant, what will be the effect of a
d the
onstant.
b. The effect of decrease in price of Y on the budget line when price of X and
of X?
decline in price of both commodity X and commodity Y by the same proportion?
Explain your answer with the help of graph(s).
4. If the price of commodity X is 10 Birr per unit and the price of commodity of Y is 8
Birr per unit, write the budget line equation assuming that the consumer spends all
of his 500 Birr income on the two commodities, X and Y.
5. Mention at least one assumption which is common for both the cardinal an
ordinal utility approaches.
6. Graphically explain:
a. The effect of increase in price of Y on the budget line when price of X and
income are c
income of the consumer remain constant.
Income Offer Curve and Engel Curve
Previously when we were discussing the behavior of a budget line, we were able to
identify that the budget line changes with changes in income of the consumer (I) and
prices of the commodities (Px and Py). When the budget line changes due to change in
income or prices or both, the equilibrium of the consumer will also change since the most
preferred attainable indifference curve of the consumer also changes with the new budget
line. With the new equilibrium there are also new levels of equilibrium quantities.
Hence, in this section we see the effect of changes in income of the consumer on the
quilibrium of the consumer. And in the next section we will see the effect of a change in
th
e
the price of a commodity on the equilibrium of the consumer and on the level of the
quantity consumed.
In analysing the effect of a change in income on the equilibrium of the consumer, we use
e concepts of Income Offer Curve and Engel Curve.
56
Suppose that the initial income of the consumer is I1 with the budget line BL and the
initial indifference curve is IC1. Thus, the initial equilibrium point of the consumer is E1
here the consumer consumes X1 units of commodity X (See Figure 2. 17). Given these
rence curve, IC2.
successive
uilibrium points which result from changes in income, we will find an Income Offer
urve. Income offer curve is also called income consumption curve or income expansion
th.
r a normal good, incom curve is pos ively sloped as the new equilibr ts
e to the right of the or es. On the er hand, the income offer cu
ferior good is negativ ed since the new successive equilibrium points of the
onsumer (caused by increases in income) lie to the left of the original equilibrium point.
w
initial conditions, suppose that the consumer’s income rises, ceteris paribus. If the income
of the consumer increases, say, from I1 to I2, the budget line will shift upward from BL to
B’L’ in a parallel manner and the consumer will be able to consume on a higher level of
indifference curve, IC2. Thus, the equilibrium of the consumer will also change from E1
to E2 at the tangency point of the new budget line B’L’ and the now affordable
indiffe
Here, when the equilibrium changes from E1 to E2, E2 will be to the right of E1 if the
good is normal3. In this case, the consumption of commodity X increases from X1 to X2.
But, if the good is inferior good E2 will be to the left of E1 and the level of consumption
will decline from X1 to X2.
If income continues to increase, there will be successive equilibrium points with the
changed budget lines and higher indifference curves, and the quantities of the commodity
will also be changed. As can be seen from Figure 2.17, if we connect those
eq
C
pa
Fo e offer
iginal on
ely slop
it ium poin
rve for an li oth
in
c
od ormal’ when its demand changes in the same direction as income, i.e., the
reases with increase in incom the commodity mmodity is called an inferior good. That is, for an inferior good d with an increase in income an
3 Ad
comm ity is defined as ‘Nemand of the commodity inc
changes inversely with income, the coemand for the commodity decreases
e and vice versa. However, if the demand for
d vice versa.
57
For each level of income, I, there will be some optimal/equilibrium choice for each of the
oods, X and Y. Let us focus on good X and consider the optimal choice at each set of
rices and income (Px, Py, I). This is simply the demand function for good X.
look at the how demand for X changes as we
hange income, we generate a curve which is known as the Engel Curve. That means,
g
p
Y
B’ B
X
I
Y
B’ B
E1
E2 Income Offer Curve for normal good
E2 E1
O X
X1 X2 L L’ Figure 2.17a: Income Offer
Curve for a Normal Good X
O X1 X2 L L’
Income offer curve for inferior good
IC2
IC2
e Offer
Good X
IC1 IC1
Figure 2.17b: Incom
Curve for an Inferior
If we hold the prices of X and Y fixed and
c
2
I
1
Engel Curve for an Inferior Good
X
I
X
IEngel Curve
I1
I2
for Normal Good
X X O 1 2O X1 X2
Figure 2.17c: Engel Curve
for a Normal Good X
Figure 2.17d: Engel Curve
for an Inferior Good X
58
depicting the relationship between changes in income and changes in the quantity
consumed of a commodity while all commodity prices are held constant, will give as
what is called Engel curve of the commodity. An Engle curve is a graph of the demand
for one of the commodities as a function of income, with all prices held constant.
The Engel curve is positively sloped for normal goods since consumption of the good
increases with increase in income or since it decreases with a decrease in income. On the
ther hand, the Engel curve for an inferior good is negatively sloped since consumption o
of the good decreases with an increase in income or increases with a decrease in income.
Derivation of the Demand Curve using the Indifference Curves Theory: Price Offer
Curve and the Demand Curve
From the equilibrium of the consumer under the indifference curves theory, we can
derive the demand for a good graphically.
As the price of a commodity (Px) falls, assuming that Py and I are constant, the budget
line of the consumer rotates upward from its initial position to a new position (from BL
to BL’ in Figure 2.18a) with a constant vertical intercept. This is due to the increase in
the purchasing power of the given money income of the consumer. With more purchasing
in his/her possession, the consumer can buy more of X and/or more of Y. This
L’) is now tangent to a new indifference curve (I2)
hich is higher than the original indifference curve (I1).
we allow the price of the commodity (Px) to fall continuously and join the points of
ngencies of the successive budget lines and higher indifference curves (equilibrium
oints with the changed prices), we form the so call Curve.
he price consumption curve is also referred to the price offer curve.
rom the price consumption curve due to change in price of commodity X, we can derive
e demand curve for commodity X. In the figure 2.18a below, at point E1, the consumer
power
means that the new budget line (B
w
If
ta
ed the Price Consumptionp
T us
F
th
59
buys X1 units of commodity X at the original level of price (say P1). At point E2, price has
duced from P1 to P2, thus the quantity demanded of commodity X has increased from
1 to X2, and so on. Now we can plot the price quantity pairs defined by the points of
quilibrium (on the price consumption curve) to obtain a demand curve for commodity X
ee Figure 2.18b below).
re
X
e
(S
Y
E2E3
B
E1
I1
I2
I3
O X X1 X2 X3 L’ L’’
Price- consumption curve
L
Figure 2.18a: Price Consumption/Offer Curve
P
P1
P2 P3
X O X1 X2 X3
Demand Curve
Figure 2.18b: The Demand Curve
60
The demand curves for normal goods always have negative slope, denoting the ‘law of
demand’. The law of demand states that price and quantity demanded are
oppositely/negatively related, i.e. the quantity bought increases as the price falls.
Substitution and Income Effects of a Change in Price
So far we have seen that a fall in price of X (say, from P1 to P2) results in an increase in
the quantity demanded (say, from X1 to X2). This is the total effect which can be split in
to two separate effects, a substitution effect and the income effect.
In the indifference curves theory, the ‘law of demand’ is derived from what is known as
iation can
e shown graphically by a parallel shift of the new budget line until it becomes tangent to
2 to the right of the original tangency (equilibrium E1), because this line
parallel to new budget line which is less steep than the original one when the price
f X falls.
the Slutsky’s Theorem, which states that the substitution effect of a price change (relative
to the price) is always negative; if the price increases, the quantity demanded decreases
and vice versa.
The substitution effect is due to the tendency of the consumer to consume more of a
relatively cheaper good. Thus, it is assumed that the consumer will increase the
consumption of the good whose price has declined by reducing the consumption of the
other commodity and remain on the same level of satisfaction. Substitution effect is the
increase in the quantity bought as the price of the commodity falls, after ‘adjusting’
income so as to keep the real purchasing power of the consumer the same as before. This
adjustment in income is called compensating variation. The compensating var
b
the initial indifference curve (See Figure 2.19). The purpose of the compensating
variation is to allow the consumer to remain on the same level of satisfaction as before
the price change. The compensated budget line will be tangent to the original indifference
curve I1 at point E
is the
o
61
62
pensated Budget line Com
hus, the movement from E1 to E2 shows the substitution effect of the price change, i.e.
ecause of decline in price of X, the consumer buys more of X which is now cheaper,
bstituting X for Y (movement from X1 to X2).
owever, the compensating variation is a device which makes possible the isolation of
e substitution effect, but does not show the final equilibrium of the consumer. The final
quilibrium of the consumer after the price decline is defined by point E3 at the tangency
oint of the new budget line and a higher indifference curve I2. Since the consumer’s
urchasing power has now increased due to the decline in price of X he/she will spend
me of his/her increased real income on X, if the commodity (X) is normal. Thus, the
onsumer moves from X2 to X3. This is the income effect of the price change.
T
b
su
H
th
e
p
p
so
c
The income effect of a price change for normal goods is negative; when purchasing
power increases due to a decline in price, quantity consumed increases and when
purchasing power decreases due to an increase in price, quantity consumed declines if the
good is normal.
Y
O
X
B
X1 X2 L X3 L’’ L’
B’
E3
E2
E1
I1I2
New budget line
Original budget line
Substitution Effect
Income Effect
Total Price Effect Figure 2.19a: Substitution and Income Effect for a Normal Good X
If, however, the commodity is inferior, the income effect of the price change is positive
.e., for an increase in price, the quantity demanded of an inferior good will also increase
ue to the decline in purchasing power; and conversely, for a decrease in price, the
uantity demanded of an inferior good will also decline due to the increase in purchasing
ower). But the substitution effect of a price change is negative for normal goods as well
s inferior goods – for price rise quantity will decline, and for price decline quantity will
or normal goods, the negative substitution effect reinforces the negative income effect
negative. Similar to the case of normal goods,
e substitution effect is negative for inferior goods as well. However, unlike the case of
ormal goods, the income effect is positive for inferior goods. Nevertheless, since the
substitution effect is stronger than the income effect for most of the inferior goods, the
(i
d
q
p
a
rise.
Y
O
X
B
X1 X3 X2 L L’’ L’
B’
E3
E2
E1
I1
I2
New budget line
Original budget line
Substitution Effect
Income Effect
Total Price Effect
Figure 2.19b: Substitution and Income Effects for an Inferior Good X
Compensated Budget line
F
and as a result the total price effect is also
th
n
63
total effect is also negative. Thus, the negative substitution effect is in most cases
dequate to establish the law of demand (the negative relationship between price and
uantity demanded/consumed). It is when the income effect is positive and stronger than
e substitution effect that the law of demand does not hold. This is the case of the Giffen
Goods giffen
goods, like the case of inferior goods, the substitution effect is negative and the income
sitive. But the positive ng iv
e case of giffen goods otal i
e for e, an
ncome Effects of a Fall in the Price of X
a
q
th
, which are inferior goods with a positive sloping demand curves4. Thus, for
effect is po income effect is stro er than the negat e substitution
effect in th . As a result, the t price effect for g ffen goods is
positive (quantity will increas an increase in pric d vice versa).
Summary of Substitution and I
Type of Good Substitution Effect Income Effect Total Effect
Nor ) mal Good Negative (X ) Negative (X ) Negative (X
Infe ) Positive (X ) Negative (X ) rior Good (that is not giffen) Negative (X
Giffen Good Negative (X ) Positive (X ) Positive (X )
4 Giffen goods are very rare in practice.
E3
Y
B
B
IC2 ’
E1
E2
X
IC1
X3 X1 X2 L’ L’’ L
Figure 2.19c: Substitution and Income Effects for a Giffen Good X
O
64
Check Your Progress
ferior one
2. Explain the difference between the Engel curves for normal and inferior goods.
regardless of
whether the good is normal or inferior?
p sated budget line represent?
Mathematical
1. Explain the difference between the income offer curves for a normal good and for
an in .
3. Why is the substitution effect of a price change always negative
4. What does the com en
Derivation of Individual’s Demand for a Commodity
rived from the
ave seen previously, the equilibrium condition of the consumer is given by the
ta r. At this
al. Thus
The demand (function) of a consumer for a commodity can be de
equilibrium condition of the consumer.
As we h
ngency point of the indifference curve and the budget line of the consume
point, the slope of the two curves is equ ,
NYX PPP
=== ... NYX MUMUMU .
And, the budget line is given by:
I =∑=
N
iiiQP
1
.
For Example, consider the case of two goods, X and Y. If the total utility function is
given by: XYU4
= ; where U is total Utility, X1 is quantity of good X and Y is quantity of
he demand functions for the two goods as follows. good Y, we can derive t
Y
X
Y
XYX P
PMUMUMRS ==, . Step 1: At equilibrium,
65
Given the total utility function, the marginal utilities of X and Y are5:
Y XU
=∂∂
= ………………….……..……… (1) MU X 41 ………………………………
XYUMUY 4
1=
∂∂
= …………………………….…………………….……..……… (2)
By substituting the marginal utilities into the equilibrium conditionYY
obtain:
XX
PP
MUMU
= , we
YPX41
XPY=4
1…………………………………………………………………………..… (3)
Y
X
PP
XY
=Rearranging the above equation gives: .
ss multip
PxX = PyY ………………………………………………………………….………….(4)
ends on the specific form of the utility function.
Step 2
By criss-cro lying we obtain:
Note that the equality of the expenditures on the two commodities is not a general rule
rather it dep
: Now we c X by substituting
quation number (4) above into the budget line equation.
PxX + PxX = I since PyY = PxX from (4)
an derive the demand function for commodity
e
(Recall that the budget line is PxX + PyY = I).
PxX + PyY = I
2PxX = I
XX
X
PI
PXP
222
= dividing both sides by 2Px.
XP2
IX = Or XP
IX 5.0= → Demand for X
e use the derivative 1−=∂∂ nnXXY
. 5 W rule, i.e., if Y = Xn, then
66
Thus, the demand for X is negatively related to its own price, Px, and positively related to
me, I. inco
the
since PyY = PxX from (4).
2PyY = I
Similarly, we can derive the demand for commodity Y by substituting equation (4) into
budget line equation PxX + PyY = I.
PxX + PyY = I
PyY + PyY = I
Dividing both sides by 2Py gives:
YP2
IY = Or YP
Thus, the demand for Y is negatively related to its own price, P
IY 5.0= → Demand for Y
y, and positively related to
income, I.
Critiques of the Indifference Curves Approach
Although the advantages of the indifference curves approach are important, the theory
s indeed its own severe limitations.
. The main weakness of this theory is its axiomatic assumption of the existence and the
e ndifference curves
2. F
p references of
t der the influence of various factors, so that any
lid for the
3. T
w
d
ha
1
convexity of the indifference curves. The theory does not establish either the
xistence or the shape of the indifference curves. It assumes that i
exist and have the required shape of convexity.
urthermore, it is questionable whether the consumer is able to order his/her
references as precisely and rationally as the theory implies. Also the p
he consumer changes continuously un
ordering of these preferences, even if possible, should be considered as va
very short run.
he theory has also retained some of the weaknesses of the cardinal utility theory
ith the strong assumption of rationality and the marginal utility implicit in the
efinition of the marginal rate of substitution.
67
4. A
ef
in ce of preferences among consumers which lead to behavior that would
b
is is considered as a major breakthrough in the theory
f demand because it has made possible the establishment of the ‘law of demand’ directly
the advantage over the existence and convexity of the
difference curves as it does not accept them axiomatically. However, the indifference
urves are redundant in the derivation of the demand curve.
Assumptions of the Approach
nother defect of the indifference curves approach is that it does not analyze the
fects of advertising, the effect of past behavior (habit persistence), and effect of
terdependen
e considered as irrational.
2. The Revealed Preference Hypothesis
The revealed preference hypothes
o
(on the basis of the revealed preference axiom) without the use of indifference curves and
all their restrictive assumptions. Regarding the ordering of consumers’ preferences, the
revealed preference hypothesis has
in
c
1. Rationality: The consumer is assumed to behave rationally, in that he/she prefers
bundles of goods that include more quantities of the commodity.
2. Consistency: The consumer behaves consistently, that is, if he/she chooses bundle
A in a situation in which bundle B was also available to him/her, he/she will not
choose B in an identical situation in which A is also available.
Symbolically, if A > B, then B ≯ A.
3. Transitivity: If in any particular situation A > B and B > C, then A > C.
4. The Revealed Preference Axiom: The consumer, by choosing a collection of goods
in any one budget situation, reveals his/her preference for that particular collection.
That is, the chosen bundle is revealed to be preferred among all other alternative
maximizes the utility of the consumer. The revealed preference for a particular
collection of goods implies (axiomatically) the maximization of the utility of the
consumer.
bundles available under the budget constraint. Thus, the chosen ‘basket of goods’
68
Derivation of the Demand Curve Using the Revealed Preference Hypothesis
ssume that the consumer has the budget line BL as shown in Figure 2.20a below. If we
new batch will include a larger quantity of X
ith the help of the figure below.
A
assume that he/she chooses the collection of goods denoted by point A, this reveals
his/her preference for this batch.
Now, suppose that the price of X falls so that the new budget line facing the consumer is
BL’ (Figure 2.20a). We will show that the
w
Y
B B’
A
O X1 X2 L X3 L’’ L’ X
Figure 2.20a: Equilibrium of the Consumer
under the Revealed Preference Hypothesis
CD
Px
P1
P2
O X1 X2
X
Figure 2.20b: Demand Curve for a Normal Good
Derived Using the Revealed Preference Hypothesis
Demand Curve
69
Firstl
reduc sumer will have just enough income to enable him/her
continue purchasing bundle ‘A’ if he/she so wishes. The compensating variation is
hat the compensated
udget line B’L’’ passes through point A.
ice would be
consistent, given that all the batches on segment B’A were revealed inferior to A in the
original situation. Hence, uy A (in which case the
ubstitution effect is zero) or he/she will choose a batch on the segment AL’, such as C,
as a negative income effect). The new revealed
quilibrium position (D) contains a larger quantity of X (i.e. X3) which results from the
fall in its price. Thu tency of
choice open a direct way to the derivation of the demand curve: as price falls, more of X
is purchas
y, we make a ‘compensating variation’ in the income, which consists of the
tion of income so that the con
to
shown in Figure 2.20a, by a parallel shift of the new budget line so t
b
Since the collection A is still available to him/her, the consumer will not choose any
bundle to the left of A on the segment B’A. This is because his/her cho
in
the consumer will either continue to b
s
which includes a larger quantity of X (namely X2).
Secondly, if we remove the (fabricated) reduction in income and allow the consumer to
move onto the new budget line BL’, he/she will choose a batch (such as D) to the right of
C (if the commodity is normal – h
e
s, the revealed preference axiom and the implied consis
ed.
Check Yo
What are the differences and the simila s between the indifference curves
approac d the revealed ference hypo s?
Suppose that the total utility function of a consumer is given by TU(x,y) Y, and the prices of X and Y are 1 Birr and 2 per unit, res ively. If the income
of the consumer is 600 B nd if he spen ll of his inco on the cons on
of commodities of X and Y, find the optimu mount of X and Y that the consumer
will consume at equilibriu
ur Progress
1. ritie
h an pre thesi
2. = 3X2
Birr pect
irr a ds a me umpti
m a
m.
70
2 HE M KET DEM D FOR A MMODITY
he market demand for a given commodity is the horizontal summation of the demands
.6 T AR AN CO
T
of the individual consumers. In other words, the quantity demanded in the market at each
price is the sum of the quantities demanded by all consumers at that price.
Derivation of the Market Demand
In the real world, there may be millions of individual consumers in a market, but for
simplicity, let us consider the case of only four individual consumers in a given market.
Table 2.1 we show the quantity demanded by four consumers at various prices of a In
certain commodity and the total (market) quantity demanded. These data are also
presented graphically in Figure 2.21.
Table 2.1: Individual and Market Demands
Price
Quantity
demanded by
consumer A
(DA)
Quantity
demanded by
consumer B
(DB)
Quantity
demanded by
consumer C
(DC)
Quantity
demanded by
consumer D
(DD)
Market
Quantity
Demanded
(QM)
2 90 45 20 110 265
4 80 40 30 100 250
6 70 35 40 90 235
8 60 30 50 80 220
10 50 25 60 40 175
12 40 20 70 20 150
14 30 15 80 10 135
16 20 10 90 5 125
71
From the table, we observe that the market demand is negatively sloped as the individual
demands are. Sometimes, one or two of the individual demands may be positively slo
if the good is giffen for those individuals.6 For example, the demand for individual C
positively sloped implying that the good is giffen for consumer C. Although the
commodity is giffen and the demand is positively sloped for consumer C, the ma
demand has the normal positive slope, because the demands of other consumer more than
offset the giffen case of consumer C.
Economic theory does not define any particular form of the demand curve. In textbooks,
market demand is sometimes shown as a straight line (liner demand curve) and
sometimes as a curve convex to the origin. The linear demand curve may be written in
the form: Q = a – bP. This linear form implies a constant slope but with a changing
elasticity at various prices. [We will see elasticity later on].
ped
is
rket
iffen for another.
Figure 2.21: Individual and Market Demand Curves
0
250
300
2 4 6 8 10 12 14 16
100
150
200
50
Price
DA DB
DCDD DM
QD
6 The classification of goods as normal, inferior or giffen depends on the individual consumer. That is, depending on the income, attitude, and preferences of the consumer, what is normal for one consumer may be inferior or g
72
Determinants of Demand
Deman te variable; it is determined by many variables. Traditionally the
most im terminants of the market demand are considered to be the price of the
e prices of other commodities, consumer’s income and
tastes.
1. Own Price (Price of the Commodity)
The law of demand states that the quantity demanded of a commodity increases when
ere is a decline in the price of the commodity (and vice versa), for an ordinary good7.
his results in movement along the same demand curve as shown in Figure 2.22 below.
. Price of Other Commodities
d is a multivaria
portant de
commodity under consideration, th
th
T
P
Qx O
P1
P2
X1 X2
Figure 2.22: Movement along the Demand Curve as the
A
B
Price of X Changes
2
A change in the price of another related commodity, which could be either a substitute or
a complement, is also a factor that affects the demand for a commodity. When the price
7 An ordinary good is a good which is either normal or inferior but not giffen. If the good is giffen the
demand curve will be upward sloping as there is direct relationship between quantity demanded and price of the commodity.
73
of a substitute good increases, the quantity demanded of the commodity under
conside n will also increase. Thus, this change shifts the market demand curve
outward. For instance, if the price Coca Cola rises, the quantity demand of Pepsi is
expected to rise at the prevailing price. When the price of a complementary good
increases, the quantity demanded of the commodity under consideration will decline, and
thus it will make the demand curve shift upward. As an example, if the price of petroleum
rises, the quantity demanded of car falls.
. Income of the Consumer
s income of the consumer increases, the quantity demanded of a good will increase if
e good is normal, and thus the demand curve will shift outward. However, if the good is
bility, etc.
ratio
3
A
th
inferior the quantity demanded of the commodity declines with an increase in income,
and the demand curve will shift downward.
P
Qx
Apart from the above determinants, market demand is also affected by numerous other
factors, such as tastes and preferences, the distribution of income, the size of total
population and its compositions, wealth, credit availa
O
Figure 2.23: Shift of the Demand Curve as, for example, Income Increases
P1
X1 X2
74
As can be seen from the above two figures, Figure 2.22 and Figure 2.23, the result of a
change in the price of the commodity itself is shown by a movement from one point to
anot the effect of changes in other determinants is
show e other factors are considered as the shift
fact
ssumption; the shift factors (factors other than the price of the commodity) are assumed
2.7 ELASTICITY OF DE
many elasticities of demand as its determinants. The most important of these
and.
Price Elasticity of Demand
her on the same demand curve, while
n by a shift of the demand curve. Thus, thes
ors of the demand curve. The demand curve is thus drawn under the ceteris paribus
a
to remain constant in drawing the demand curve.
MAND
Elasticity can be defined as the responsiveness of a variable for a change in one of its
determinants, holding the other factors constant. Thus, elasticity of demand is the
measure of responsiveness of quantity demanded as a result of a change in one of its
determinants, holding all the other factors constant.
There are as
elasticities are:
a) The Price Elasticity of Demand,
b) The Income Elasticity of Demand , and
c) The Cross- Price Elasticity of Dem
Let us start with the first one: the price elasticity of demand
asticity of demand is the relative measure of the responsiveness of quantity
an d o changes in the commodity’s own price. If the changes in price are very
small, we use the point elasticity of demand as a measure of the responsiveness of
emand. If the changes in price are not small, we use the arc elasticity of demand as the
The price el
dem de t
d
relevant measure.
75
At e h poac int on the market demand curve, the price elasticity of demand is defined as
the percentage change in the quantity demanded resulting from a one percent change in
price of the commodity. In other words, it is the sensitivity of the quantity demanded to
changes in price.
Symbolically, the point elasticity of demand is given by the proportional/percentage
change in quantity demanded divided by the proportional/percentage change in price.
dpε = commodity theof Pricein change %age
demandedQuantity in change %age
P/P Q/Q
dd =
dpε =
P Q
dd .
Q P
If, for instance, the demand curve is linear with an equation of the form Q = a – bP, its
slope will be P Q
dd = -b
Substituting this into the elasticity formula we obtain:
= -bdpε Q
P .
his implies that the price elasticity of demand differs at the various points of the linear
emand curve. That is, even though a linear demand has a constant slope, the price
lasticity of demand is not constant.
bove formula for the price elasticity is applicable only for infinitesimal (very small)
hanges in price. If the price changes appreciably (significantly), we use the following
rmula which measures the arc elasticity of demand:
T
d
e
The a
c
fo
dpε =
P Q
dd )
QQ PP
(21
21
++ .
The arc elasticity of demand measures the average elasticity, that is, the elasticity at the
id point of the chord that connects two points, lets say A and B, on the demand curve.
hese two points are defined by the initial and the new price levels. It should be clear that
m
T
76
the measure of the arc elasticity is an approximation of the true elasticity of the section
om A to B on the demand curve. It is used when we know only the two points A and B
ut not the intermediate ones.
For a
the rat nd curve and above the point. For
fr
b
We can also estimate the price elasticity of demand graphically. Suppose that we want to
estimate the price elasticity of demand plotted in Figure 2.25 below.
P
Q O
A
B
Arc Elasticity
Figure 2.24: Arc Elasticity of Demand
a linear demand curve, price elasticity of dem nd can be determined geometrically by
io of a segment below the point on the dema
P
A
QxOB
C
Figure 2.25: Geometrical Dem nstratioo n of the Price Elasticity of Demand
(/ε / = ∞) dp
(/ dpε / = 1)
(/ dpε / = 0)
(0 < / dpε / < 1)
(1 < / dpε / < ∞)
77
exa
above i
ence, if point C is the midpoint of the demand curve (i.e., if CB = AC), the price
f demand would be one at this point; and, at this point demand is said to be
uni
greater gment
abo
coefficient of the price elasticity of demand is less than one (in absolute value) as the
segmen t a , u p ine s .
t the two extreme points of the demand curve, point A and point B, price elasticity of
dem rf hat means,
. At point A, demand is perfectly elastic (/ / = ∞)
. Between points A and C, demand is elastic (1 < / / < ∞) (a small change in
price induces a more than proportionate change in quantity demanded).
At point C, demand is unitary elastic (/ / =1) (a change in price results in a
proportionate change in quantity demanded).
<
induces a less than proportionate change in quantity demanded).
5. At point B, demand is perfectly inelastic ( / = 0)
ote that:
Price elasticity of demand is always negative due to the inverse relationship
between price and quantity dem mand).
mple, the price elasticity of demand at point C on the demand curve in Figure 2.25
s the ratio of the segment CB to the segment AC, i.e., CB/AC.
H
elasticity o
tary elastic. To the left of point C, the coefficient of price elasticity of demand is
than one (in absolute value) as the segment below is greater than the se
ve, and thus demand is price elastic. To the contrary, to the right of point C, the
t below is less than the segmen bove th s demand is rice la tic
A
and is perfectly elastic and pe ectly inelastic respectively. Tdpε1
dpε2
dpε3.
4. Between point C and B, demand is inelastic (0 < / dpε 1) (a change in price /
/ dpε
N
anded (i.e., because of the law of de
We usually talk of the coefficient ignoring the sign; or equivalently, we
sometimes define elasticity as dpε = –
P Q
dd .
Q P instead of d
pε = P Q
dd .
Q P .
78
P P P
Q Q Q
/ dp / = 0: Perfectly
Inelastic Demand ε
/ d
pε / = ∞: Perfectly Elastic Demand
0< / dpε / <1, / d
pε
or / dpε / =
/ > 1
1
Figure 2.26: Examples of Demand Curves with Different Elasticities
Factors Affecting Price Elasticity of Demand
and is elastic or inelastic is an important consideration, especially for
ent policy in individua
Whether dem
governm l commodity markets. For example, suppose the demand
for wheat were high
result in a proportionately greater redu
expenditures on wheat decline. Now, suppos
wheat price above the market equilibrium
would farmers’ incom
sales guaran
Price e
of de
1.
ubstitutes for a specific good are, the greater its price
ple,
ticity of demand. Goods with
many and very close substitutes will have higher elasticities.
ly price elastic. An increase in the price of wheat would accordingly
ction in quantity demanded. Thus, total
e the government established a minimum
price. Wheat sales would be reduced, and so
es be, unless the price support were accompanied by a minimum
tee.
lasticities range quite widely. The major factors that determine the price elasticity
mand are:
The availability and closeness of substitute goods:
The more and closer the s
elasticity of demand tends to be. Goods with few and poor substitutes, for exam
foods and fuel, will always tend to have low price elas
2. The nature of the need that the commodity satisfies:
79
Goods can be either luxuries or necessities in satisfying human needs. Thus, the price
elasticity of demand is more elastic for luxurious goods and less elastic for necessity
goods.8
3. The proportion of income the good have in the total income of the consumer:
is spent on a commodity, the price elasticity of demand
would be less elastic. For example, the price elasticity of demand for salt may be less
elastic for most individual consumers as it has a small share in the budget of many
run, the price elasticity of demand is less
elastic.
If large proportion of the income of the consumer is spent on a commodity, the price
elasticity of demand for the commodity would be more elastic. On the other hand, if
small proportion of income
individuals.
4. The available time for the consumer:
In the long run, the price elasticity of demand is more elastic as the consumer has
enough time to respond to the price change by adjusting his/her consumption pattern
and finding new substitutes. In the short
5. The number of uses to which a commodity can be put:
The more the possible uses of a commodity, the greater its price elasticity will be.
Income Elasticity of Demand
income elasticity of demand is defined as the proportionate change in the quantity
anded resulting from a proportionate change in income. Symbolically, we may write:
The
dem
dIε =
I Qd .
Q I
d
he income elasticity of demand is positive ( > 0) for normal goods and negative (
< 0) for inferior goods. So city for classifying goods
to luxuries and necessities. A commodity is considered to be luxury if the income
dIε
dIε T
me writers have used income elasti
in
8 The classification of goods as luxuries and necessities depends on the income and preferences of the
consumer; what is luxury for one individual may be necessity for the other.
80
elasticity for its demand is greater than unity ( dIε > 1). A commodity is a necessity if the
income elasticity for its demand is less than one (0 < ε dI < 1).
The main determinates of income elasticity of demand are:
1. The nature of the need that the commodity covers. Generally, luxurious goods have
t is a luxury good in an underdeveloped,
poor country while it is a necessity in a country with higher per capita income.
Cross Price Elastic f Demand
greater income elasticity than necessity goods.
2. The initial level of income of a consumer or a country: The percentage of income
spent on food declines as income increases (this is known as Engel’s Law and has
sometimes been used as a measure of welfare and of the development stage of an
economy). As another example, a TV se
3. The time period: Because consumption patterns adjust with a time lag to changes in
income, demand income tends to be elastic in the long run.
ity o
emand for a given commodity is determined not only by price of the commodity but
a
defined as the proportionate change in the quantity demanded of X resulting from a
p
D
lso by prices of other related commodities. The cross price elasticity of demand is
roportionate change in the price of Y. Symbolically,
YX , dε = X
YPdQx . QdPy
The s
g
relate ther, the cross price elasticity of demand is zero. The higher the value of
e cross price elasticity, the stronger will be the degree of substitutability or
complementarily of the
ign of the cross price elasticity of demand is negative if X and Y are complementary
oods and positive if X and Y are substitutes. If the two commodities X and Y are not
d to each o
th
two goods, X and Y.
81
The main determinant of the cross price elasticity of demand is the nature of the
com odities relative to their uses. If two commodities can satisfy the same need equally
well, the cross price elasticity is high, and vice versa.
m
Check Your Progress
Price Elasticity and Total Expenditure
1. Graphically show the effect of an increase in price of Coca Cola on the demand of
Pepsi Cola.
2. If the price elasticity of a commodity is -5, what will be the change in the quantity
demanded of the commodity as a result of a 4 % rise in the price of this
commodity?
3. Interpret the expression: "The cross price elasticity of demand between two
commodities A and B is equal to 3". What can you say about the two commodities?
4. Explain the difference between arc elasticity of demand and point elasticity of
demand.
he total amount spent on a good (Total Expenditure) varies directly with the change in
t l expenditure. However, if demand is inelastic (if < 1), an increase in price raises
esult is straight forward. A price increase means that more is
spe ount spent.
Off gher price. If
the If the quantity
ffect outweighs the price effect, then total expenditure falls. Elasticity is the measure of
the relative strengths of the two effects.
T
price when price elasticity of demand is less than one, and inversely related to the price
when price elasticity of demand is greater than one. In other words, if demand is elastic
(if dPε > 1), an increase in price reduces total expenditure and a decline in price increases
a dPεto
total expenditure and a decrease in price reduces total expenditure.
The intuition behind this r
nt on each unit of the good purchased, which tends to increase the am
setting this is the fact that fewer units of the good are purchased at the hi
price effect outweighs the quantity effect, then total expenditure rises.
e
82
If the price elasticity of demand is less than one (if dPε < 1), then a one percent increase
in price induces a less than one percent decrease in quantity demanded. Thus, the price
effect swamps (more than offsets) the quantity effect, and thus total expenditure rises.
But, when price elasticity of demand exceeds one (if dε > 1), a small increase in price
induces a larger decrease in quantity, so the quantity effect dominates and consequently
al expenditure falls.
Note: Since total expenditure and total revenue are two sides of the same coin, the effect
of change in price o
P
tot
n total revue is the same as its effect on total expenditure when
emand is elastic and inelastic. The total expenditure of a consumer (the buyer) is the
total
An important relationship exists between t e price elasticity of demand and the total
expenditure o on ( d n
the price of a commodity:
results in an increase in total expenditures if dem d is price elastic;
leaves total expenditure unchanged if demand is unitary elastic; and
results in ine in total expenditure if dema rice inelastic.
Specifically, when he price of t ommodity falls, total expenditure (price times
uantity) increases if demand is price elastic > 1 because the percentage increase in
e
to an inc ease in the quantity demanded
f the commodity that is smaller than the percentage reduction in price, and so total
d
revenue for the producer (the seller).
h
f consumers the commodity total revenue of pro ucers). A decline i
an
a decl nd is p
t he cdPεq
quantity (which by itself tends to increase total expenditure) exceeds the percentage
decline in price (which, by itself, tends to decrease total expenditure). Total expenditures
is at its maximum when dPε = 1, and d cline thereafter as d
Pε falls below 1. That is, when dPε < 1, a reduction in the commodity price leads r
o
expenditure on the commodity declines. The hypothetical data in Table 2.2 below
illuminate this point.
83
Table 2.2: The Relationship between Price Elasticity of Demand and Total
Expenditure
Price of X
(Px)
Quantity of X
(Qx)
Total Expenditure
(TE
Absolute Value of
Point ) (/ /) d
Pε
A 2.00 0 0 ∞
C 1.50 3 4.50 3
E 1.00 6 6.00 1
F 0.50 9 4.50 1/3
H 0 12 0 0
rom the above table, we see that between points A and E, / / > 1 and total expenditure
total
re and the price elasticity of demand as follows:
When demand is price elastic ( > 1): when demand is elastic, a small increase in
price results in a large declin uantity demanded, then total revenue and total
expenditure decline (↑P (↑P.Q↓) = ↓TE = ↓TR). Price and total
s if > 1.
large increase in
ll
dF Pε
on the commodity increases as the commodity price declines. The opposite is true
between points E and F over which / dPε / < 1. Total expenditure is maximized at point E
(the geometric mid-point of the demand curve).
Given that total revenue or total expenditure is the product of price and quantity
demanded (i.e., TE = TR = P.Q; where TE is total expenditure, TR is total revenue, P is
price and Q is quantity demanded), we can summarize the relationship between
expenditudPε
e in q
Q↓
dPεexpenditure change in opposite direction
When demand is inelastic (ε d < 1): when demand is inelastic, aP
price results in a sma decline in quantity demanded, then total revenue and total
84
expenditure increase (↑P Q↓ (↑P.Q↓) = ↑TE = ↑TR). Price and total
expenditure move in the same direction if < 1.
Market Demand, Total Revenue (TR) and Marginal Revenue (MR)
dPε
e can derive the total expenditure of consumers (or the total revenue of firms selling
e particular product) from the market demand curve. As seen earlier, total revenue is
e product of the quantity sold and the price, i.e., TR = P.Q.
the market demand is linear, the TR curve will be a curve which initially slopes
pwards, subsequently reaches a maximum, and then starts declining. We can prove this
om our previous discussion of the relationship between elasticity and TR (or TE).
e third and fourth
ue (MR). The marginal revenue is the
W
th
th
If
u
fr
Another important point in the theory of firm (to be discussed in th
chapters in some detail) is the marginal reven
change in total revenue resulting from selling an additional unit of the commodity.
O Q1 Q* Q2 Q O Q* Q
A
C
B
D
D’
/ dPε / = 1
P
P1
P* P2
85
TR
TRmax
TR
Figure 2.27: Price Elasticity of Demand and Total Revenue
D
P
raphically, MR at any one point is the slope of total revenue curve at that particular
point. If the nd curve.
vative of the TR f ction:
G
demand curve is linear, the MR curve is twice as steep as the dema
This can be proved mathematically as follows:
MR is the deri un
)()(
QdTRdMR =
)(Qd
= ).( QPd
)()( PdQd)()( QdQd
QP +=
)(Qd
QPMR += )(Pd
If the demand curve is linear, its equation in terms of price is:
Substituting P into the TR function, we find:
The MR is then:
P = a – bQ
TR = PQ = (a – bQ)Q = aQ – bQ2
)(Q)(
dTRdMR =
86
)(
)bQ-a( Q 2
QddMR =
= a – 2bQ.
that the MR curve starts from emand curve, and
that the MR is a straight line with a negative slope (-2b) twice as steep as the demand
urve (with a slope of -b).
The Relationship between MR and Price Elasticity of Demand
This proves the same point (a) as the d
c
The MR is related to the price elasticity of demand with the formula
)//
1( dPMRε
−=
Proof
1
p
:
Assume that the demand function is P = f(Q)
The
Above, just before a moment, we have shown that
total revenue is TR = PQ = [f(Q)]Q
)()(
QdPdQPMR +=
We o o als kn w that the price elasticity of demand could be defined as: dpε =
P Q
dd .
Q P
ing this definition of elasticity, we obtaRearrang in:
dpε .
P Q =
P Qd (criss-cross m tion).
d ultiplica
dpεQ.
= PdQd P (taking reciprocal).
Substituting dQd P = dε
P into the expression of the MR, we find: pQ.
)()(
QdPdQPMR +=
dp
QPMRεQ. P
+=
87
)Q.
Q1( dp
PMRε
+=
) 11(MR dpε
P +=
)//
11( dp
PMRε
−= (Since is negative, = – / /)
Total Revenue, Marginal Revenue and the Price Elasticity of Demand
dpε d
pεdpε
t its slope, the MR, is equal to zero. That is,
We said that if the demand curve is falling linearly, the total revenue (TR) curve initially
increases, subsequently reaches its maximum, and then starts declining. We can use the
relationship among the marginal revenue (MR), price (P) and dPε derived earlier to
establish the shape of the total revenue curve.
The total revenue curve reaches its maximum at the point where / dε / = 1, because
at this poin
P
)1
1( −= PMR = P(0) = 0.
If / dPε / > 1, the TR curve has a positive slope, that is, it is still increasing and
hence has not reached its maximum point.
1
If / dPε / > 1, then
// dpε
< 1 implying that1 0)//
1( >− dpε
. Given that P > 0, then 1
)//
11(PMR −= dε > 0.
p
If / dPε / < 1, the TR curve has a negative slope, that is, it is falling.
If / dPε / < 1, then
//1
d > 1 implying that 0)11( <− d . Given that P > 0, then // pε
pε
)// d
pε11(PMR − < 0. =
88
Check Your Progress
1. What will happen to the total expenditure of a consumer as a result of a rise in the
2. oint
of a linear demand curve?
amined so far implicitly assumed a risk free world. It
as mplete certainty as to the results of the choices they
ake. Clearly, this is not the case in most instances. In contrary to our earlier
A
b
price of a commodity if the demand for this commodity is highly price elastic?
Why?
What is the value of the price elasticity of demand for a commodity at the mid p
2.8 CHOICE UNDER UNCERTAINTY
The traditional theory of demand ex
sumed that consumers face co
m
assumptions of price, income and other variables to be known with certainty, many of the
choices that people make involve considerable degree of uncertainty.
lthough risk and uncertainty are usually used interchangeably, some people distinguish
etween the two.
(I) Uncertainty: refers to a situation when there are more than one possible outcomes
to a decision-maker and where the probability of each specific outcome is not
(I
known. This may be due to insufficient past information or instability in the
structure of the variables.
I) Risk: refers to a situation where there are more than one possible outcomes to a
decision-maker and the probability of each specific outcome is known or can be
estimated.
(III) Certainty: refers to a situation where there is only one possible outcome to a
decision and this outcome is known precisely. For example, investing on treasury
bills leads to only one outcome (i.e. the amount of the yield), and this is known
with certainty.
89
Expected Value and Variation of Risky Choices
We usually need two measures to describe and compare risky choices. These measures
are: expected value and variation.
1. Expected value: is the weighted average of all possible payoffs/outcomes that can
result from a decision the probability of those
payoffs used as weights. It measures the value that we would expect on average.
en by P1
nd P2, then the expected value is:
under the various states of nature, with
If we multiply each possible outcome or payoff by its probability of occurrence and add
up these products, we get the expected value. If, for instance, there are two possible
outcomes having payoffs X1 and X2 and if the probability of each outcome is giv
a
E(X) = P1X1 + P2X2
Example: If the probability that an oil exploration project will be successful is ¼ and the
probability that it will be unsuccessful is ¾, and if success yields a payoff of 40 Birr per
share while failure yields a payoff of 20 Birr per share, the expected value is:
E(X) = P(success)(yield from success) + P(failure)(yield from failure)
. Variability:
= ¼ (40 Birr/share) + ¾ (20 Birr/share)
= (10 + 15) Birr/share
= 25 Birr/share
is the extent to which the possible outcomes of an uncertain event may
differ. We measure variability by recognizing that large differences between the
actual and expected value imply greater risk.
tandard deviation is the often used measure of variability. Standard deviation measures
e dispersion of the possible outcomes from the expected value. The smaller the value of
e standard deviation (σ), the tighter or less dispersed the distribution is and thus the
wer would be the risk attached to it, and vice versa.
2
S
th
th
lo
90
Standard deviation (σ) = 2222
2111 )]([)]([ XEXPXEXP −+−
two alternatives to choose from have the same expected value, the one with the
aller standard deviation is less risky and is hence the preferred one. If, however,
but is much riskier than the other one and
ice versa, the preference depends on the individual – whether he/she is a risk averse, a
tral, or a risk loving person.
Different Preferences towards Risk
If
lower/sm
one alternative offers a higher expected value
v
risk neu
A Risk Averse Person:
1. is a person preferring a certain income to a risky income with
e expected value. For a risk averse person, losses are more important (in terms of
I
have a certain income of 20 Birr, or an
come of 30 Birr with probability of 0.5 and an income
ed income from this second alternative (A2) is:
) = 0.5(30) + 0.5(10) = (15 + 5) Birr = 20 Birr. This is the same as the income
ers to consume the risk free 20 Birr to trying
the sam
the change in utility) than gains. Losses hurt him/her more seriously than gains benefit
him/her. Thus, the marginal utility of income (MU ) diminishes as income rises.
To illustrate, assume that a person can either
alternative decision yielding an in
of 10 Birr with probability 0.5. The expect
E(A2
earned without risk (from the first alternative – A1).
A risk averse person facing this situation pref
the alternative in which he/she could have consumed 30 Birr if successful or 10 Birr if
unsuccessful. The figure below makes this point more clear.
91
Figure 2.29: Utility Function for a Risk Averse Individual
18
16
14
10
E
C
B
A
D
Utility
0 10 16 20 30 Income
From the figure, we see that utility at point B is greater than utility at point C. The utility
of this risk averse person from the risk free income of 20 Birr is 16 (point B) and the
expected utility from the risky alternative is:
E(U) = 0.5U(10 Birr) + 0.5U(30 Birr)
ote that the expected utility, E(U), is the sum of the utilities associated with all possible
Birr) to avoid taking risk. The
aximum amount of money (4 Birr in our case) that a risk averse person will pay to
void taking a risk is called a risk premium.
= 0.5(10) + 0.5(18)
= 14 (point C).
N
outcomes weighted by the probability that each outcome will occur.
The risk averse person achieves the expected utility of 14 at a lower, but a risk free,
income of 16 Birr. That is, a risk free income of 16 Birr gives the same level of
satisfaction as a risky alternative with an expected income of 20 Birr. Thus, he/she is
willing to pay or forgo 4 Birr (20 Birr – 16 Birr = 4
m
a
92
2
Figure 2.30: Utility Function for a Risk Neutral Individual
18
12
E
C
Utility
6 A
0 10 20 30 Income
. A Risk Neutral Person: is a person who is indifferent between a certain income and an
ncertain income with the same expected value. For this person, the marginal utility of
come is constant.
he utility of this risk neutral person from the risk free income of 20 Birr is 12 (point C)
same point C).
As 12 = 12, the risk neutral person is indifferent between the risky and the risk free
alternatives.
u
in
T
and the expected utility from the risky alternative is:
E(U) = 0.5U(10 Birr) + 0.5U(30 Birr)
= 0.5(6) + 0.5(18)
= 12 (the
3. A Risk Loving Person: is a person who prefers a risky income to a certain income
given that the risky alternative has the same expected value as the certain income. This
person may prefer an uncertain income to a certain one even if the expected value of the
uncertain income is less than that of the certain income. The expected utility of the
uncertain income is greater than the utility of a certain income for a risk loving person
and thus their utility of income curve is upward bending.
93
Figure 2.31: Utility Function for a Risk Loving Individual
18
Utility
3
E
B
A
10.5
8
C
0 10 20 30 Income
The utility of this risk loving person from the risk free income of 20 Birr is 8 (point B)
nd the expected utility from the risky alternative is:
E(U) = 0.5U(10 Birr) + 0.5U(30 Birr)
(18)
(point C).
s 10.5 > 8, the risk loving person prefers the risky alternative to the risk free alternative.
Risk loving people prefer alternat xpected value and high standard
eviation (risk) to a lower paying but less risky alternative (unlike the risk averse people).
Risk Aversion and Indifference Curves
a
= 0.5(3) + 0.5
= 10.5
A
ives with high e
d
However, risk loving people are few at least with respect to major purchases or large
amounts of income or wealth.
curves
at relate the expected income to the variability of income, the latter being measured by
the standard deviation.
We also describe the extent of a person’s risk aversion in terms of indifference
th
94
An indifference curve shows the combinations of the expected value and the standard
deviation of income that give the individual the same level/amount of utility. Indifference
curves are upward sloping. This is because risk is undesirable (a ‘bad’) so that the greater
the amount of risk, the greater the amount of income needed to make the individual
equally well-off. An increase in the standard deviation (a higher variability of income)
ust be compensated by a higher expected value of income so as to a leave a person on
a large increase in the standard
eviation of income (σ).
m
the same level of utility.
As opposed to the case of a highly risk avert person, a slightly risk avert person requires
only a small increase in expected income, E(I) for
d
E(I) U3
U2
U1
O σ O σ
Panel (a): Indifference Curves of Person A Panel (b): Indifference
Curves of Person B
U3
U2
U1
E(I)
Figure 2.32: Person A is more Risk Averse than Person B
Reducing Risk
e face of a broad variety of risky situations, people are generally risk averse.
umers and managers commonly reduc ris
In th
Cons e k using various ways. The major ones are:
d
iversification, insurance and obtaining more information.
95
1. Diversification: refers to reducing risk by allocating resources to a variety of activities
e outcomes are not closely related –“Don’t put all your eggs in one basket.” whos
2. Insurance: If the cost of insurance is equal to the expected loss, risk averse people will
nough insurance to recover fully from any losses they might suffer. For a risk averse
mer, the guarantee of the same income regardless of the actual outcome generates
utility than would be the case if that person had a high income when there was no
nd a low income when a loss occurred.
e value of information
buy e
consu
more
loss a
3. Th : People often make decisions based on limited information. If
information were available, one could make better predimore ctions and reduce risk.
E
study
2.9 L
f utility: Cardinal Utility and
Under the cardinal utility approach, the consumer reaches equilibrium when the
marginal utility of the commodity is equal to its price in the case of one commodity
(MUx = Px), and when the ratio of the marginal utilities of the commodities to their
ven though forecasting is inevitably imperfect, it may be worth investing in a marketing
that provides a reasonable forecast for the future.
ESSON SUMMARY
The theory of consumer behavior is the basis for the theory of demand.
There are two approaches for the measurement o
Ordinal utility approaches. The cardinal utility approach argues that utility is
measurable and quantifiable with a unit of measurement of utils while the ordinal
utility approach argues that utility has ordinal value and could only be ordered and
ranked.
PnMUn
PyMUy
PxMUx
=== ...............prices is equal for all commodities ( ).
lity approach, using the indifference curve theory, the
consumer reaches equilibrium at the tangency point of the indifference curve and
Under the ordinal uti
96
the b the
same as the slope of the budget line (
udget line. At the tangency point, the slope of the indifference curve is
Y
XPMRS = ). XY P
The i v curve is derived from the equilibrium of the consumer, and
ndividual demand curves.
By using the revealed preference axioms, the revealed preference hypothesis allows
the derivation of the equilibrium of the consumer without the use of the indifference
curve
The total effect of a change in price of a commodity, while income and price of
other m nstant, can be decomposed into substitution and income
negative substitution effect is
stronger than the positive income effect, and as a result the total price effect is
negative. In the case of giffen goods, the positive income effect is stronger than the
negat ion effect, and the total effect is positive.
Elasticity of demand measures the responsiveness of quantity demanded to a change
in on f terminants of demand. In this module, we have tried to see three
to a change in income), and the cross price
elasti uantity demanded of a good to a
chang ty).
The s nd/or other variables is different
from other variables; hence, the optimum
decision of the consumer is depends on the expected value and variation of income
ndi idual demand
then the market demand is derived from the individual demand curves, as the
horizontal summation of the i
s.
co modities is co
effects. For normal goods, both the substitution and income effects are negative;
and for inferior and giffen goods, the substitution effect is negative but the income
effect is positive. In the case of the inferior goods, the
ive substitut
e o the de
types of elasticities: the price elasticity of demand which is the responsiveness of
quantity demanded to a change in price), the income elasticity of demand (the
responsiveness of quantity demanded
city of demand (the responsiveness of q
e in the price of another related commodi
con umer’s decision with certain income a
the decision with uncertain income and/or
and the resulting expected utility of the consumer.
97
2.10 REVIEW QUESTIONS
I. Choose the Best Answer
1. For norm
nd is positive and greater than one.
offer curve and the demand curve are negatively sloped.
he income offer curve are positively sloped.
are true.
2. price elasticity of demand between two commodities X and Y is
negat ,
lements
goods
ed is twice the marginal utility of the last unit of Y consumed,
the c
al good,
a. the income elasticity of dema
b. both the price
c. both the Engel curve and t
d. b and c
e. All are true.
If the cross
ive then X and Y are:
a. substitutes
b. giffen goods
c. normal goods
d. comp
e. inferior
3. Assume a budget line is drawn for two commodities: X on the x-axis and Y on the
y-axis. If the income of the consumer is 100 Birr, the y-intercept is 4, and the slope
of the budget line is -2, the price of commodity X is:
a. 25 Birr
b. 12.5 Birr
c. 50 Birr
d. 8 Birr
e. None
4. Assume that there are only two commodities, X and Y. If the marginal utility of the
last unit of X consum
onsumer is in equilibrium when:
a. the price of Y is twice the price of X.
b. the price of Y equals the price of X.
c. the price of Y is half of the price of X.
98
d. the consumer can’t reach equilibrium.
5. An indifference curve will be L-shaped when the two goods are:
t substitutes
complements
ect substitutes
ed
d good commodities
alled:
e
7. One
commodi
a. er
c.
d.
f.
8. If the dem is given by Q = 16 – 2P, where Q is
the qu t
is the pric
a.
c.
d. astic
e. Elastic
e. None
a. perfec
b. perfect
c. imperf
d. unrelat
e. bad an
6. The line joining the different points of consumer’s equilibrium resulting from the
change only in the price of the commodity is c
a. demand curve
b. income consumption curve
c. Engel curve
d. price consumption curv
e. None
of the following is not a shift factor of the demand curve for a given
ty.
Income of the consum
b. Price of other related commodities
Tastes and preferences
Price of the commodity
e. All
None
and function for a certain commodity
an ity demanded of the commodity and P is the price of the commodity, what
e elasticity of demand when price is equal to 4 Birr per unit?
Inelastic
b. Perfectly elastic
Perfectly inelastic
Unitary el
99
9. One of the following is not true about the characteristics of well-behaved
indifference curves.
Indifference curves farther from the origin represent higher utility
10. ility function of a consumer is given by U = X2Y2, what is the MRSxy?
X/Y2
f. X/Y3
consumption of different commodities as
1st , 2nd and 3rd etc, we are measuring utility:
y
12. If price of an inferior good (which is not giffen) is rising,
fect increases the
result the total effect is a
effects increase the quantity
as a result the total effect is an increase
modity.
e quantity
total effect is a decrease in the
quantity demanded of the commodity.
a. Indifference curves do not intersect
b. Indifference curves have negative slope
c. Indifference curves are concave from the origin
d.
e. None
If the ut
a. Y/X
b. X/Y
c.
d. Y2/X
e. X2/Y
11. When we rank the utility gained from the
a. ordinally
b. cardinall
c. in both approaches
d. traditionally
a. the substitution effect decreases but the income ef
quantity consumed of the commodity, and as a
decrease in quantity.
b. both the substitution and the income
consumed of the commodity, and
in the quantity demanded of the com
c. both the substitution and the income effects increase th
consumed of the commodity, but the
100
d. both the substitution and the income effects decrease quantity consumed
of the commodity, and as a result the total effect is an increase in the
quantity demanded of the commodity.
e
II. True or Fa
e. the substitution effect increases but the income effect decreases th
quantity consumed of the commodity, but the total effect is an increase in
quantity.
lse Questions
1.
e consumer
2. n is the same for a consumer along the same indifference
3. sticity of demand for a good is always positive
5.
III. S
The revealed preference hypothesis is different from the indifference curves theory
as the revealed preference hypothesis determines the equilibrium of th
without the use of the indifference curves, unlike that of the indifference curves
theory.
The level of satisfactio
curve.
Income ela
4. For a normal good, both the Engel curve and the demand curve are positively
sloped.
The firm’s total revenue decreases for an increase in price of the commodity if
demand is price inelastic.
hort Answer and Workout Questions
1. Defin
c. Marginal Rate of Substitution
d. Engel Curve
2. Distinguish between the following pairs of economic concepts:
a. An indifference curve and an indifference map
b. Budget line and budget set
e the following terms:
a. Utility
b. Marginal Utility
101
c. Income offer cu
d. Normal good and inferior good
e. Ordinal
f. Indifference curve theory and revealed preference hypothesis
MRSy,x is 12.
4. Suppose that the consumer is asked to contemplate a gamble with a probability of
ing Birr 10,000 with a utility of 10 utils, and a 40% probability of
12 utils.
cted income and expected utility of the consumer?
tive which gives him
come of the risky alternative given
risk averse? Why?
Y = 4Y, Price of X is 3 Birr per unit and price of Y is also 3
e of the consumer is 1200 Birr, find the amounts of X and
Y that the consumer chooses to consume so as to maximize his utility.
tion P = 20 – 5Q, find the price elasticity of demand when
Birr per unit. Mention if the demand is price elastic or
inelastic at this point.
rve and price offer curve
utility and cardinal utility
3. Explain the interpretation of
60% of winn
winning Birr 15,000 with a utility of
a. What will be the expe
b. If the utility of this consumer from a risk free alterna
an income equal to the expected in
above is equal to 11 utils, is this consumer risk lover or
Illustrate your answer with the help of a diagram.
5. Given MUx = X, MU
Birr per unit. If the incom
6. Given the demand func
price of the commodity is 5
7. Explain the substitution and income effects of a price rise for a normal good using a
diagram.
8. Suppose Martha earns an of income 400 Birr currently, and her utility function is
given by: U(m) = 4m, where m represents income. She has two options:
Option 1: to buy a share. If she is successful her income will be 700 Birr and if she
is not successful her income will be 100 Birr.
Option 2: to do nothing and keep on earning 400 Birr.
are equally likely,
a. What would be her expected income if she buys the share?
the share?
Assuming that success and failure
b. What would be her expected utility of buying
c. Would Martha buy the share? Why?
d. Is Martha risk averse, risk lover or risk neutral?
102
CHAPTER THREE
THEORY OF PRODUCTION
ESSON STRUCTURE
.1 Introduction
of the Production Function
.7 Equilibrium of the Firm: Choice of Optimal Combination of Factors of Production
N
Production is the process of conversion of
consumable form (goods and services). In this regard, in the production process or
activity, firms turn inputs Th on o rs of
production) into output is defined at a particular time period and at a given technology.
By technology we mean the state of knowledge about the various methods that might be
used to to outpu and it is described by a production function.
.2 CHAPTER OBJECTIVES
illustrate the short-run production function and stages of production
L
3
3.2 Chapter Objectives
3.3 The Production Function
3.4 The Short Run Production Function and Stages of Production
3.5 Laws of Production
3.6 Returns to Scale and Homogeneity
3
3.8 Lesson Summary
3.9 Review Questions
3.1 INTRODUCTIO
inputs (factors of production) into a
into output. is transformati f inputs (facto
transform inputs in ts,
3
After studying this lesson thoroughly, you would be able to:
understand the context of the production function
103
understand and explain the laws of production
explain the returns to scale and homogeneity of the production function
ge of equilibrium theory of firms and optimum combination of
ction.
DUCTION FUNCTION
function is a function that shows the highest output that a firm can
roduce for every specified combination of inputs. It is a purely technical relation which
onnects factor inputs to outputs. Assuming labor (L) and capital (K) as the only inputs,
e production func here Q stands for the total
uantity produced
produced by
e following processes:
have a edknowl
factors produof
3.3 THE PRO
The production
p
c
th tion can be written as: Q = f(L, K); w
q of an output/product.
The production function allows inputs to be combined in varying proportions so that
output can be produced in many ways (say, using either more capital and less labor, or
more labor and less capital). For example, a unit of commodity X may be
th
Table 3.1: Three Processes for Producing a Unit of X
Process 1 (P1) Process 2 (P2) Process 3 (P3)
Units of Labor 1 2 3
Units of Capital 3 2 4
These activities or methods of production can be shown by lines from the origin to the
point determined by the labor and capital inputs combination.
104
method of production ‘A’ is technically efficient if it uses less of at least one input and
no more of the other facto mpared with any
ther method ‘B’. For example, suppose commodity Y can be produced by two methods
method of production ‘A’ is technically efficient if it uses less of at least one input and
no more of the other facto mpared with any
ther method ‘B’. For example, suppose commodity Y can be produced by two methods
0 2 3 4 L
2
1 P3
K
3
P2
P1
The production function, which is a purely technical relationship that connects factor
inputs and outputs, includes all the technically efficient methods of production. The
technically inefficient methods are not included in the production function.
The production function, which is a purely technical relationship that connects factor
inputs and outputs, includes all the technically efficient methods of production. The
technically inefficient methods are not included in the production function.
Figure 3.1: Alternative Production Processes
AA
rs to produce a given level of output as cors to produce a given level of output as co
oo
(Method A and Method B) as shown below:
Method A Method B
(Method A and Method B) as shown below:
Method A Method B
Labor 2 3
Capital 3 3
If these are considered to be the only methods of production, method A is considered as
technically the efficient method. This is because the two methods, A and B, use the same
amount of capital (3 each), but method A uses less units of labor (2) than B does (3).
105
The basic theory of production concentrates only on the efficient methods, and thus
inefficient methods are excluded as a rational producer will not used them. If a process A
uses less of one factor (say, L) and more of another (say, K) as compared to B, then A
nd B cannot be directly compared on the criterion of technical efficiency. For example, a
the two activities in the table below are not directly comparable.
Method A Method B
Labor 2 1
Capital 3 4
In such cases, both processes are considered as technically efficient and included in the
production function. Which one of them will be chosen at any particular time depends on
the price of factors (inputs). The choice of any particular technique among the set of
chnically efficient processes is an economic one, which is based on the price of factors
ap
te
of production. Note that a technically efficient method is not necessarily economically
efficient.
Isoquants and an Isoquant M
two inputs used to produce an item, the output
chievable for various combinations of inputs can be shown by using isoquants.
n isoquant:
In addition to defining the production function mathematically, it is also common to
depict the technically efficient production processes with the help of isoquants. Assuming
that labor (L) and capital (K) are the only
a
A is the locus of all the technically efficient methods (or all the technically
fficient combinations of factors of production) for producing a given level of output. It
a curve showing all the possible combinations of inputs that yield the same level of
utput. Isoquants may assume different shapes depending on the degree of substitutability
etween the factors of production. The following are the common ones:
e
is
o
b
106
1. Linear isoquant: this type assumes perfect substitutability of factors: a given output
ay be produced by using only labor, or only capital, or by an infinite number of
ombinations of K and L. See Panel (A) of Figure 3.2 below.
uant
m
c
2. Input-output isoq : this assumes strict complementarily (i.e., zero substitutability)
f production. There is only one method of production for producing any
articular level of a commodity. The isoquant takes the shape of a right-angle. This type
f isoquant is also called “Leontief Isoquant” after the name Leontief who invented the
put output analysis. Panel (B) of the figure below depicts such isoquants.
ant
of the factors o
p
o
in
3. Kinked isoqu : this assumes limited substitutability between factors of production,
processes of a
omm y. Substitutability of the factors is possible only at the kinks. See Panel (C) of
.
. Smo or c nvex isoquant
say K and L, and that there are only few for producing a particular amount
c dito
Figure 3.2 be wlo
4 oth o : this form assumes a continuous (and a less than perfect)
bstitutability between factors (K and L) only over a certain range, beyond which factors
nnot substitute each other. The isoquant is a smooth curve which is convex to the
rigin. This is depicted in Panel (D) of the figure below.
ven though the kinked isoquant is more realistic, most of the time the smooth or convex
oquant mic the ly simpler
hand
su
ca
o
E
is is used in the traditional econo ory because it is mathematical
to le by the simple rules of calculus.
107
An Isoq of several isoquants. An isoquant map is another way of
describing a production function, just as an indifference map (discussed in Chapter Two)
ove upward
n isoquant (See points A, B and C in the
An Isoq of several isoquants. An isoquant map is another way of
describing a production function, just as an indifference map (discussed in Chapter Two)
ove upward
n isoquant (See points A, B and C in the
uant map: is simply a set
uant map: is simply a set
is a way of describing a utility function. The level of output increases as we mis a way of describing a utility function. The level of output increases as we m
to the right where as it remains constant along ato the right where as it remains constant along a
O L
K
O L
Panel (A): A Leontief Isoquant
P1
X (Level of Output)
X
K
A Linear Isoquant Panel (B):
P2
P3 X
X
P4
O L O L
K
Figure 3.2: Isoquants of Different Shapes
Panel (C): A Kinked Isoquant Panel (D): A Convex Isoquant
108
figure below; 100 units of good X are produced both at A and C while 50 units are
produced at B).
K
X = 100
B
A
C
O L
X = 50
Figure 3.3: Movement on an Isoquant versus Movement from an
Isoquant to Another
Check Your Progress
n? What is the use of production function in
production analysis?
2. Explain some important/common types of production function.
4. W ves?
itional theory generally assumes the form:
1. What is meant by production functio
3. What are isoquants? Explain their main properties.
hat are the differences between isoquant curves and indifference cur
5. What is the reason behind an isoquant curve that is convex to the origin? When
will an isoquant be straight-line, and when will it be right-angled?
3.4 THE SHORT RUN PRODUCTION FUNCTION AND STAGES
OF PRODUCTION
The production function in the trad
X = f(L, K, r, y)
109
Where L is labor, K is capital, r is returns to scale which refers to the long run analysis of
the laws of production since it assumes change in the plant, and y is the efficiency
parameter related to the organizational and entrepreneurial aspect of the production.
e long run) can be shown graphically, as follows:
the production function shifts upwards. If, for instance, the levels of
e three fixed inputs rise from (k1, r1 and y1) to (k2, r2 and y2), the curve X shifts upward
We usually abstract from the availability of many factors of production to two factors of
production (L and K) only in order to simplify things. In this simplified case, any change
in the amount of factors other than L and K is considered to shift a production function.
The short run production function and its behavior for a change in amount of the fixed
factors (as time goes to th
In Figure 3.4, the quantity of output X produced is drawn as a function of the amount of
labor, for fixed amounts of the other factors. For a given curve (X), as labor increases,
ceteris paribus (the others factors fixed at k1, r1 and y1), output increases and we move
along the curve depicting the production function. If any one or all of the fixed factors
(K, r, y) increases,
th
to X’’, and so on.
O L
X X’’ = f(L)k3,r3,y3
X’ = f(L)k2,r2,y2
Figure 3.4: The Short Run Production Function and How It Shifts as the Amount
X = f(L)k1,r1,y1
of Fixed Factors of Production Change with the Passage of Time
110
The time period for which we assume that some factors are fixed in amount is called the
short run. Thus, curve X in the figure above is drawn for the short run. If we could
increase (or change in general) the amount of all factors, then we are in a long run.
The slope of the production function (say, X = f(L)) is the marginal product of the factor
function X = f(K) is the
m
chan
facto
of production L (MPL) . Similarly, the slope of the production
arginal product of capital (MPK). The marginal product of a factor is defined as the
ge in output resulting from the change in the factor by a unit, keeping all other
rs constant. That is:
LXMPL ∂∂
= andKXMPK ∂∂
= .
G he
PK is shown by the slope of the production function X = f(K). As you remember from
hapter two, the slope of a curve at any one point is the slope of a tangent line at that
oint.
he average product of an input is the total product divided by the units of the input used
produce it. Graphically, the average product of a factor at a given point is given by the
ope of a straight line from the origin to the point.
et’s derive the average product and marginal product of labor from the total product of
bor graphically. By doing so, we will also distinguish among three stages of production.
s shown in Panel (A) of Figure 3.5, as the units of labor used in the production process
oes on increasing, the output initially increases at an increasing rate (up to point A), then
ses at a decreasing rate (from point A to point C), reaches a maximum (at point C), and
en starts falling.
s a result, since marginal product is the slope of the total product curve, the marginal
roduct of labor initially increases, reaches maximum, and then starts declining. The
arginal product of labor (MPL) is even negative when the total product declines (beyond
raphically, the MPL is shown by the slope of the production function X = f(L) and t
M
c
p
T
to
sl
L
la
A
g
ri
th
A
p
m
111
point C). The average product of labor (APL), which is the slope of the line drawn from
e origin t e corresponding point on e total product (TPL) curve, initially increases,
aches maximum (at point Z) and then starts d ing. The APL and MPL curves are
own in Panel (B) of the sam
he following points are clearly reflected in Figure 3.5 below:
Before point Z is ched, in Panel A of the figure, the slope of a tangent line at a
point on the TPL curve is greater than the slope of a line from the origin to the point.
In other words, the MPL is above the APL.
At point Z, where the APL reaches its maximum, the slope of a tangent line at a
point on the TPL curve is greater than the slope of a line from the origin to the point.
PL are equal at the maximum of the APL (Panel B of Figure 3.5).
When TPL curve reaches its maximum (point C in Panel A), the MPL equals zero.
th o th th
re eclin
sh e figure.
T
rea
That is, APL and M
112
Now, let us study the three stages of production. Figure 3.6 below is partly reproduced
from Panel B of the above figure to assist us to this end.
Accordingly, we divide this production function into three stages as: Stage I (from zero
TPL up to the maximum of APL), Stage II (from the maximum of APL to zero MPL), and
Stage III (from zero MPL onwards).
A
B
C
D
Z
X
O LA LZ LB LC LD L
TP = f(L)
MPL
AP
MPL
AP
Panel (A): The TPL Curve
L
A’
C’
Z’
O LZ’ LC’ L
L
Panel (A): The MPL and APL Curves
Figure 3.5: The Relationship among TPL, MPL and APL
113
ile MPL falls latter on.
ince each additional unit of labor is coming up with a contribution larger than the
tion is negative).
Thus, it is in the second stage that a rational firm operates. Here each additional labor
tes positively to the production but less than the average. Where exactly in this
ces.
riable input (labor) increases with other inputs (like capital)
t (MPL) will eventually decrease. This manner
as the law of variable proportions or the law of
At stage I, MPL > APL, and both of them are rising initially wh
S
average (MPL > APL), it is rational to hire more labor and produce more output. Thus, it
is not reasonable to produce at this stage. A rational producer (firm) observes that using
more labor is preferred to the existing situation and thus moves out of this stage.
At the third stage, where both APL and MPL are declining and MPL < APL, it is not
rational to produce at all because each additional unit of labor makes the total product to
decline (i.e. its contribu
contribu
stage does a rational firm produce? The answer is, it depends on factor pri
At this stage as the use of a va
being fixed, the resulting additions to outpu
is captured by a principle known
diminishing marginal returns.
MPL
APL
APL
C’
O LZ’ LC’ L MPL
Z’
Stage I
Stage II
Stage III
Figure 3.6: The Three Stages of Production
114
In summary, the p ficient part of the
roduction function, that is, on the ranges of output over which the marginal
l
ge
roduction theories concentrate only on the ef
p
productivities are positive but declining. The second stage of production in the above
analysis corresponds to this efficient stage in the short run. No rational firm wou d
employ labor less than OLZ’ or beyond OLC’ (in Figure 3.6). This means over the ran
where MPL > 0 but L∂
MPL∂ )( < 0
In the long run, where all factors of production (L and K for simplicity) are variable, we
s to define the rational/efficient stage of production. In this case, the
ex to the origin. In the figure
elow, the production function is depicted by a set of isoquants.
s of points of isoquants where the marginal products of the factors are zero
e ridge line. At points a, b and c, the MPK is zero. This forms the upper ridge
rl the lower ridge line shows the path along which the MPL is zero (points d,
. Outside the ridge lines the marginal product of the factors is negative and the
f output. Thus, production techniques are efficient only
side the ridge lines.
use isoquant
traditional theory of production defines the rational stage of production as the range of
the isoquants over which their slopes are negative and conv
b
The locu
forms th
line. Simila y,
e and f)
methods of productions are inefficient, since they require more quantities of both factors
for producing a given level o
in
Upper Ridge Line (MPK = 0) b
a
c K
Lower Ridge Line (MPL = 0)
e
f
O L
Figure 3.7: The Ridge Lines and the Region of Efficient Production
d
115
The Marginal Rate of Technical Substitution
solute value) defines the degree of substitutability of the
f roduction. As we move downwards along the isoquant, the slope (
The slope of the isoquant (in ab
dLdK
−=factors o p )
tion,
or the marginal rate of technical substitution (MRTS) of factors:
decreases in absolute terms, showing the increasing difficulty in substituting L for K.
The absolute value of the slope of the isoquant is called the rate of technical substitu
isoquantan of slope −==dLdKMRTSLK
is defined as the amount of K that the firm must sacrifice in order to use one
can be proved that the MRTSLK is equal to the ratio of the marginal products of the
factors.
hat is,
MRTSLK
more unit of L so that it produces the same level of output.
It
T
K
LLK MP
MP
KX
LX
dLdKMRTS =
∂∂
∂∂
==
Proof:
The production function can be written as X = f(K,L) = C. It is equal to C because the TP
is constant along an isoquant.
is defined by the total differential. The total differential (dX) is zero along an isoquant
The slope of a curve is the slope of a tangent line at that point. The slope of a tangent line
since the TP is constant. Thus,
0)()( =∂∂
+∂∂
= dLLXdK
KXdX
0)()( =+ dLMPdKMP LK
dLMPdKMP LK )()( =−
116
K
L
MPMP
dLdK
=− which is the definition of the MRTSLK
long the upper ridge line, we have: A
∞==⇒=K
LLKK MP
MPMRTSMP 0
the lower ridge line,
And along
00 ==⇒=K
LLKL MP
MPMRTSMP
The MRTS as a measure of the degree of substitutability of factors has a serious defect
since it depends on the units of measurement of the factors. A better measure of factor
substitutability is provided by the elasticity of factor substitution (σ). It is given by:
LKMRTSinChangePercentage
LKinhangePercentage
=σ
C
)()(
)()d( LK
LKMRTSMd
LK
he elasticity of su t nit of measurement of
h the numerator and the denominator are measured in the same unit.
=σLKRTS
T bsti ution is a pure number independent of the u
K and L since bot
Factor Intensity
Factor intensity refers to a measure of the intensity of a method of production in the sense
that it measures whether a given method of production is labor intensive (uses more labor
tensive (uses mo capital and less labor). It can be measured
by the slope of the line from the origin to a particular point on the isoquant representing a
s r equivalently, it is measured by the capital labor ratio at a particular
and less capital) or capital in re
particular proces . O
point.
117
In the figure belo itw, process P1 is more cap al intensive than process P2 because the slope
of line OP is higher than the slope of line OP or the ratio 1 21L1K is greater than
2L
lies t at the upper part of the isoquant includes more capital intensive techniques
2K . This
imp h
Exa
where as the lower part includes more labor intensive techniques.
mple:
us illustrate the above concepts with a specific form of production function, namely
Cobb-Douglas production function. This form is the most popular in applied research,
ause it is easier to handle mathematically. It is of the form:
cb
Let
the
bec
KALX =
he marginal product of factors: 1. T
cbL KbAL
LXMP 1−=∂∂
=
1)( −= LKALb cb
)(APbL
=
)( Xb=
)( 1LXb= −
P1
P2
K1
K
O L L L
K2
1 2
Figure 3.8: Factor Intensity
L
118
Similarly, )()(1K
cbK APc
KXcKcAL
KXMP ===∂∂
= −
e marginal rate of substitution of labor for capital: 2. Th
cLbKL
Xb
KXcK
XMRTSLK ==L
X
∂∂
=)(
.
3
∂∂ )(
. The elasticity of substitution:
)()(
)( LK=σ
)d( LK
LK
LKMRTS
MRTSd
)()(
)()d(
LKLK
=σ
cLbKcLbKd
)(
)(.)()d(
cLbKdcLbK
LKLK
=σ
)().(
)).(()()d(
LKdcbLKcb
LKLK
•=σ
.1)(
)((
)d(=
LKK
LKσ)
=•LKdL
. Factor intensity: In a Cobb-Douglas function factor intensity is measured by the
ratio
4
cb . The higher the r chnique is and vice atio, the more labor intensive the te
versa.
Given that )(LXbMPL = , we can rearrange to find that )(
LMPXbL = .
Similarly, )(KXcMPK = gives us )(
KMPXcK =
Then, )(
)(
K
L
MPXc
MPXb
KL=
)()( K
MPcMPb
= L
119
LKMRTScb
=
c
The higher the
b= since MRTSLK = 1 (as shown above).
cb ratio means the higher the
KL ratio, and hence the technique is labor-
intensive.
5. The efficiency of production. The effici
production is measured by the coefficient A. It
ency in the organization of factors of
is clear that if two firms have the same
K, L, b and c, and still produce different quantities of output, the difference can be
efficient firm will have a higher A than the less efficient one.
the Cobb-Douglas production function, the returns to scale are
due to the superior organizational and entrepreneurial quality of one firm. The more
6. The returns to scale. In
measured by the sum of the coefficients b + c. This point will be discussed latter on.
Check Your Progress
(c) the upper and the lower ridge lines
2. Define and distinguish between marginal product and average product. Draw the
al product and average product curves from your own hypothetical data. And
check whether there is any relation between them.
nsity? When do we say a technique of production is labor
is capital intensive?
of factor substitution?
1. Distinguish between the following and show their importance in production theory:
(a) short run and long run
(b) variable input and fixed input
margin
3. Define marginal rate of technical substitution. Why does it decrease along the
isoquant?
4. What is factor inte
intensive? When
5. What is elasticity
120
3.5
The
production. This can be done in various ways. Output can be increased by changing all
, output can be increased by changing only the variable input
fixed inputs constant, which is possible in the short run. Let us see
LAWS OF PRODUCTION
laws of production describe the technically possible ways of increasing the level of
factors of production which is possible in the long run. This is called the law of returns to
scale. On the other hand
while keeping the
these laws one by one.
The Law of Variable Proportions
This is a law for the case of short run where there is at least one fixed input. The MP of
the ctor are
ombined with the fixed amounts of other factors. This is known as the law of variable
d stages of
ariable input and capital as a fixed input. From
at graph, what we can understand is that as the use of a variable input (labor) increases
variable factor will decline eventually as more and more quantities of this fa
c
proportions. In our earlier discussion of the short run production function an
production, we have assumed labor as a v
th
with other inputs (capital) fixed, the resulting addition to output will eventually
decreases. This is shown by a downward sloping MPL curve after its maximum point.
This principle is known as the law of variable proportion or the law of Diminishing
returns.
The Law of Returns to Scale
The law of returns to scale refers to the long run analysis of production. In the long run,
here all inputs are variable, output can be increased by changing all factors by the same
w
proportion. The rate at which output increases as inputs are increased by the same
proportion is called returns to scale. We have three cases of returns to scale: increasing,
constant and decreasing returns to scale.
121
Increasing returns to scale: this is the case where increasing all factors by the same
roportion, say m, leads to an increase in output by more than m scale. p
Constant returns to scale: if we increase all inputs by some factor m and output is
incr is called constant returns to
sca ect the productivity of its
fact .
sing returns to scale
eases by the same proportion as inputs, m, and then it
le. In this case the size of the firm’s operation doesn’t aff
ors
Decrea : if scaling up all inputs by m scales output up by less than m,
may be difficulties in organizing
eration leads to decreased productivity of both labor and
it is called decreasing returns to scale. This is because,
and running a large scale op
capital.
Examples:
1. Suppose Q = 2K + 3L. To tell the returns to scale, we will increase both K and L by a
factor m and create a new production function Q*. Then we will compare Q* and Q.
Q* = 2(mK) + 3(mL)
, we can replace (2K + 3L) by Q, as we were given that from the start.
Since doing so gives Q* = mQ, we note that by increasing all of our inputs by the
r multipliers and create our new production function.
Q* = 0.5(mK)( mL)
n m2 > m. Th r new production has
y more than m. so we have increasing returns to scale.
. Q = K0.3L0.2. Again we put in our multipliers and create our new production function.
= 2mK + 3mL
= m(2K + 3L)
= mQ.
After factoring
multiplier m, we have increased production exactly by a factor of m. So we have
constant returns to scale.
2. Q = 0.5KL. Again we put in ou
= 0.5KLm2
= Qm2. Since m > 1, the is implies that ou
increased b
3
122
Q* = (mK)0.3(mL)0.2
= K0.3L0.2m0.5
= Qm0.5. Since m > 1, then m0.5 < m. So we have decreasing returns to scale.
.6 RETURNS TO SCALE AND HOMOGENEITY OF THE
PRODUCTION FUNCTION
uppose we increase both factors of production in the function X = f(L,K) by the same
roportion m, and we observe the resulting new level of output X* as X* = f(mK,mL). If
can be factored out (that is, can be taken out of the bracket as a common factor), then
tions since m can be
ctored out in each case.
hus, a homogeneous function is a function such that if each of the inputs is multiplied
b
the degree of homogeneity and is a measure of the returns to scale.
urns to scale.
If n > 1, we have an increasing returns to scale.
e is measured by
e sum of the powers of the factors. That is,
3
S
p
m
the new level of output can be expressed as a function of m (to the power n) and the
initial level of output X as follows: X* = mnf(L,K) or X* = mnX. If so, the function is
called homogeneous. If m cannot be factored out, the production function is called non-
homogeneous. The above three examples are homogeneous func
fa
T
y m, then m can be completely factored out of the function. The power n of m is called
If n = 1, we have a constant returns to scale.
If n < 1, we have a decreasing ret
Given a Cobb-Douglas production function X = ALbKc, returns to scal
th
If b + c = 1, then there is a constant returns to scale.
If b + c > 1, then there is an increasing returns to scale.
If b + c < 1, then there is a decreasing returns to scale.
Proof
L and K increases by m. The new level of output iLet s
123
Thi
sca um.
duct curve passes thro h the origin if both factors are variable. But if only one
factor is variable (the other being kept constant), the product line is a straight line parallel
X* = A(mL)b(mK)c
= AmbLbmcKc
= Amb+cLbKc
= mb+c(ALbKc)
X* = mb+c(X)
s implies the function is homogeneous of degree b+c and the type of the returns to
le depends on the s
Product Line: It shows a physical movement from one isoquant to another as we change
either both factors and a single factor. It describes the technically possible alternative
paths of expanding output. What path will actually chosen by the firm will depend on the
prices of factors.
The pro ug
to the axis of the variable factor.
124
Product Lines Product Lines Product Line
O L O L O L
K K K
Panel (A): Product Lines Panel (B): Product Lines for Panel (C): A Product Line
where K is Fixed
K
for a Homogenous Function a Non-Homogenous Function
erent Kinds of Product Lines Figure 3.9: Diff
A special type of product line which is the locus of points of different isoquants at which
e MRTS of factors is constant is called an isocline. For homogeneous production
nctions, the isoclines are straight lines through the origin. In such a case, the K/L ratio
constant along any isocline (refer to the Panel A of Figure 3.9).
th
fu
is
Check Your Progress
1. What is the law of variable proportions? How does it differ from the laws of returns
2. How is the degree of homogeneity of a production function related to the returns to
TIMAL
BINATION OF FACTORS OF PRODUCTION
Max . In this case, total cost and prices are
given and the problem may be stated as follows:
Max П = R – C = PxX – C
П (profit) is achieved in this case if X (quantity of output) is
maximized, since C (cost) and Px (price of the product) are constants.
II. Maximize profit for a given level of output.
П = R – C = PxX – C
Clearly in this case maximization of profit is achieved by minimizing cost, since X
and Px are given.
of the firm graphically, we will use the isoquant map and the
isocost lines. As discussed earlier, an isoquant is a curve that shows the various
to scale?
scale of the production function?
3.7 EQUILIBRIUM OF THE FIRM: CHOICE OF OP
COM
A firm is said to be in equilibrium when it employs those levels of inputs that will
maximize its profit. This means the goal of the firm is profit maximization (maximizing
the difference between revenue and cost). Thus the problem facing the firm is that of
constrained profit maximization, which may take one of the following forms:
imizing profit subject to a cost constraintI.
Clearly maximization of
Max
To derive the equilibrium
125
combinations of K and L that will give the same level of output. It is convex to the origin
whose slope is defined as:
KMPLMP
KX
LXdK
dL=
∂∂
∂∂
=−
The
C = rK + wL;
where w = wage rate, and r = price of capital services.
ors of production in absolute terms,
isocost line is defined by the cost equation:
The isocost line is the locus of all combinations of factors that the firm can purchase with
a given monetary cost or outlay. The slope of the isocost line is equal to the ratio of the
prices of the factrw
− .
From the isocost equation given by: C = wL + rK
=>
=> rK = C - wL
Lrw
rCK −= .
From this the slope is r
− w
Now, let us see how the equilibrium of the firm is determined in the two cases mentioned
above.
KrC
O L wC
Figure 3.10: An Isocost Line
126
Case 1: Maximization of Out Subject to a Cost Constraintput
Given le will be in
utput it prod e . This is at the point of
tangency of the isocost line to the highest possible isoquant curve.
) are desirable but not attainable due to the cost constraint. Other
oints below the isocost line lie on a lower isoquant than X2. Hence X2 is the maximum
d given the above a umptions (C, w, r and Px being constant).
the vel of cost and the price of the factors and output, the firm
equilibrium when it maximizes the quantity of o uc s
In the following graph (Figure 3.11), the equilibrium of the firm is obtained at point e,
where the firm produces X2 with K1 and L1 units of the two inputs. Higher levels of
output (to the right of e
p
output that can be achieve ss
At the point of tangency:
a. Slope of isoquant = slope of isocost
rw
− LKK
L MRTSMP
== . This is a necessary condition for profit maximization.
b. The isoquant is convex to the origin. This is the sufficient condition for profit
maximization.
MP
K
K1
L L O
X
1
X2
e X3
1
Figure 3.11: Maximizing Output subject to Cost
127
The mathematical derivation of the above equilibrium condition is as follows. A rational
roducer seeks the maximization of its output, given total cost outlay and the prices of
ctors. That is,
Maximize X = f (K, L) subject to C = wL + rK
his is a constrained optimization which can be solved by using the Lagrangean method.
he steps are:
a. Rewrite the constraint in the form:
wL + rK – C = 0
b. Multiply the constraint by a constant λwhich is the Lagrangean multiplier:
λ(wL + rK – C) = 0
c. Form the composite function:
Z = X – λ(wL + rK – C)
d. Partially d
multiplier, and then equate to zero.
p
fa
T
T
ifferentiate the function with respect to each factor as well as the
* 0=−∂∂
=∂∂ w
LX
LZ λ
wMPL λ=
w
=λ …………………………………………………………………… (1) MPL
* 0=−∂
=∂ rXZ λ
∂∂ KK
rMPK λ=
rMPK=λ …………………………………………………………………… (2)
* 0=−+=∂∂ CrKwLZ
……………………………………………………………… (3)
λ
CrKwL =+
From e ioquat ns (1) and (2) we understand that: rw
MPMP KL = or LKKMPr
L MRTSMPw==
128
This sh s e marginal
shown that e econd order conditions
for the equilibrium of the firm require that the marginal product curves of the two factors
ow that the firm is in equilibrium when it equates the ratio of th
productivity of each factor to its price. It can be th s
have a negative slope.
,0)(2
2
<∂∂
=∂
∂LX
LMPL Slope of the MPL =
and ,0) Slope of the MPK = (2
2
<∂∂
=∂
∂K
XK
K MP
.).
(. 22
2
2
2
2
KLX
LX
LX
∂∂∂
<∂∂
∂∂
Case 2: Minimization of Cost for a Given Level of Output
quant and the lowest possible isocost line, and the
i u
the desired level of output, but we have a set of isocost lines.
Curv a lower total cost outlay. Since isocosts are drawn on the
ssumption of constant prices of factors, they are parallel to each other and their slopes
The condition for the equilibrium of the firm is formally the same as in case 1. That is,
there must be tangency of the given iso
soq ant must be convex. However, in this case we have a single isoquant which denotes
es closer to the origin show
a
(rw
− ) are equal.
Thus, the firm minimizes its cost by employing the combination of K and L determined
by e isocost li e. Points below
e in Figure 3.12 below are desirable because they show lower cost but are unattainable
o t X. Points above e show higher costs. Hence, point e is the least cost point.
the point of tangency of X isoquant with the lowest possibl n
for utpu
129
In this case also, the Lagrangean method can be followed to derive the equilibrium
condition mathematically. But the problem is different. That is,
Minim
a. The Lagrangean function will be:
Z
b. Partially differentiate Z with respect to L, K and λ and equate to zero.
*
K
ize C = wL + rK subject to X* = f(K,L)
= (wL + rK) + λ[X*- f(K,L)]
0),(=
∂∂
−=∂∂
LKLfw
LZ λ
LMPw .λ=
LMP
w=λ …………………………………………………………………… (1)
* 0),(=
∂∂ KK
KMPr .
∂−=
KLfrZ λ ∂
λ=
KMP
r=λ …………………………………………………………………… (2)
* 0 ),(* =−=∂∂ KLfXZλ
…………….………………………………………………… (3) ),(* KLfX =
K1
X
L
Figure 3.12: Minimizing Cost for a Given Level of Output
1 L O
e
130
From equations (1) and (2) we understand that: KL MP
rMP
w= or LK
K
L MRTSMPMP
rw
==
s is the same as the conThi dition in case one. In a similar way, the second condition will
e: b
Slope of the MPL = ,0)(2
2
<∂∂
=∂ L
XL
∂ MPL
Slope of the MPK = and ,0)(2
2
<∂∂
=∂
∂K
XK
MPK
.).
(. 22
2
2
2
2
KLX
LX
LX
∂∂∂
<∂∂
∂∂
Th
discussed above.
E
are r
a. the level of output for a total
b. inimize the cost of the firm for producing
53,747,712 units of output.
olution:
. Maximize subject to
e following numerical example clarifies the optimization of a firm for the two cases
xample: If the production function of a firm is given by ,32 LKQ = and the input prices
= Birr 8 per unit and w = Birr 2 per unit,
Find the levels of labor and capital that maximize
outlay of Birr 240.
Find the units of labor and capital that m
S
a 32 LKQ = KL 82240 += , with respect to L and K.
The equilibrium condition (from case 1 above) is given by: .K
L
MPMP
rw=
,3 22 LKLL ∂QMP =∂
= and .2 31LKKQMPK =∂∂
=
Thus, KMPrLMPw
= .28
323
22
KLLK
=⇒
131
L24K31
=⇒ .62
22
12212 KLLKLK =⇒=⇒=⇒
Substitute KL 6= into the budget constraint: KL 82240 += and solve.
12 =⇒ 20
20
240 8122408)6(224082 +=⇒+=⇒+= KKKKKL
20240 =⇒
20240 =⇒
K
K
Sinc
K
e L = 6K, we also have 6 =⇒= LKL .72)12(6 =
The p ital under the given constraints (or, the
optim or and capital) are L = 72 units and K = 6 units.
b. Mini h respect to L and K.
The
out ut maximizing levels of labor and cap
um combination of lab
mize KLC 82 += subject to 712,747,5332 == LKQ , wit
equilibrium condition (from case 2 above) is given by: .K
L
MPrw=
MP
,3 22 LKL
PL =∂
= and QM ∂ .2 31LKK
MPK =∂Q∂
=
Thus, K
L
MPr=
MPw .28 3KL
=⇒ 32 22 LK
L24
=⇒K31 .6
2212 LK
2212 LK ⇒=⇒ KL =⇒=
S and solve. ubstitute KL 6= into the output constraint: 712,747,5332 == LKQ
122488325 =
248832
2
63
=
⇒
⇒
⇒
⇒
=
K
K
KK
LQ
=L
The evels of labor and capital under the given constraints (or, the
o and capital) are L = 72 units and K = 6 units.
712,747,53)(712,747,53
32 =KK 32 =
712,747,5316 5 =K 712,747,5365 =
216==
712,747,535
Hence, .72)12(66 == K
cost minimizing l
ptimum combination of labor
132
Verify that the second order conditions are fulfilled in both cases!
Check Your Progress
1. ze production given a fixed total
outlay? sary condition required for minimizing cost for a
giv e
3.8 LESS
Firms produce outputs by combining inputs. The
en profit private sector
a n profit
fi the
P u elationship between factors of production and
o
In e g-run, all factors are variable.
In the short-run, as variable factors are added to the fixed factor, the firm may
tput but eventually will incur
d levels of output.
F s on to maximize output
su
What is the necessary condition for a firm to maximi
Is this the same as the neces
en l vel of output?
ON SUMMARY
are organized by entrepreneurs to
trepreneur does this in such away as to maximize profit. Non-
nd on-profit governmental enterprises face different incentives than for-
rms. We are concerned with for-profit firms. The single proprietorships are
dominant form of business organization by number.
rod ction function is the technical r
utputs.
th short-run, some factors are fixed; but in the lon
experience increasing returns at low levels of ou
iminishing returns at some higher
irm choose their input mix from the production functi
bject to cost constraints.
133
3.9 RE I
I. Choose the Best Answer
V EW QUESTIONS
1. :
ly of certain inputs is perfectly inelastic
c. in which supply of all inputs is perfectly inelastic
d. None of the above
2. Long run is period:
a. which is longer than three years
b. in which supply of labor is elastic
c. in which supply of all inputs is elastic
d. None of the above
3. When total production increases at a constant rate, then
a. average and marginal output increase at the same rate
b. average product increases faster than the marginal product
c. marginal product increases faster than the average product
d. marginal product equals average product
4. When total production increases at increasing rates, then
a. average and marginal output increase at the same rate
b. average product increases faster than the marginal product
c. marginal product increases faster than the average product
d. marginal product equals average product
5. In case of a convex isoquant, as we move from left to right, MRTSLK:
a. decreases at a decreasing rate,
b. decreases at increasing rate,
c. neither increases nor increases,
d. increases along the isoquant.
6. When an isoquant is L-shaped, then
a. MRTSLK = 0
Short run is a period
a. less than one year
b. in which supp
134
b. MRTSLK > 1
c. MRTSLK < 1
d. MRTSLK = 1
7. When MRTSLK = 1, then
b. MPL / MPK = 1
PK =0
proportion are associated with:
ts
input is decreasing.
input is increasing but at a decreasing rate.
c. quantity of output is either decreasing or increasing at a decreasing rate
is either decreasing or increasing at an increasing rate
10. The law of diminishing returns comes into force because of:
ale apply only when there is:
a. a change in one input only.
a. MPL / MPK = 2
c. MPL / M
d. MPL / MPK = ∞
8. Laws of variable
a. change in the variable input
b. change in all the inpu
c. change in return to scale
d. None of the above
9. The law of diminishing returns implies that:
a. quantity of an
b. quantity of an
d. quantity of output
a. indivisibility of variable input
b. indivisibility of fixed factors
c. indivisibility of both variable and fixed factors
d. indivisibility of products
11. Laws of returns to sc
b. proportionate and simultaneous changes in all inputs.
c. disproportionate change in inputs
d. more than proportionate changes in outputs
12. A Cobb-Douglas production function shows:
a. A constant returns to scale,
b. An increasing returns to scale,
135
c. A decreasing returns to scale
d. One of the three returns to scale
13. The laws of variable proportions and the laws of returns to scale:
a. Are exactly the same
c. Of any form
b. Are different and have no similarity
c. Are similar but not exactly identical.
d. No answer
14. Expansion path is a strait line when production function is:
a. Homogeneous
b. Non-homogeneous
136
CHAPTER FOUR
THE THEORY OF COST
duct Curves and Cost Curves in the Short Run
Long-Run Costs
Questions
In the previous chapter, we saw the laws of
the amounts of input(s) are changed. The laws s of
physical quantities, e.g., labor as num
achinery, and output as unit or some other measurements of output, e.g., tones or
rding price and production are taken on the basis of money
r we go beyond the technical analysis of the
– theories of production – and look at the economic analysis in firms’
aking process. The two chapters (chapter three and four) together make up a
plete discussion of the behavior of business firms. Do you recall that, in the theory of
consumer behavior of Chapter Two, we derived the demand for a commodity? As you
LESSON STRUCTURE
4.1 Introduction
4.2 Chapter Objectives
4.3 Short-Run Costs
4.4 The Relationship between Pro
4.5
4.6 The Relationship between Short-Run and Long-Run Average and Marginal Costs
4.7 Derivation of the Cost Function from the Production Function
4.8 Dynamic Changes in Costs – The Learning Curve
4.9 Lesson Summary
4.10 Review
4.1 INTRODUCTION
production, i.e., how output is changed when
of production are expressed in term
ber of workers, capital as unit of plants or
m
quintals of wheat.
However, most decisions rega
value of inputs and outputs. In this chapte
theory of the firm
decision m
com
137
complete this chapter, you would be ready to derive the other component of a market –
e s commodity, and to bring together the two sides (the demand and supply
des) of a market in the subsequent chapters.
ost functions are derived functions (derived from production functions). Economic
eory distinguishes between short-run and long-run costs. Both in the short-run and in
e long-run, total cost is a multivariate functio otal cost is determined by many
ctors such as output, technology, prices of variable and fixed factors. To simplify the
nalysis, we consider cost as a function of output [C = f(X)] on a ceteris paribus
ssumption. Thus, determinants of costs, other than output, are called shift factors.
.2 CHAP R OBJECTIVES
fter studying this lesson thoroughly, you would be able to:
understand the theory of cost;
product curves and cost curves
d marginal costs; and
4.3 SHORT-RUN COSTS
In t
at least one input (factor of production) cannot be changed. Practically, this is a time
eriod that is so short that the firm cannot alter its current plant size. In other words,
th upply of a
si
C
th
th n, i.e., t
fa
a
a
4 TE
A
differentiate between short-run costs and long-run costs;
know the details of the relationship between the following pair of concepts:
average total cost and average variable cost
marginal cost and average total cost
marginal cost and average total cost
short-run and long-run average an
derive the cost function from the production function.
heory of the firm, the short run is defined as any time period in which the quantity of
p
during the short run, a firm works with whatever heavy equipment and factory size it
already has. No matter how much more it wants to produce, say because of an increase in
138
the demand for its product, it cannot change its plant size in the short run. However, it
may change the amount of other inputs like labor. Thus, in the short run, we have two
types of inputs – fixed inputs and variable inputs.
The following are the types of cost a firm incur to produce a given good in the short run:
Total Costs (TC): are all costs of a firm incurred to produce goods and services. The
total cost (TC) includes both implicit costs (sacrifices) and explicit (out of pocket) costs.
The total cost can be divided into two: the Total Fixed Cost (TFC) and the Total Variable
Cost (TVC), i.e., TC = TFC + TVC
Total Fixed Costs (TFC): are those costs that must be incurred by the firm whether or
ot production takes place, or whether the firm produces less or more quantity of a given
nchanged.
xamples of the fixed cost include:
Property tax,
Fire insurance
Salaries of the administrative staff, say, salaries of a secretary and a guard,
Payments for the land (rent) and expenses for land maintenance,
s for depreciation and repairs (of machinery, building, etc).
raphically, the total fixed cost can be depicted as follows:
n
product. In other words, these are costs that do not fluctuate/vary with the level of output;
whether the firm changes (increases or decreases) its production level or not, they remain
u
E
Expense
G
139
C= Cost
TTotal Variable Costs (TVC): are the costs of production th
140
otal Variable Costs (TVC): are the costs of production that vary with the level of
utput the firm produces. Unlike the total fixed costs, these costs depend on the level
mount) of output produced. If the firm wants to increase its production, it must use
ore of the variables inputs and incur more variable costs. If there is no production, there
ill be no va le input used, and thus, there won’t be any variable cost incurred.
xamples of the total variable costs include:
n agriculture
Electricity bills,
Wage payments for direct labor,
Q
TFC
O
Figure 4.1: The Total Fixed Cost
o
(a
m
w riab
E
Payments for raw materials used for production (like cotton in textile factory,
seed i , etc.),
The running expenses of fixed capital, such as fuel, ordinary repairs and routine
maintenance.
The total variable cost has usually an inverse-S shape, which reflects the law of variable
proportions. According to this law, at the initial stage of production with a given plant
140
size, as more of the variable factor is employed, its productivity increases and thus total
variable cost(TVC) increases at a decreasing rate. For example, to increase the level of
output by one unit may require one more worker, and if the price of this additional
worker (the wage rate) is 10 Birr (per given period of time), the TVC increases by 10
s the pr ivity of the variable input (labor) falls, larger and larger units of the
ill be needed to increase output by the same unit. To continue with our
ypothetical example, two more workers may be needed to increase output by a unit in
ses by 2x10 = 20 Birr. Thus, the total variable cost (TVC) first
creases at a slower rate and then increasing rate because of the law of variable
a ter Three).
ince the TC is the sum of the TFC and the TVC, and as the TFC doesn’t change, the TC
ehaves just like the TVC. Figure 4.2 below shows the TC, TFC, and TVC curves a firm.
Birr.
A oduct
variable input w
h
which case the TVC increa
in at an
proportions (discussed pin Ch
S
b
Cos TC
TVC
TFC
Output (X) O
t
Figure 4.2: The TC, TVC and TFC Curves
141
From the total fixed cost, the total variable cost and the total cost curves, we obtain the
average fixed cost, the average variable cost and the average (total) cost curves
respectively.
Average F eix d Cost (AFC): is the total fixed cost divided by the amount of output, i.e.,
X
TFCAFC = .
n increase in X reduces the ratioX
TFCSince TFC is constant, a , and thus the AFC
approaches the quantity (output) axis as output rises. This is depicted in Figure 4.3 below.
Average Variable Cost (AVC): is the total variable cost divided by the level of output,
Cost
O X
AFC
Figure 4.3: The Average Fixed Cost (AFC) Curve
i.e., X
raphica e AVC at a given level of output is equal to the sl line drawn from
e origin to the point on the TVC curve corresponding to the particular level of output.
or example, in Figure 4.4 below, the AVC at X is the slope of the ray OA; and
milarly, the AVC at X2 is the slope of the ray OB; and so on. It is clear from the figure
that the slope of a ray through the origin de es continuously until the ray becomes
TVCAVC = .
G lly, th ope of a
th
F 1
si
clin
142
tangent to the TVC curve at point C. To the right of this point the slope of ray through the
falls initially as the productivity of the
erated optimally and
he graphical derivation of the ATC curv e way as the derivation of
e AVC curve. That is, the ATC at any on
origin starts increasing. Thus, the AVC curve
variable factor increases, reaches a minimum when the plant is op
ses beyond that point. ri
O X1 X2 X3 X4 X
A B
C
D
Cost TVC
($)
O X1 X2 X3 X4 X
AVC Cost ($)
Figure 4.4: Deriving the AVC Curve from the TVC Curve
C
A
B D
T e is done in the sam
e level of output is the slope of a line from the th
143
origin to the point on the TC curve corresponding to the level of output. Like the AVC
urve, the average (total) cost (AC or ATC) curve is also U-shaped, reflecting the law of
ariable proportions.
c
v
Note that: AVCAFCX
TVCX
TFCX
TVCTFCX
TCATCorAC +=+=+
==
arginal Cost (MC): is the additional/extra cost incurred in order to produce one more
nit of output. That is,
M
u
)()(
XdTCdMC =
It is straight forward to prove that marginal cost could be defined as the change in the
total variable cost for a unit increase in output, i.e.,)()(TVCdMC = .
Xd
Proof:
)()(
XdTCdMC = (As defined earlier)
.)()(MC
cost) fixedin ange)(
TVCdXd
=
l of production is the slope of the TC curve
hich of course is the same at any point as the slope of the TVC). The slope of the TC
comes flatter and flatter as
output expands up to X3 level of output, and then becomes steeper and steeper as the
output goes on increasing. This means that the slope of the TC (or TVC) curve (MC)
ch no is there(Since )(0
)()(
)()(
)()(
TVCdXd
TVCdXd
TFCdXd
TVCTFCdMC
+=
+=
+=
Xd
Graphically, the marginal cost at a given leve
(w
curve at any one point is the slope of a tangent line at that point. As we can see from the
following graph (Figure 4.5), the tangent line initially be
144
initially decreases, reaches a minimum, and then starts increasing. Thus, the MC curve is
also U-shaped.
In summary, the traditional theory of cost postulates that in the short run the average and
arginal cost (AVC, ATC and MC) curves are U-shaped, reflecting the law of variable
proportions. In the short run with a fixed plant there is a phase of increasing productivity
(falling unit costs) and a phase of decreasing productivity (increasing unit costs) of the
variable factor. Between these two phases of plant operation, there is a single point at
hich unit costs are at a minimum. In general, these short run cost curves are as shown
Cost ($)
c
d
m
w
in Figure 4.6 below.
O X1 X2 X3 X4 X
a
b
MC
d
TVC
Cost ($)
a
b
c
O X X2 X3 X4 X
Figure 4.5: Deriving the MC Curve from the TVC Curve
1
145
Fig tween the following pairs: AVC and
AT d below.
(A) The Relationship between AVC and ATC
Cost ($) AC
MC
AVC
AFC
c
a
b
O XM XV XT X
Figure 4.6: The Short Run Unit Cost Curves
ure 4.6 above also shows various relationships be
C; ATC and MC; and AVC and MC. These relationships are discusse
The AV AVC and ATC are U-shaped,
flecting the law of variable proportions. However, the minimum point of the ATC
ATC declines. But later on, the rise in the
VC more than offsets the fall in the AFC and thus the ATC will start rising. The AVC
be
elationship between MC and ATC
C is a part of the ATC: ATC = AFC + AVC. Both
re
occurs to the right of the minimum point of the AVC. This is due to the fact that ATC
includes AFC which falls continuously with increase in output. Initially, the fall in the
AFC offsets the rise in the AVC and thus the
A
approaches the ATC asymptotically as X increases since the AFC, which is the difference
tween the two, declines continuously.
(B) The R
146
Th
producing an extra unit of output. To illustrate the relationship, assume that we start from
a l
If
production of the (Xn+1)th unit. That is, MC = TCn+1 – TCn.
Th
of Xn
e MC cuts the ATC at its minimum point. We said that MC is the change in TC for
evel of Xn units of output.
we increase the output by one unit the MC is the change in TC resulting from the
e AC at each level of output is found by dividing TC by X. Thus, the ATC at the level
is:
n
nn X
TCATC =
And at the level of Xn+1:
1
11
+
++ =
n
nn X
TCATC .
Clearly, from the first relationship above, TCn+1 = TCn + MC.
n+1 will be smaller than the ATCn. On the other hand, if the MC of the
(Xnth unit is higher than ous Xn units), the ATCn+1 will
be higher than the ATCn.
far as the MC is below the ATC (i.e., MC < ATC), it pulls the ATC
downward; and, whenever the MC is above the ATC (i.e., MC > ATC), it pulls the latter
upward. From this, it follows that the MC curve intersects the ATC at the minimum point
TC.
b tween the ATC and the MC can also be proofed by using a simple
Thus, if the MC of the (Xn+1)th unit is less than the ATCn (the ATC of the previous Xn
units), the ATC
+1) the ATCn (the ATC of the previ
In general, as
of the A
This relationship e
calculus:
XATCTCX
TCATC •=⇒= )( , and From
)()(TCdMC = by definition.
Xd
147
ATC) theof (SlopeX MC )(
)()()(
)()(
)()(
•+=
•+•=
•=
=⇒
ATCXd
ATCdXXdXdATC
XdXATCd
XdTCdMC
Given that X and ATC are positive, the last line above shows that:
MC < ATC if the slope of ATC is negative.
MC = ATC if slope of ATC = 0, (at the minimum of the ATC).
MC > ATC if slope of ATC > 0.
(C) The Relationship between MC and AVC
s similar to the relationship between MC and
TC seen above; the MC curve intersects the AVC curve at the minimum point of the
tter one.
The relationship between MC and AVC i
A
la
From XAVCTVCX
TVC•=⇒= )( , and
AVC
TFC.in change no is therebecause )()(
)()(
)()(
XdTVCd
XdTVCTFCd
XdTCdMC =
+==
AVC) theof (SlopeX MC )(
)()()(
)()(
)()(
•+=
•+•=
•=
=⇒
AVCXd
AVCdXXdXdAVC
XdXAVCd
XdTVCdMC
Given that X and AVC are positive line above shows that:
MC < AVC if the slope of AVC is negative.
, the last
148
MC = AVC if slope of AVC = 0, (at the minimum of the AVC).
MC > AVC if slope of AVC > 0.
.4 THE RELATIONSHIP BETWEEN PRODUCT CURVES AND
COST CURVES IN THE SHORT RUN
short, assuming that there is only one variable factor of production, the average
va oduct; and similarly, the marginal cost
is product.
That is, if :
e f labor (APL) rises, the average variable cost of
e product of labor (APL) falls, the average variable cost of
rises;
product of labor (APL) is at its maximum, the average variable
AVC) is at its minimum;
when the marginal product of labor (MPL) rises, the marginal cost of production
when the marginal product of labor (MPL) falls, the marginal cost of production
he mathematical proofs of the above inverse relationships between average product and
4
In
riable cost is the mirror image of the average pr
the mirror image of the marginal
labor is the only variable factor of production, the following relationships hold
wh n the average product o
production (AVC) falls;
wh n the average
production (AVC)
when the average
cost of production (
(MC) falls;
(MC) rises; and
when the marginal product of labor (MPL) is at its maximum, the marginal cost of
production (MC) is at its minimum.
T
marginal product of labor on the one hand and the average variable cost and marginal
cost on the other hand are as follows.
Given TVC = w.L, where w = the market wage rate (assumed fixed) and L = the quantity
of labor input.
149
QLw
QTVCAVC .
==1. , where Q is the level of output
LAPw
QLw
1.
.
=
=
AVC⇒
LAP
wAVC =⇒
2. Q
TVCQ
TCMC∂
∂=
∂∂
=)()( ,
Q
wQ
MC∂
=∂
=⇒ . because w is a constant (fixed).
LLw ∂∂ ).(
LMPw 1.=
LMP
C =
he same set of relationships is shown graphically:
wM⇒
Below, t
150
APL MPL
A B
Check Your Progress
1. Why is the cost function a derived function?
2. Distinguish between/among:
a. The short run total fixed cost, total variable cost and total cost.
The short run average fixed cost, average variable cost and average total cost.
Implicit and explicit costs
3. Discuss the relationship between each of the following pairs (in the short run).
b.
c.
151
a. MC and AVC
b. MC and ATC
c. MC and MPL
d. AVC and APL
. 5 LONG-RUN COSTS
he long-run is a period of time of such length that all inputs are variable. It is a planning
orizon in the sense that economic agents can plan ahead and choose many aspects of the
), doubling
utput requires doubling of inputs, which implies doubling of total output (cost) for given
we consider the case where total cost first increases at a deceasing rate due to
creasing returns to scale (which implies economies of scale), and then increases at an
creasing rate attributed to decreasing returns to scale after the optimum size, the long-
4
T
h
“short-run” in which they will operate in the future. Thus, the long-run consists of all
possible short-run situations among which an economic agent may choose.
If a production technology is characterized by constant returns to scale (CRS
o
factor prices. Hence, the long-run total cost curve in this case is a straight line through the
origin. This implies that the long-run average and marginal cost curves are horizontal
lines and are identical (i.e., LAC = LMC).
LT
LMC = LAC
O Q O Q
Figure 4.8: The Long-Run Total, Average and Marginal Cost Curves under CRS
C LTC LMC
If
in
in
152
run total cost curve will look like the following. Consequently, the LAC and LMC curves
ill be U-shaped.
scale, which means output can be doubled for less than doubling of cost.
he range to the right of the minimum point of the LAC curve is called the range of
ant size. With this plant size all
ossible economies of scale are fully exploited. If the firm expands production further
are
verworked and the decision making process becomes less efficient.
w
LTC
LTCLAC LMC LMC
LAC
The range to the left of the minimum point of the LAC curve is called the range of
economies of
O Q O Q
Figure 4.9: The Long-Run Total, Average and Marginal Cost Curves
T
diseconomies of scale, because a doubling of output requires more than a doubling of
cost.
The traditional theory of the firm assumes that economies of scale exist only up to a
certain plant size, which is known as the optimum pl
p
than this optimum size, there are diseconomies of scale arising from managerial
inefficiencies. It is argued that management becomes highly complex, managers
o
When a firm is producing an output level along the falling part of the LAC curve, the
LMC is less than the LAC. Conversely, when the LAC curve is rising, the LMC is greater
153
than the LAC. The two curves intersect at the point where the LAC curve achieves its
minimum.
Like the short run average cost (SAC) and short run marginal cost (SMC) curves, the
LAC and the LMC curves are also U-shaped. But the reason behind the U-shape of the
long run curves is different from the reason behind the U-shape of the short run curves. In
the long-run, the source of the U-shape is increasing and decreasing returns to scale,
ther than diminishing returns to a factor of production which is the source of the U-
ape fro the short run.
.6 THE RELATIONSHIP BETWEEN SHORT-RUN AND LONG-
RUN AVERAGE AND MARGINAL COSTS
ssume that a firm is uncertain about the future demand for its product and is considering
ree alternatives plant sizes: Small, Medium and Large. The short-run average cost
urves are SAC1, SAC2 and SAC3 as shown in the figure below.
ra
sh
4
A
th
c
If the firm expects that the demand will expand further than Q1, it will install the medium
plant, because with this plant outputs larger than Q1 are produced with a lower cost. For
O Q1 Q1* Q2 Q2
* Q
Cost ($)
AC1
AC2
AC1*
AC2*
Figure 4.10: Short Run Average Cost Curves and the Long Run Average Cost
SAC1
SAC2 SAC3
154
instance, the average cost of producing Q1* units with the medium plant (AC1
*) is less
than the average cost of producing the same units with the small plant (AC1).
Similar considerations apply for the decision of the firm once the level production passes
Q2. For instance, the average c with the large plant (AC2*) is
ss than the average cost of producing the same units with the medium plant (AC2).
Thus, the firm follows the path which is drawn in bold in the figure above. This bold
e
If we relax the assumption of the existence of only three plant sizes and assume that there
i v tain a continuous curve, which is
e planning LAC curve of the firm.
oducing various
lanning curve because the firm decides what plant size to set up
um cost on the basis
aped and it is often called the envelop curve because
ost of producing Q2* units
le
nvelope is thus the long run average cost curve for the case of three plant sizes assumed.
s a ery large (an infinite) number of plant sizes, we ob
th
Cost ($)
SAC4
SAC7 LAC
SAC1SAC2
SAC5
SAC6
SAC3
The LAC curve is the locus of points denoting the least cost ways of pr
levels of output. It is a p
in order to produce optimally the expected level of output at minim
of this curve. The LAC curve is U-sh
it envelopes the short run curves.
O Q* Q
Figure 4.11: The LAC Curve as an Envelope of Var
M
ious SAC Curves
155
Because there are economies of scale and diseconomies of scale in the long-run, the
minimum points of the short run average cost curves (plants 1 up to 3, and 5 up to 7 in
the figure above) do not lie on the long-run average cost curve. For example, a plant size
of 2 op ing at its m
advantage of increasing returns to scale to produce the same level of output at a lower
averag o
Each p o curve.
The point of tangency occurs on the falling part of the SAC curves for points lying to the
left of M, i.e., for the plant sizes such as 1, 2 and 3. Since the slope of the LAC is
negativ cause at the
lope.
um.
t the falling part of the LAC curve the plants are not worked to full capacity. To the
The LMC is derived from the SMC curves but does not envelop them. The LMC is
formed from points of intersections of the SMC curves with vertical lines drawn from the
points of tangency of the corresponding SAC and the LAC curve. Figure 4.12 below
erat inimum average cost is not efficient because a larger plant can take
e c st.
oint f the LAC curve is a point of tangency with some corresponding SAC
e up to M, the slope of these SAC curves must also be negative, be
point of tangency the two curves have the same s
By the same logic, the points of tangency of the LAC curve and the SAC curves for
outputs larger than Q* (to the right of M) occur on the rising part of the SAC curves.
Only at the minimum point (M) of the LAC is the corresponding SAC also at a minim
A
rising part of the LAC curve the plants are overworked. Only at the minimum point M is
the plant optimally utilized.
illustrates how this is done.
156
SMC1
SMC2
SAC1
SAC2
SAC3
SMC3
LAC
LMC Cost ($)
a
To the left of a, SAC1 is greater than LAC so that SAC1 declines at a faster rate than the
LAC. As the larger (SAC1) is falling at a faster speed than the smaller (LAC), the two
ill be equalized at some point – at point a in the figure above. This implies the LMC is
ental cost is added to the short-run cost than to the
g-run cost). At the minimum point of the LAC, the LMC intersects the LAC. At this
= SMC = LAC = LMC.
w
greater than SMC1 to the left of a. At a, LMC = SMC1 (the same amount of additional
costs accrue to both the short-run and the long-run costs so that SAC1 = LAC). To the
right of a, LMC < SMC1 (more increm
lo
point, SAC
Check Your Progress
1. Are the short run and the long run cost curves similar in shape? If so, do you see any
difference between the two?
2. The long run average cost curve is an envelope curve. What does this mean?
Explain.
3. Why don’t we have a long run average fixed cost?
157
4.7 DERIVATION OF COST FUNCTION FROM PRODUCTION
Cost curves are derived functions in that they are derived from the production function.
Costs are not incurred for their own sake but only to produce output.
Graphically, the total cost curve is determined by the locus of points of tangency of
successive isocost lines with the corresponding highest isoquants.
Mathematically, the cost function can be derived as follows. As usual, we use the Cobb-
FUNCTION
cbKALX = Douglas production function:
rKwLC +=Given this production function and the cost function , we want to derive the
cost function, that is, cost as function of output: C = f(X).
e begin by solving the constrained output maximization problem: W
Maximize cbKALX = subject to rKwLC +=
Form the composite function:
)( CrKwLXZ −+−= λ
Partially differentiate Z with respect to L, K, λ and equate each to zero.
* 0=−∂
=∂ wXZ λ
∂∂ LL
wMPL λ=
w
MPL=λ …………………………………………………………………… (1)
* 0=−∂∂
=∂∂ r
KX
KZ λ
rMPK λ=
r
MPK=λ …………………………………………………………………… (2)
158
* 0=−+=∂∂ CrKwLZλ
CrKwL =+ ……………………………………………………………… (3)
equations (1) anFrom d (2) we understand that: rw
MPMP KL = orKMPr
g the Cob-Douglas production function given above,
LMPw=
Usin
XKc
KKcALKcALMP
LLcb
cbL
L
=== −1similarly, and
XbKbALKbALPcb
cb === −1
sing the equilibrium condition and these marginal products, solve for K in terms of L,
r for L in terms of K. Let us solve for L in terms of K.
M
U
o
XKc
XLb
rw=
cLbK
rw= ⇒
)4...(..............................................................................................................wc
rbKL
rbKwcL
=⇒
=
ubstitute this term for L into the production function and solve for K in terms of X:
⇒
S
....(*)................................................................................])([
)
1
Kwc
KrbA
cbb
cbb
=
=
+
+(
)(
)(
X
KrbAX
Kwc
rbKAX
cbb
cb
⇒
⇒
=
=
+
we know tha
⇒
wcXwc
rbA
twc
rbKL = . From equation (4) above,
159
cbb
rbwc
AX
wcrb
wcrbKL +==
1
])([ Then,
*)........(*......................................................................][)(1
cbcbc
AX
wcrbL ++=⇒
rKwLC += As a final step, substitute (*) and (**) into the isocost equation:
cbcbcbcbcb XAwc
r +++++ ]})([bbb
cbcbc
cbc
cbb
cbcbcbb
cbb
cbb
cbcbcbc
cbc
cbb
cbbcbcbc
bAcbrwC
XAwcbrXA
cbrwC
rbwc
AXr
AX
wcrbw
−−−+−
+++
++−
++−
+−
++−
+++
+++
+=⇒
+=
+=
1111
11111
11
])({[
])([])([
}])([{}][)({
C
⇒
constan a is which )([])([ v where;}{ cbcbcbcbcbcbcbcb AwcbrA
cbrwcbXvC ++++++++ +=+= t
1111 bbbccb −−−−
⇒
Don
eas
’t worry if you find the above derivation cumbersome. A numerical example makes it
31
32
ier. Suppose we have a production function given by KLX = , w = 2 Birr per unit
nd r = 4 Birr per unit. Derive the cost function. a
Solution:
The steps that are involved to derive the cost function are:
Step 1: Solve for L in terms of K or K in terms of L from the optimality
32
32
31
31
132
42
−
−
=⇒KL
KL condition
K
L
MPMP
rw= .
3
31
32
32
31
32
32
31
31
2
+
+
−
−
=L
K
KL
KL
41
21
⇒
=⇒
160
KLLK
= 4
41
=⇒
⇒
Step 2: Substitute the result from step 1 into the production function and solve for L and
s of Q from the production function. K in term
31
32
K
3
3
333
16
16
4
XK
KX
=
=
= 122
31
32
)4( KK=
+
K
X
X
LX
⇒
⇒
⇒
⇒
=
XL
Because L = 4K, XL3
3144
=⇒
=⇒
X
2
4
16−
KL3
44 ==⇒
Step 3: Substitute the results from step 2 into the cost constraint.
rKwLC +=
C KL
XXC )16
(4)4(23
3 += 142 +=⇒
⇒
⇒
XC )]1(4)4(2[ 3 +=163
XC ]22[ 32
35
+= . ⇒
4.8 DYNAMIC CHANGES IN COSTS – THE LEARNING CURVE
A l e average cost than a smaller firm because of
implies that growing firms with
incr i me.
arg firm may have a lower long run
increasing returns to scale in production, which
eas ng returns to scale enjoy lower average costs over ti
161
Bu is e firms, long-run average cost may
dec technological information as
wit cost (MC) and average cost (AC) of producing a
given level of output fall for four reasons:
1. s me more adapted to a given task, their speed increases.
2. schedule the production process more effectively.
3. o are initially cautious in their product designs may gain enough
t organization may
4. earn how to process materials required more effectively
is advantage in the form of lower materials cost.
gra
amount of inputs needed to produce each unit of output is known as the learning curve.
t th may not be necessarily the case. In som
line overtime because workers and managers absorb new
they become more experienced at their jobs. As management and labor gain experience
h production, the firm’s marginal
A workers beco
Managers learn to
Engineers wh
experience to be able to allow for tolerances in design that save cost without
increasing defects. Better and more specialized tools and plan
also lower cost.
Suppliers of materials may l
and may pass on some of th
As a consequence of this, a firm “learns” overtime as cumulative output increases. The
ph (curve) that describes the relationship between a firm’s cumulative output and the
Am
ount
of i
nput
s ne
per
Cumulative output
Learnin
eded
unit
of o
utpu
t
g Curve
Figure 4.13: The Learning Curve
162
Overtim oduction can decline because of:
from A to B in
igure).
e, a firm’s average cost of pr
a. Growth of sales when increasing returns are present (movement
the figure below), or
b. The existence of learning curve/effect (movement from A to C in the f
A
B
AC1
AC2
Q
4: Economies of Scale versus Learning Effect
AC
C
O Figure 4.1
Check Your Progress
ing the cost function from the production
m that has been in business for long could
d learning effect?
4.9
– derived from the production function.
rt and the long run, economists calculate implicit as well as explicit
o hose costs implied by the alternatives given
iture or bookkeeping costs.
1. Outline the steps to be followed for deriv
function
2. Discuss the reasons for which a fir
experience low average unit cost of production.
3. What is the difference between economies of scale an
LESSON SUMMARY
The cost function is a derived function
In both the sho
c sts of production. Implicit costs are t
up, and explicit costs are direct expend
163
n ri le factor(s) are added to the
i ing returns to the variable
owever, eventually the firm reaches a point (some higher level of output) at
egin to increase at an increasing rate. Such increasing and
returns to the variable factor of production (the law of variable
e short-run average and marginal cost
u
Except that we don’t have a fixed cost in the long run, the short and the long run
ver, the U-shape of the long-run average and
marginal cost curves is due to economies and diseconomies of large-scale
f increasing returns to scale (economies of scale) in
ore
I. M
I the short run, as more and more units of the va ab
f xed factor, the firm may initially experience increas
factor and thus total costs of production rise slowly at lower levels of output.
H
which total costs b
diminishing
proportions) account for the U- shape of th
c rves.
cost follow similar patterns. Howe
production.
There a predictable relationship between short run cost functions and production
functions as well between short run and long run cost functions.
A large firm may have a lower long run average cost than a smaller firm because of
two reasons: because o
production, and/or because of the learning effects (as workers and managers of a
large firm could easily absorb new technological information as they become m
experienced at their jobs).
4.10 REVIEW QUESTIONS
ultiple Choice Questions
If we have a linear cost function of the firm C = a +
1. bQ, then the average cost will:
a. remain constant as prod
b. decrease continuously as production expands.
c. increase with in
d. first increase and then decrease with increases in output.
eases beyond its minimum, the average cost,
a. increases
uction expands.
creases in output
2. When the marginal cost incr
164
b. decreases
c. remains constant
d. first decreases and then increases
3. Which of the following is the general sequence?
a. nomies end
b.
c. ies begin
ether
incurs in purchasing or hiring any factor of production from
ferred to as:
a. explicit cost
c. variable cost
d
b. rise at a decreasing rate
Economies of scale begin when diseco
Diseconomies begin where economies end.
Diseconomies end where econom
d. Economies and diseconomies of scale go tog
4. The cost that a firm
outside the firm is re
b. implicit cost
d. fixed cost
5. An entrepreneur running a business earns $20,000 per year as his/her salary from the
total receipts of the firm; the implicit cost of this entrepreneur is:
a. $20,000/year
b. more than $20,000/year
c. less than $20,000/year
d. any of the above is possible
6. If only part of the labor force employed by a firm can be dismissed at any time an
without pay, the total wages and salaries paid out by the firm must be considered:
a. a fixed cost
b. variable cost
c. partly fixed and partly variable cost
d. any of the above
7. When the law of diminishing returns begins to operate, the TVC begins to:
a. fall at an increasing rate
c. fall at a decreasing rate
d. rise at an increasing rate
165
8. All the following curves are “U” shaped except:
a. the AVC curve
b. the AFC curve
d. the MC curve
c. curve, but not by the slope of the TVC curve
10. The its minimum point before the AVC and the ATC curves do so.
the MC curve intersects both the AVC and the AC curves at their lowest
a. always
d. sometimes
from the origin is tangent to the TC curve, the ATC
is:
2. The LAC curve is tangent to the SAC curve at the lowest point of the latter when the
statement is true:
a. always
is due to:
a. economics of scale
c. the ATC curve
9. MC is given by:
a. the slope of the TFC curve
b. the slope of the TVC curve, but not by the slope of the TC curve
the slope of the TC
d. either by the slope of the TC curve or by the slope of the TVC curve
MC curve reaches
In addition,
points. The above statements are both true:
b. never
c. often
11. At the point where a straight line
a. at its minimum
b. equal to MC
c. equal to AVC plus AFC
d. all of the above
1
LAC curve is falling. This
b. never
c. sometimes
d. cannot say
13. If the LAC curve falls as output expands, this
166
b. the law of diminishing returns
c. diseconomies of scale
d. any of the above
14. The LAC curve:
a. falls only when the LMC curve falls
b. rises whenever the LMC curve rises
t point of the LMC curve
d. falls when LMC < LAC and rises when LMC > LAC
n the long run total cost. This statement
is:
a. always true
b. often true
c. sometimes true
d. never true
I
c. goes through the lowes
15. The short run total cost can never be less tha
I. Discussion and Workout Questions
1. Distinguish between: (a) short-run and long-run costs, (b) explicit and implicit costs.
2. Explain the relationship between the marginal and average cost curves. Show the
relationship between marginal cost, average variable cost and average total cost.
3. Explain why the average total cost and the average variable cost become closer and
closer as output increases.
. Show the circumstances when the marginal cost is constant throughout but the
int: think of the geometric derivations of the two costs.)
from the short run average cost curves.
curve.
that at the output where SAC = LAC, SMC also equals LMC?
+ re a cost
TVC, TC, AFC, AVC, MC, and ATC. Is this cost
function? Why? Draw the cost curves on the
4
average cost is falling. (H
5. Derive the long run average cost curve
6. Write a short note on the derivation of long run marginal cost
7. Why is it
8. Suppose the cost function is given as C = 135 + 75Q – 15Q2 Q3. Prepa
schedule (table) showing the TFC,
function a short run or a long run cost
basis of cost data obtained from the cost function.
167
CHAPTER FIVE
PERFECT COMPETITION
LESSON STRUCTURE
5.1 Introduction
bjectives
.3 Characteristics of Pure and Perfect Competition
um
5.4.1 Equilibrium in the Market Period
son Summary
.7 Review Questions
.1 INTRODUCTION
The type (or
ature) of competition firms face from competitors, which in turn determines the degree
f power of a firm over the price of its product, is the basis for categorizing markets into
n is the only type of competition firms
perating in perfectly competitive markets will face from competitors both price and non-
5.2 Chapter O
5
5.4 Market Equilibri
5.4.2 The Short Run Equilibrium of a Firm and Industry/Market
5.4.3 The Long Run Equilibrium
5.5 Perfect Competition and Consumers’ Welfare
5.6 Les
5
5
The market in which an individual firm operates or sells its product (good or service) to
consumers can be categorized broadly into perfect and imperfect market9.
n
o
perfect and imperfect. While price competitio
o
price competitions are common in imperfect markets. In short, Perfect Competition is a
market structure characterized by complete absence of rivalry among individual firms.
9 Markets dominated by one firm (monopoly), very few firms (oligopoly), and relatively large numbers of
firms selling closely substitutable products (monopolistic competition) are the three common types of imperfect markets in which firms use different means of deterring other firms from entering into the market or the means of influencing their market share. The later two are characterized by rivalry among individual firms.
168
In neoclassical economics and microeconomics, perfect competition describes a market
in which no buyer or seller has market power or where all buyers and sellers are price-
takers; that is, perfect competition is a market structure in which firms treat price as a
arameter. It is this distinction which differentiates perfectly competitive markets from
petitive markets are characterized by
llocative and productive efficiency. In general, a perfectly competitive market is
CTIVES
Distinguish between pure and perfect competition
.3 CHARACTERISTICS OF PURE AND PERFECT COMPETITION
perfectly competitive market has several distinguishing characteristics. The main
1. Many Buyers and Many Sellers
ingness and ability to buy the product at a certain
rice and many producers with the willingness and ability to supply the product at a
p
imperfectly competitive ones. Perfectly com
a
characterized by the fact that no single firm has influence on the price of the product it
sells. Because the conditions for perfect competition are very strict, there are few
perfectly competitive markets in the real world.
5.2 CHAPTER OBJE
After completing this chapter, you will be able to:
Determine the short and long run equilibrium output and price of a competitive
firm and industry.
Describe why perfect competitive market is an ideal market in terms of ensuring
consumer welfare.
5
A
features include:
There are many consumers with the will
p
certain price. Since each firm supplies only small part of the total market supply any firm
cannot affect the market price by altering (increasing or decreasing) its output.
169
2. Homogeneous Products
The industry or market is defined as group of firms supplying homogeneous products
(goods or services). That is, products supplied by the different firms are exactly the same.
Example, salt supplied by two sellers are identical to the extent that buyers are unable to
differentiate which firm supplied which product.
The assumption of large number of sellers and product homogeneity together imply that
ectly competitive market is a price taker. Thus, a
a completely horizontal or perfectly elastic demand curve for its
it can sell any amount of output only at the ongoing market price
an individual firm operating in a perf
competitive firm faces
product indicating that
( P ). Moreover, the demand curve is also the average revenue (AR) and marginal
venue (MR) curve.
quality of the ongoing market price (
re
P
Figure 5.1: The Demand Curve Faced by a Firm under Perfectly Competitive Market
The reason for the e P ) and the demand curve is that
ny firm receives, for any unit of output sells, the price which is determined by the
igure 5.2 below.
a
intersection of market demand and market supply. This is depicted in F
O Q
MRARDDP === P
170
SS
P MC
−
P ME −
P FE MCDDP ==−
DD
irm
Q FQ Q MQ
(a) Industry/Market (b) F
Figure 5.2: Determination of Equilibrium Price under Perfect Competition
Why do the relationships ARP = and MRP = hold? Let us show these mathematically.
QQPTRAR .
== )().( dQPPQddTRMR === Q dQdQdQ
PAR =⇒ PMR =⇒
3. Free Entry/Exit
Unl im rf t ma ets, ry to an xit fr a business is not blocked in a perfectly
t m t w f a e f
arrier that restricts firms from entry into and/or exit out of a perfectly competitive
arket.
t a point where the marginal cost of production meets the
arginal revenue from sales. More on this will be discussed in Section 5.4.
ike pe ec rk ent in d e om
competi ive arket. In o her ords, irms h ve fre dom o movement or there is no
b
m
4. Firms Aim to Maximize Profit
The objective of firms in perfect competition is profit maximization. To this end firms
operate (produce and sell) a
m
171
5. Absence of Government Intervention
This is to say the no er nt regulation or intervention in th arket in any way,
say through imposing tariffs, granting subsidies, rationing, etc., which are considered as
disturbances to the ma . notion is based on the argum of sical
economists led by Adam Smith who regard the government intervention as unnecessary.
A m et t ful on he a ve f cha is c u p Pure
com tio nd petition are diff o t ui e f ent of
the w additional charac istic um s.
6. P ct bil f F tors Pro tio
This implies that all factors of odu n, s a al free to
move from e se to othe r fro ne o r is e change
their jobs without any restriction for labor is not unionized and the supply of raw
mat s ot no ized ithe o ir h o es full
employme re ce
7. P ct rm n Bo Con er P r
and buyers have
omplete information and knowledge of the market. The implication is that the current
er a perfectly competitive market.
re is gov
rket
nme
This
e m
ent the clas
ark tha fils ly t bo ive racter tics is alled p re com etition.
peti n a perfect com erent f r the la er req res th ulfillm
follo ing ter s/ass ption
erfe Mo ity o ac of duc n
pr ctio such a labor nd raw materi s, are
on ctor an r o m o firm t anothe . That , work rs can
erial is n mo pol e r by ne or few f ms. T is als impli
nt of sour s.
erfe Info atio for th sum s and roduce s.
It is assumed that in a perfectively competitive market both sellers
c
and future price of products, quality of products supplied by different firms, etc., are
certainly known. In other words, information is costless: there is no uncertainty about
future prices, and no non-price competition exists und
Check Your Progress
1. Distinguish between pure competition and perfect competition.
172
2. Discuss the implication of the notion that there is no barrier to entry and exit under
equilibrium of a perfectly competitive firm as well as that of industry
erent cases: the market period, the short run and the long run equilibria.
ket Period Equilibrium
market period refers to a very short period in which supply is absolutely fixed. For
D3
ctly Competitive Market
r that different level of demand gives different equilibrium
ut equilibrium output remains the same. This implies that, at any market period demand
alone determines the equilibrium price. A market period is thus different from short run
perfect competition.
5.4 MARKET EQUILIBRIUM
We will see the
under three diff
5.4.1 The Mar
A
instance, the quantity of agricultural products available in the market cannot be increased
instantly with demand as production is seasonal. Put it differently, though different levels
of demand give rise to different prices, supply will remain the same for it cannot be
increased until the next harvest.
P S
D2
D1
Figure 5.3: Market Period Equilibrium under Perfe
3P
2P
1P
From the above figure it is clea
b
O SQ Q
173
and long run in which both the supply and demand conditions determine the equilibrium
price and quantity.
5.4.2 The Short Run Equilibrium of a Firm and Industry/Market
The Short Run Equilibrium of a Firm
Shot run is a production period in which the amount of one or more of the inputs a firm
uses is fixed or constant. In other words, in the short run, the quantity of output produced
by a competitive firm can be increased (decreased) only by increasing (decreasing) the
ariable inputs. The short run equilibrium of a firm or an industry (a market) is thus the
hat maximizes profit or minimizes loss under such conditions. This profit-
using any of the two
al R r ch
s in equilibrium when total revenue less total cost is the
aximum. That is, the firm maximizes profit when the difference between total revenue
ollowing hypothetical example for a competitive firm
ow we determine the equilibrium output and maximum profit using the TR –
C approach.
t run output (Q)
w.
Q 3 4 5 6 7 8 9 10 11 12
v
output level t
maximizing level of output and the profit level can be determined
approaches discussed below.
1. The Tot evenue – Total Cost (TR – TC) App oa
Using this approach, a firm i
m
and total cost is the greatest. The f
clarifies h
T
Example 1: Suppose the short run market price is $5. Moreover, the shor
and associated total cost of a competitive firm as are shown in the table belo
0 1 2
TC 5 19.5 20 2 5 24.75 27.48 32.48 38.88 46.66 55 65.2810 15 17 18. 2.2
ter Four that the total cost wh10 Recall from Chap en output is equal to zero is the short run total fixed cost
174
G the abov iniven e formation, we need to compute only TR (i.e., price multiplied by the
vel of output, Q) in order to determine the equilibrium output and maximum profit le
using the TR – TC approach. The profit/loss of the firm for each output level is computed
by subtracting TC from TR and is shown in the last column of table 5.1. Other variables
are computed for latter use.
Table 5.1: Determination of Equilibrium of a Firm Using the TR – TC Approach
) Q)
Pric
e (P
Out
put (
Q)
TR
(P.Q
)
AR
(TR
/Q)
TR
/∆Q
)
TFC
TV
C
TC
(FC
+VC
)
C/Q
)
∆TC
/∆
/Los
s
(TR
–T
C)
M (∆
AT
C (T
MC
(
Prof
it
$5 0 0 - - 15 - 15.00 - - (15.00)
$5 1 5 5 5 15 2.00 17.00 17.00 2.00 (12.00)
$5 2 10 5 5 15 3.50 18.50 9.25 1.50 (8.50)
$5 3 15 5 5 15 4.50 19.50 6.50 1.00 (4.50)
$5 4 20 5 5 15 5.00 20.00 5.00 0.50 0
$5 5 25 5 5 15 7.25 22.25 4.45 2.25 2.75
$5 6 30 5 5 15 9.75 24.75 4.13 2.50 5.25
$5 7 35 5 5 15 12.48 27.48 3.93 2.73 7.52
$5 8 40 5 5 15 17.48 32.48 4.06 5.00 7.52
$5 9 45 5 5 15 23.88 38.88 4.32 6.40 6.12
$5 10 5 50 5 15 31.66 46.66 4.67 7.78 3.34
$5 11 55 5 5 15 40.00 55.00 5.00 8.34 0
$5 12 60 5 5 15 49.20 64.20 5.35 9.20 (4.20)
$5 13 65 5 5 15 59.36 74.36 5.72 10.20 (9.36)
Note: The values o Af ATC (S C) are rounded to two decimal places.
175
176
n ormal (zero) profit or is at its break even
ut. Moreover, the firm obtains maximum
rofit when it produces either 7 or 8 units of output.
he most important points in the total revenue – total cost approach are depicted
Figure 5.4: Profit Maximization of a Firm
The profit (loss) of e (negative) distance between the
total revenue (TR) and total cost (T In the above figure, first the TC curve lies
above the TR curve until exac
the firm achieves economic
and lines gradually af
ce again, the firm breaks even at point B when it produces
ofit becomes negative beyond point B.
From Table 5.1 it is clear that the firm obtai s n
point when it produces 4 or 11 units of outp
p
T
graphically as follows.
T
The maximum profit = 7.52
TRTC
0
T
Q
B55.0 40.00 32.48 20.00
A
15.00
O 4 7 8 11
T
Depicted Using the TR – TC Approach
a firm is represented by the positiv
C) curves.
tly 4 units of output is produced at point A implying that
profit is negative (there was loss) prior to this point. Secondly, the intersection of the total
revenue and total cost curves at point A implies that the firm has reached its breakeven
ofit). Thirdly,point (no loss and no gain or obtains zero pr
(positive) profit at any level of production between point A and B. In this region, profit
increases gradually, reaches maximum towards the middle, dec ter 8
units of output is produced. On
exactly 11 units of output. Finally, pr
Therefore, profit maximizing level of output is achieved at a point where the positive
tal cost curves is the longest. At this point, the
he MC (see the TT line which is tangent to the TC curve) is equal
the slope of the total revenue curve, the MR. In other words, the short run equilibrium
f the firm is achieved when 8 units if output is produced.
2. The M
reason is that the short run equilibrium output (profit maximizing level of
utput) and the associated profit can be clearly determined by equating marginal revenue
ATC
distance between the total revenue and to
slope of the total cost, t
to
o
arginal Approach
The total revenue – total cost approach indicates only the amount of profit (or loss) at
different levels of production. In the above example, for instance, both 7 and 8 units of
output generate 7.52 units of profit and the TR – TC approach doesn’t tell us why we
choose 8 as a profit maximizing level of output (and why not 7). Hence, it does not help
for analytical interpretation of business behavior. In this regard, the marginal approach is
a useful analytical tool at least for the following reasons.
The first
o
to marginal cost, i.e., MCMR = .
Graphically:
MR MC
Profit MRP =
Figure 5.5: Short Run Equilibrium of a Firm Depicted Using the Marginal Approach
0.50
4.06
MC
ATC
5.00
4 EQ = 8 Q
177
The amount of profit )(π at any level of output could be calculated using:
QATCP )( −=π . This is derived from the TR-TC approach as follows:
TCTR −=π
QATCQP .. −=π
QATCP )( −=π .
ATCP > , there is excess profit; if ATCP = the firm gets normal (zero) profit; Thus, if
and, if ATCP < the firm incurs loss. For instance, at the equilibrium output (EQ) profit is,
8)06.45( −=π , which is
52.78)94.0( ==π .
The second reason is that comparing the value of MR and MC to the left and right of
whether to expand or reduce output. For example, to the left of E
short run equilibrium output (EQ) has an important implication for a firm’s decision on
ta nce price is greater than unit cos
to expand production. On the other
is lower than MC to the right of the equilibrium output implying that the firm
sho
Alterna
from th m.
Q (for any output level
less than 8), the MR ( = P) exceeds the MC, indicating that the sale of a unit of output
would increase total revenue more than to l cost si t
(ATC) of production. Therefore, it pays for the firm
hand, MR
uld reduce its production.
tively, the short run equilibrium of a firm can also be derived mathematically
e given level of market price and total cost function of a fir
Example 2:
Suppose the market (per unit) price a firm faces is $10 and its cost function is given by:
12 += QTC . Calculate the profit maximizing level of output and the maximum profit.
In this case,
QdQ
dTCMC 2== andQ
TCATC 12 +== .
Equating the market price to the MC will give the equilibrium output. That is,
178
MCP =
Q210 = .
us, the output level that maxim zes profit is: 5Th i =Q .
Substituting this output level into the TC and ATC equations gives the values 26 and 5.2,
respectively.
Furthermore, the profit of the firm obtains is:
TCTR −=π
1)1( 22 −−=+−= QPQQPQπ
242650)15()5(10 2 =−=+−=⇒ π .
The same result can also be obtained using: QATCP )( −=π .
245)8.4(5)2.510( ==−=π .
Check Your Progress
1. A perfectly competitive firm is faced with the following output and total cost
schedule.
Q 0 1 2 3 4 5 6 7 8 9 10
TC 9 20 30 32 39 47 60 67 77 90 109
If the market price is Birr 13,
a. Compute a table that shows the short run equilibrium of the firm using the TR –
roaches.
b. What is the equilibrium output of the firm?
c. Using the marginal approach, show the profit level graphically.
. Assume a two product firm is operating in a perfectly competitive market. The market
prices of its products are $12 and $18, respectively. Furthermore, the production cost
of the firm is given by . Based on this information:
a. Find the short run equilibrium outputs, and , that in combination maximize
profit.
b. Calculate the total profit of the firm
c. Show graphically the profit the firm arns from each market separately.
TC and marginal app
2
2221
21 22 QQQQTC ++=
1Q 2Q
.
e
179
180
MR1
P
P1
D F H P2 P3G P4
P5
O q5 q4 q3 q2 q1 Q
MR2
ATC
MR5
MC
MR3
MR4
AVC
E1
E2
E4E5
E3
A B C
K
So far we h ch. Thirdly,
is approach will provide the basis weather to shutdown a loss making firm or not. This
ilibria of a Firm for Different Market Prices
ave seen two reasons for the usefulness of the marginal approa
th
can be illustrated with the help of the figure below.
Figure 5.6: Short Run Equ
In the above figure, five short run equilibrium points are established at different market
prices. The equilibria are established at points where MCMRP == . As a result, the
quantity of output produced by a firm as well as its profit or loss varies. For example,
when the ongoing market price is 1P , the short run equilibrium is at point 1E . At this
price, the total amount of output produced by a firm operating in a perfectly competitive
market is 1Oq . On the other hand, the unit cost (ATC) of producing one unit of output is
given by the distance OF or Cq1 .Since )( 11 CqATCP > , the area CFEP 11 indicates the
excess profit the firm obtains.
to . In this case, the short run equilibrium
established at point and amount of output is supplied. Since, price is
equal to unit cost , the firm is in its breakeven point; that is it earns normal (zero)
Suppose the market price declines from 1P 2P
2E 2Oq 2OP
22 Eq
is
profit. However, for any price level below 2P , the firm will incur loss or will earn
negative profit as the market price will be less than ATC.
s that, should a loss making firm close down? The
answer to this question is that one should observe whether the market price is greater than
or equal to th
An interesting question one might ask i
e AVC at that equilibrium output in order to decide whether to close down
r not. That is, a loss making firm should stay in business by continuing production as far
the market price is greater than the AVC. This is because not all fixed costs incurred
re lost if the market price is greater than AVC. In other words, since all fixed costs will
e lost if the firm discontinues production, th rm will lose less by staying in business
osts. However, a loss making firm should shut down
hen the market price becomes less than the minimum of AVC. Recall from earlier
iscussion in Chapter Four that, graphically, AVC will be at its minimum when it is
rossed by the MC curve from below. Therefore, the point where thee minimum AVC is
qual to MC is called the shutdown point.
The reason as to w o stay in business
is established at and hence the
e cost of producing
or . Since
o
as
a
b e fi
and covering some part of the fixed c
w
d
c
e
hy it is a sensible strategy for a loss making firm t
and shutdown when the market price is greater than and less than the AVC respectively
can be justified by considering the situations at market price 3P and 4P in Figure 5.6
above.
First, consider the situation when the market price declines from P to P . When the
ongoing market price is , the short run equilibrium
2 3
3P 3E
firm produces 3Oq amount of output. At this level of production, th
one unit of output (ATC) is given by OH Bq3 BqP 33 < , or , the area
esides,
Total cost, which is equal to output multiplied by ATC, is
VC) is
OHP <3
BHEP indicates the loss incurred by this competitive firm. 33
B
BHOq3 .
AVC is OG or Kq . This implies that, total variable cost (T3 KGOq3 .
181
The difference between total cost and total variable cost gives us the total fixed
BHG .
cost (TFC), which is equal to
But the market price is greater than average variable cost, i.e.
ften less costly to
ducing at a loss than to shutdown and still be forced to bear the high fixed
aking firm should shutdown as soon as the market price falls below
i produce. The mark
ed cost by shutting down. If it were to produce at
e point where MC equals the very low market price, it would lose more than fixed cost.
herefore, it is a wise decision to shutdown the business.
he Short Run Market/Industry Equilibrium
he short run industry supply curve is the horizontal summation of the short run supply
urves of individual firms. The short run supply curve of an individual firm is derived
om the intersection of its MC curve with its successive demand (MR) curves. It is part
f the MC curve above the intersection of the MC and the AVC curve. As the market
rice increases gradually we expect that each higher demand curve (price line) cuts the
K
KqEqOP 3333 )( >=
Therefore, if the firm decides not to produce 3Oq amount of output it will lose the whole
of TFC given by area KBHG . However, by deciding to stay in business it will lose only
BHEP 33 , which is less than KBHG . This is because it has covered the part of the TFC
given by the area GPKE 33 . Profit maximizing firms may in the short run continue to
operate even though they are losing money. This is the case particularly for firms that
own great deal of capital and therefore high fixed costs, because it is o
continue pro
cost.
However, a loss m
.4P Because, when it produces 4Oq amount of output at 4E , the firm will lose all of its
TFC amounting to 44 ADPE ; and, as soon as the price falls short of 4P , it won’t even
cover its variable cos rice ( 4P ) that is equal to the
minimum of the AVC ( 44 Eq ) and the MC is the dividing line between the decision to
shut down and to continue operation. When the market price is below 4P , the firm should
shut down since it will lose only its fix
t if it dec des to et p
th
T
T
T
c
fr
o
p
182
MC curve at a s that quantity
pplied by firms will increase as price increases.
herefore, the industry supply curve is simply the horizontal summation of the individual
ibrium
ill be obtained after determining the industry demand curve which is downward
point to the right of the previous intersection. This indicate
su
Figure 5.7: The Supply Curve of a Perfectly Competitive Firm
T
firms’ supply curves. Given the industry supply curve, the short run industry equil
w
sloping. Assuming that there are 100 identical firms in the industry, the short run
equilibrium will be as shown in the figure below.
Figure 5.8: The Short Rum Equilibrium an Industry
5.4.3 The Long Run Equilibrium
P P3
100*q3 Q
The Industry Supply Curve
Market Demand Curve
q1 q2 q3 Q q1 q q2 3 Q
P1
P2
P3
MC ATC
AVC
The Supply Curve of a Firm P
183
Unlike the short run, the long run is a period of time in which a firm can vary/change the
amounts of all of its inputs. Since all inputs are variable in the long run, a firm has the
opt of adjusti
It is als o
is poo
areas/e into the industry if profit prospect is
attractive or are g s
in the i
run equ
The Long R
In the l
produc
will be
ion ng its output through adjusting its plant size to achieve maximum profit.
o p ssible some businesses can be liquidated /shutdown/ entirely if profit prospect
r. The resources are thus transferred into more profitable investment
ndeavors. Similarly, new firms will enter
reater than profits elsewhere. Hence, adjustment of the number of firm
ndustry in response to profit motives is the key element in establishing the long
ilibrium.
un Equilibrium of a Firm
ong run, firms are in equilibrium when they have adjusted their plant size so as to
e at the minimum of the long run average cost (LAC) curve. At this point the LAC
tangent to the demand curve defined by the market price. Therefore, the equality:
MRPLACSACSMC ==== is the long run equilibrium condition of a
itive firm.
LMC =
compet The implication is that competitive firms will earn only normal profit in
e long run.
Assume for simplicity that there are 100 identical firms that are supplying the same
th
SMCSACLMC
LAC
Lq Q
DD = MRP
Figure 5.9: The Long Run Equilibrium of a Firm
amount of output in the short run. Further assume that the business they engaged in is
184
profit
each
able. The short run market/industry supply is thus 100 multiplied by the supply of
firm or simply 100(q1) indicated on the industry supply curve, ∑ 1q . As m d
r, we can now expect that the short run excess profit enjoyed by the firms in the
try will attract new firms into the industry.
∑ 1q
∑ 2q
DSMC SAC
185
q2 q1 100(q1) 180(q2)
D
D P
P1
A MR
ES
2
B
C MR
1
2
EL
entione
earlie
indus
Firm
Figure 5.10: Derivation
supplies
indus
ti
curve
curve
busin
mark
The L
The i
firms inimum p
LAC
Market
of Long Run equilibrium of Firms from the Short Run
Equilibrium
As shown in Figure 5.10, the individual firms are in the short run equilibrium when each
1q units of output. It cannot be the long run equilibrium because each firm in the
try earns excess profit shown by area 1ABDP in the first graph as ATCP >1 . Each
me new firms (attracted by the excess profit) enter into the market, the market supply
will shift to the right. The entry of firms will continue until the industry supply
shifts to ∑ 2q , the market price falls to P2, each firm produces q2, and firms in the
ess obtain normal profit. At this point, suppose 80 new firms have entered into the
et. Therefore, the long run industry equilibrium output will be 180(q2).
ong Run Equilibrium of the Industry/Market
ndustry is in the long run equilibrium when a price level reaches a point where all
are in equilibrium. That is, when all firms produce at the m oint of the
curve or when MRPLACSACSMCLMC ===== , and each firm just makes a
SMCSAC
LMC LACSS
normal profit. With all firms in the industry being in equilibrium and with no entry and
remains stable and given the demand curve, the price
ill be the long run equilibrium price.
e Industry
T hat although
emand equals supply in both cases, the long run equilibrium is defined at a point where
and no excess profit is obtained.
exit, then the industry supply curve
w
Figure 5.11: The Long Run Equilibrium of th
herefore, the difference between the short run and long run equilibrium is t
d
demand is equal to supply
Check Your Progress
Referring to Figure 5.10 above, what is the price elast
1) icity of supply if an individual
fi supplied 18 units of output when P s $6 12 ts w the rket e
fa to P2 3?
2) Based on the price and output information in question 1, calculate the elasticity of
3) Do r why
5.5 PERFECT COMPETITION AND CONSUMERS WELFARE
rm 1 wa and uni hen ma pric
lls = $
market demand?
you expect any of the 180 firms to exit out of the business at P2? Why o
not?
186
Perfe
resource a
When the long run equilibrium is achieved, the economy operates at the maximum
econ
level of
This that each consumer buys those quantity of goods at which the marginal rate
of su goods.
Put d
competitive equilibrium, which in turn equals the marginal cost (MC) of producing the
good
ct competition is regarded as the most ideal market from the point of view of
llocation; resource utilization; resource employment; and consumers’ welfare.
omic efficiency. This is because:
individual firms operate at the optimal plant sizes and produce optimal
output,
consumers buy different units of each output at the price equal to the minimum
attainable average cost per unit (P = LAC).
implies
bstitution (MRS) between any two goods is equal to the price ratio of the two
ifferently, the marginal utility of the consumed good (MU) equals the price (P) at
. The discussion in the following three steps show that, if MCPMU == , allocation
is eff
of satisfaction from the last
rices of goods
2. ium condition of a perfectly competitive firm is given by
plying their sweaty
g that last bit of
to produce the last unit of the good (output price/value) exactly
irm’s of producing the last unit of the good supplied11.
3. Putting these two equations together, we see that
icient or optimal.
1. MUP = : Consumers choose to purchase a good up to the amount corresponding
to MUP = . As a result, every person is gaining utils
unit of the good consumed as good as what he/she pays. Since the p
are the lowest, consumers’ welfare is maximized.
:MC= The equilibrP
.MCP = From the viewpoint of laborers, workers are sup
labor up to the point where the utils of satisfaction lost by workin
time needed
equals the f MC
MCMU = . This means that the
utils gained from the last unit of good consumed exactly equals the utils lost for
sweaty labor required to produce that last unit. It is exactly this condition – the
marginal gains of society from the last unit consumed equal the marginal costs of
11 The MC (of the firm) is the price/wage paid to the laborer for the cost they incur in terms of the utility of
leisure forgone and the disutility of the sweaty labor needed to produce the last unit of the good.
187
society for that last un guarantees that a competitive
equilibrium is efficient.
ence, both the allocation and utilization of resources are optimal under perfect
h this quality of perfect competition, as we will see in subsequent
rkets (monopoly, monopolistic competition, and oligopoly) fall
a equilibrium.
e firm is the one that can sell an amount of output it wants at
ompetitive firms are assumed to maximize their profit
mize profits, the competitive firm will choose that
e equals marginal cost of production, i.e.,
D he competitive firm’s equilibrium will come where the rising
MC curve intersects its horizontal demand curve.
) costs must be taken into account in determining firm’s
short-run decision to shutdown or to continue operation. Below some critical price
rm shuts down and produce
nothing when price falls below the shutdown price.
in the industry. So as free entry
it produced – which
H
competition.
To t e contrary of
chapters, the imperfect ma
short of reaching such an efficient and welfare-maxim
5.6 LESSON SUMMARY
A perfectly competitiv
the ongoing market price. C
(or minimize losses). To maxi
MCP = . output level at which pric
iagrammatically, t
Variable (or avoidable
(the shutdown point), the firm’s revenue will not even cover the variable cost that
could be saved completely if it shuts down. Rather than end up losing more than
fixed costs by operating, it would be better if the fi
The rising part of the MC curve of each firm above the shutdown price is its supply
curve. To obtain the supply curve of a group of independent competitive firms, we
add horizontally their separate supply curves. Hence, the supply curve of an
industry represents the marginal cost curve for the competitive industry as a whole.
In the long run when firms are free to enter and leave the industry and where no one
firm has any particular advantage of skill or location, competitors will compete and
eat away any excess profits earned by existing firms
188
means P cannot persist above th Pe breakeven point and free exit means cannot
fall below that point, all firms just earn normal profit in long-run equilibrium.
light on the efficient organization of a
h that anyone’s satisfaction or profit can
where no single
g other(s) worse off.
al conditions, a competitive economy attains allocative efficiency. This
in
market, they buy that amount for which the marginal utility just equals the price. (b)
ly goods where the marginal cost is
The analysis of competitive markets shed
society. Productive and allocative efficiency occur when there is no way of
recognizing production and distribution suc
be improved without hurting others. A different way of defining efficiency (in
production and consumption) is to say that it is a situation
individual/firm is made better off without makin
Under ide
occurs because of three step conditions: (a) First, when consumers buy goods
Secondly, competitive producers choose to supp
just equal to price. (c) Since, PMU = and PMC = , it follows that
u
5.7
I. Discu
MCMU = .
Thus, the social cost of producing a good under competition just equals its marginal
tility.
REVIEW QUESTIONS
ssion Questions
hy a competitive firm is a price taker?
1. W
2. What is the difference between market period (momentary run) and short run?
e
) It is only the excess profits that are wiped out by
competition. Managers get paid for their work; owners get a normal return on capital
in compet ive lo ru
ct competition?
3. What is the profit maximizing (or loss minimizing) condition of a competitive firm?
4. Does a firm is in its short run equilibrium necessarily mean that the firm enjoys
xcess profit?
5. Interpret this dialogue. A) “How can competitive profits be zero in the long run?
Who will work for nothing?” B
it ng n equilibrium – no more, no less.”
6. Under what condition should perfectly competitive firm supply goods at a loss?
7. What are the three conditions for the efficiency of perfe
189
II. Workout Questions
1. Suppose the market price a competitive firm faces in the short-run is Birr 10.
Moreover, its fixed cost is Birr 40. The output level (Q ) and the correspon ingd
) are as given in the table be
Q 0 5 10 15 20 25 30 35 40 45 50
variable costs (TV low. C
VC 0 30 60 80 120 170 225 287 340 410 520
(A) Compute the oss of the firm at each
results in a tab
(B) What will be the short run equilibrium output?
oach
) and
interpret the implication of the lowest point from which the supply curve
he increase in output
following the entry of the new firms has also dampened market price from Birr 10 to
n equilibrium output of a firm and the industry?
rofit do firms in th of the
profit?
(C) Derive the short run and long run supply curves of the industry.
3.
that follow.
TR, MR, TC, ATC, AVC, and profit or l
level of production and present the le similar to Table 5.1.
(C) Show the short run equilibrium and profit levels graphically using the marginal
appr
(D) Derive the short run supply curve of the firm from your graph in (C
begins.
(E) Calculate the producer’s surplus at the equilibrium.
(F) Calculate the elasticity of demand at the equilibrium price and output.
2. Suppose there were 80 identical firms operating in the industry in the short run.
Price was Birr 10. Further assume that the short run profit the existing competitive
firms enjoy attracts 80 more firms to enter the industry. T
Birr 8.
(A) What will be the long ru
(B) How much p e industry enjoy? What is the implication
(D) What happens to the consumers’ surplus?
Suppose the short run market price a competitive firm faces is Birr 9 and the total
cost of the firm is: 202.0200 QQTC ++= . Answer the questions
190
(A) Calculate the short run equilibrium output and profit of the firm.
(B) Derive the MC, ATC, and AVC and calculate the values at the short run
equilibrium output.
(C) Calculate the producers’ surplus at the equilibrium output.
(D) Find the output level that will make the profit of the firm zero.
191
CHAPTER SIX
PURE MONOPOLY
LESS
istic Features of Pure Monopoly
.4 Origins of Monopoly Power
arket structure in which there is only one supplier in the market
ince there is only one firm in the market, the demand and supply curves of a
onopoly are also the industry demand and supply curves.
hen there is only one firm in the market, the firm is unlikely to take the market price as
onopolist would recognize its influence over the market price and
nd output that will maximize its overall profit. Of course, a
rm cannot choose price and output independently. Because, for any price, the
onopoly will sell only what the market will bear. If it chooses high price, consumers
ers will
constrain the monopolist’s choice of price and quantity.
ON STRUCTURE
6.1 Introduction
6.2 Chapter Objectives
6.3 The Character
6
6.5 The Short Run Equilibrium of a Pure Monopolist
6.6 The Long Run Equilibrium of a Pure Monopolist
6.7 Price Discrimination
6.8 A Multi-Plant Monopolist
6.9 The Social Cost of Monopoly
6.10 Lesson Summary
6.11 Review Questions
6.1 INTRODUCTION
Monopoly is a m
(industry). S
m
W
given. Instead, the m
choose that level of price a
monopoly fi
m
will demand small quantity. In other words, the demand behavior of consum
192
6.2 CHAPTER OBJECTIVES
fter learning this chapter, you will be able to:
he main features characterizing pure monopoly are:
arrier
A
compare and contrast a purely monopolistic market to that of perfect competition;
identify the sources of monopoly power;
examine the equilibrium conditions for a single plant and multi-plant monopolist;
examine price discriminations applied by monopoly firms; and,
figure out the social cost of monopoly power.
6.3 THE CHARACTERISTIC FEATURES OF PURE MONOPOLY
T
1. The existence of a single seller and many buyers in the market.
2. The product or service of a monopolist is unique or does not have close
substitutes.
3. A monopolist is a price-maker for its product/service.
4. Entry to and exit out of the market are difficult (if not impossible). This is because
since the fixed cost (for potential entrants) will be larger while the marginal and
average costs for the existing monopolist will be smaller, this serves as a b
for new entrants. Such a situation is referred to as natural monopoly. Some other
sources of monopoly power will be discussed in Section 6.4.
As a result of these features, price will be higher and output will be lower than
competitive market. Moreover, a monopolist operates at a point where )( ARP = is greater
than MC . This is regarded as the inefficiency of monopoly in terms of resource allocation
and maximizing social welfare. The price of a monopolist is derived from the profit
maximization equation as follows.
TCTR −=π
TCPQ −= ------------------------------------------------------- (1)
The equilibrium of a monopoly is MCMR = which is similar to the equilibrium condition
of perfectly competitive market discussed in Chapter Five.
193
We know thatdQ
dTCMC = . And, MR is derived as follows:
dQ
dPQdQdTRMR == ---------------------------------------------- (2)
Since monopoly price is not constant as in the case of perfectly competitive market, price
cannot be equal to MR for a monopolist. Using the product rule of differentiation
the MR is:
dQ
QdPPdQ
QdPdQ
PdQMR +=+= ------------------------------- (3)
Alternatively, equation (3) can also be written as:
⎥⎤
⎢⎡+=
QdPPMR 1 --------------------------------------------- (4) ⎦⎣ PdQ
ecall that the price elasticity of demandPdQQdPR
QdPPdQ
P .)( =ε . Hence, the expression in
equation (4) is the reciprocal of price elasticity of demand. Thus, the above equation can
be written as:
⎥⎦
⎤⎢⎣
⎡+=
P
PMRε11 ------------------------------------------------ (5)
In equation (P
Lε1
=5), the one in the right hand side of the bracket, i.e., is known as the
rice elasticity of demand
e greater the monopoly power to increase price, and vice-versa.
Lerner Index, which measures the degree of the monopoly power. The formula indicates
that monopoly power is the reciprocal of the price elasticity of demand. Or, it implies that
the extent to which the monopolist can influence the price of its product depends upon
the elasticity of demand for its product. That is, the lower the p
th
194
Since the price elasticity of demand for normal goods is always negative12, equation (5)
can also be written as:
⎥⎦
⎢⎣ //1
P
PMRε
-------------------------------------------- (6)
The above equation will be us opolist’s price, it
⎤⎡−=
1
s MRed to obtain either the mon , or its
rice elasticity of demand (p pε ) when any two of the three variables are known. You
should note that, this form more relevant than the usual ula is ⎥⎦
⎤⎡∆ PQ⎢⎣ ∆ QP
. in terms of
yielding accurate Pε value for the monopolist’s product unlike when discrete price and
onopolist are given.
inally, the equilibrium condition of a monopoly,
output values of a m
MCMR = , is given by: F
MCPP
=⎥⎦
⎤⎢⎣
⎡−
//11ε
-------------------------------------------- (7)
We can also use the elasticity formula to express the optimal pricing policy of a
monopolist. The optimal price of a monopolist is:
⎥⎦
⎤⎢⎣
⎡−
=
//11P
MCP
ε
----------------------------------------------- (8)
Equation (8) indicates that the market price of a monopolist is a markup over its marginal
cost; where the amount of the markup also depends on the elasticity of demand. The
markup is:
⎥⎦
⎤⎢⎣
⎡−
//11Pε
---------------------------------------------------- (9)
1
12 Recall th y of demand for normal goods is always negative due to the law of demand,
which postulates an inverse relationship between price and quantity demanded. Moreover, since the
importance of elasticity is to understand the magnitude of responsiveness of consumers to changes in
at the price elasticit
price, it is conventional to use absolute value in order to make it a positive value.
195
Since a monopolist will always operate where the elasticity of demand for its product is
elastic due to barriers to entry, we know that // Pε is greater than unity. Hence, the
markup is also greater than one. That is, since ,1// >Pε .1//
1<
pε It follows that
//11
pε− – the denominator of equation (9) – is between zero and one. Finally, 1 divided
by a number between 0 and 1 (for instance, 0.5) is greater than one.
6.4 ORIGINS OF MONOPOLY POWER
T origin of monopoly power. There are barriers to
entry and exit. The four types of barriers are:
low cost production or technology;
3. contr l egic raw mat nd
4. Government may grant a firm an exclusive right to serve the market for a
particu r e
1) The Minimum Efficiency Scale (MES):
MES refers to the level of output that minimizes average cost relative to the market size
or m
The shape of ATC or MES, which is determined by the technology of production, is an
impo a m ively or
onopolistically. If the MES of a technology is very small it means that the technology
capacities but facing similar market size in two separate markets/areas are depicted.
here are several factors that lead to the
1. The minimum efficiency scale (MES);
2. Exclusive (special) knowledge of
A o over strat erials; a
la product or s rvice.
arket demand.
rtant factor that determines whether arket will operate competit
m
of production is cheaper. Hence, the smaller the MES relative to the size of the market,
the easier will it be for other firms to enter into the market and hence we might expect
that competitive condition will prevail and vice versa. Consider the following graphs
where the ATC curves and the demand curves of two monopolists with different
196
A Monopolist with Small MES A Monopoly with Large MES
Figure 6.1: Comparison of MES under Pure Monopoly
list in
arket. Therefore, we would expect that the first market might operate as a
ountry.
P
P* P*
O MES QM Q O MES QM Q
ATCATC
MC MC
P
In the first graph of Figure 6.1, there is a room for other firms to enter into the market,
each charging a price close to P* and operating at a relatively small scale since the MES
is less than the market demand, QM. In the second graph, only one firm can make positive
profit and the firm will be a monopolist. This is because, the incumbent firm (or the firm
already in the market) in the latter case has enough cost advantage to be able to
discourage other firms from entering into the industry as compared to the monopo
the first m
competitive market and the second would operate as a monopolist.
Technology may be such expensive that relatively large firms can invest and produce at a
lower cost. Another reason is, the size of the market may not allow the existence of more
than a single large plant size monopoly. Once a monopoly power is established entry will
be difficult because any new entrant must be able to produce at a relatively low cost
compared to the already established monopoly. This is likely to result in loss for these
potential firms, as it likely corresponds to a price level below the shut-down price.
Examples include electricity, telecommunication, and other utilities in our c
197
Macroeconomic policy of a country can influence the size of the market. If a country
ternational
s, people would prefer to travel through other countries Airlines or Airways and
hence EAL wo
Conversely, if a country fo s res e tra olicy se protect domestic
firms fro petitors so that the m e i d to t citiz ts own
country, then m sti es re likely to take hold.
Hence, ono ris o E ve ma iz is not
feasible ncre si m an er thr om firms,
then the ustry is liab e of ion ove i on. In
practice th r on op w ov nt intervention are costly.
Thus, from on should be weather th
In developing countries, the deadweight
Exclusive (special) knowledge of low cost production or technology:
m may develop or invent a unique product or technique of production and steps to
being copied by competitors by having patent right or copy right. Thus,
ill give a firm an exclusive right to produce a certain
follows non-restrictive foreign trade policy, domestic firms may face competition from
foreign firms and hence the domestic firms’ power to influence price will be much less. A
good example is the competition the Ethiopian Airlines (EAL) faces from foreign
Airlines (Airways) in international flights or transporting citizens and foreigners to the
outside world. The implication is that if the EAL sets higher fares for in
flight
uld lose its market share.
llow trictiv de p in the nse to
m foreign com arket siz s limite he ens of i
onopoli c practic are mo
if m poly a es due t large M S relati to the rket s e and it
to i ase the ze of the arket d/or if th e is no eat fr foreign
ind le to som form regulat or g rnment nterventi
, bo egulati of mon oly po er and g ernme
society point of view, the questi e deadweight loss of
monopoly exceeds the cost of regulation or not.
loss of monopoly is greater than the cost of regulation. Therefore, in most developing
countries, public provision of essential public services and utilities for development is
preferred to leaving them in the hand of monopolists.
2) A control over strategic raw materials:
If a firm has exclusive control over a given raw material, the firm can become a
monopoly.
3)
A fir
keep this from
patent right or copy right w
198
commodity or to use a certain production technology and as a result the firm becomes a
monopolist established due to the above factors, will have enough cost advantage to be
ble to discourage other firms from entering into the industry. The incumbent firm (or the
ive right to serve the market for a
particular product or service:
u h en by the government to serve solely a given
r ical area within its jurisdiction is called franchise. The best example
a is the National Lottery.
monopoly.
A
a
firm already in the market) may also, under certain conditions, threaten potential entrants
that it will cut prices if they attempt to enter into the industry.
4) Government may grant a firm an exclus
A monopoly established d e to t e right giv
market or geog aph
of such a monopoly in Ethiopi
Check Your Progress
e differences between a perfectly competitive firm and a pure
t?
power.
n MC, AVC, and ATC are all U-shaped while AFC
hyperbola. Wide U-shape of ATC, as in the case of the monopolist in the second
Unlike perfectly competitive market, however, a unique supply curve cannot be derived
from th curve of a monopolist. This is because since entry to and exit from the
a
of AMC = t monopo price will be equal or below the
1. What are th
monopolis
2. Discuss the different sources of monopoly
6.5 SHORT RUN EQUILIBRIUM OF A PURE MONOPOLIST
The short run cost functions confronting a monopolist are identical with those faced by a
competitive firm. That is, the short ru
is
market in Figure 6.1, implies that the capacity of the plant installed is very high.
e MC
market is difficult, the price of monopolist cannot reach the minimum point
)( VCorAVC . The probability tha ly,
199
minimum of AVC depends on the strategy o the incumbent monopolist to discourage
potential entrants by reducing its price.
f
As mentioned under Section 6.3, the profit maximization rule is the same in both perfect
competition and monopoly markets. Accordingly, a monopolist will choose to produce
in order to maximize profit. Moreover, price is equal to
enue (
MCMR =output level for which
ARP =average rev ) in both markets. Nevertheless, the marginal revenue of a
monopolist at any unit of output/production is always less than its price ( PMR < ) unlike
that of price-taker competitive firms where marginal revenue is equal to the ongoing
market price ( PMR = ).
In order to understand the short run equilibrium price and output of a monopolist it is
portant to derive the relationship between demand, price, and average and marginal
rves. The relationship can be best explained mathematically. To this end,
l mal
goods. e demand function for normal goods is
ing. If we as me a linear demand function (for simplicity), we would
unction of the form:
im
revenue cu
recal that there is an inverse relationship between price and quantity demand for nor
This law of demand implies that th
downward slop su
;PQ βα −= where alpha )(α and beta )(βhave a demand f are
ers. From this demand function, the following important points and
o the demand function:
constant numb
relationships can be derived:
β−=dPdQ 1) The slope f
QP
QP
dPdQ
P .. βε −== 2) The price elasticity of demand:
.PQPQ βαβα −=−⇒−=3) The invers de emand function: Rearranging this gives:
QPββ
α 1−= , setting ba ==
ββα 1; we get
. From this is the vertical intercept and bQaP −= a b− is the slope.
.= 4) Total revenue: QR PT
QbQaTR )( −= 2bQaQTR −=
200
PbQaQ
bQaQQTRAR =−=
−==
2
5) Average revenue:
6) Mar inal revenueg : bQadTRMR 2−== ; where a is the vertical intdQ
ercept (the level
of MR when output is equal to zero) and b2− is the slope of the MR curve.
MR13
From equation (6) above, it is also clear that the of a monopolist is a downward
sloping straight line with the same vertical intercept as the price equation or inverse
demand function but with a slope which is tw e steeper. That is, the slope of the price
and that of the MR in equation (6) is
ic
equation in equation (3) is b− b2− . Furthermore,
elasticity of demand will b unitary and that of the will be at its maximum
when [See Figure 6.2].
Figure 6.2: The Relationship among Demand,
e TR
.0=MR
pε , MR, and TR under Monopoly
You should also note that a monopolist would always operate in the short run in the
gion ty of demand in elastic. This implies that a monopolist will
ake elasticity of demand inelastic (
re where the price elastici
not set a price that will m 1// <Pε ) (i.e., below *P in
deterring potential firms from entering into
e market (by reducing price below
the above figure), unless it has a strategy of
th *P ). The reason is that the MR of a monopolist (the Note that the values of price and MR in equations (3) and (6) corresponding to give the vertical intercept equal to , and this is the only point at which P = MR for a pure monopolist.
13 ,0=Q a
P* 1// =pε
DD
TRp 1// >ε
1// <pε
MR=0 Q
P, , TR MR
201
additional revenue accrued to the monopolist due to sale of an additional unit of output)
ill be negative when the price elasticity of demand is less than one (or inelastic).
ith the short run profit maximization condition of a monopoly firm at hand, we can
price and output as well as the profit of a
onopolist. To do so, we need to have information on either (1) a serious of output sold
uantity demanded for its product) and price per unit of output (or in short unit price)
harged by a monopolist of our concern or (2) the market demand function it faces for its
roduct and its total cost function, representing the plant capacity installed, to meet the
urrent and future demand. The main procedures one should follow in order to determine
e monopolist’s short run equilibrium price, output, and profit depending on the type of
formation provided are illustrated using two examples for normal goods.
xample 1: Suppose we have information only about the amount of output supplied by a
t
d
run e list as well as its profit associated to each
am
w
W
now determine the short run equilibrium
m
(q
c
p
c
th
in
E
hypothetical ABC monopolist and the unit price consumers are charged per outpu
emanded (as shown in columns 1 and 2 of Table 6.1). Having this information, the short
quilibrium output and price of the monopo
ount of output sold are determined as shown in the same table (Table 6.1).
Table 6.1: The Short Run Equilibrium of a Monopolist
Qd Price(P) TR MR TC ATC MC Profit
5 24.80 124.00 - 214.50 42.90 - -90.50
13 23.20 301.60 22.20 228.90 17.61 1.80 72.70
23 21.20 487.60 18.60 264.90 11.52 3.60 222.70
36 18.60 669.60 14.00 341.60 9.49 5.90 328.00
50 15.80 790.00 8.60 462.00 9.24 8.60 328.00
60 13.80 828.00 3.80 572.00 9.53 11.00 256.00
66 12.60 831.60 0.60 647.46 9.81 12.58 184.14
72 11.40 820.80 -0.18 730.40 10.14 13.82 90.40
202
From the table above, the maximum profit is 328. The monopolist achieves this profit
when the demand for its product is either 36 or 50 units. Despite this, the monopolist will
pply 50 units of output in stead of 36 since the short run profit maximization condition su
or the equality of its marginal revenue and marginal cost ( 6.8== MCMR ) holds only at
this output level. Accordingly, the short run equilibrium price is Birr 15.8. Furthermore,
the equilibrium output, price, and profit of the monopolist can be depicted graphically
using the marginal approach as follows.
After determining price, the rginal revenue and marginal cost of the monopolist, we
can also calculate the price el icity o and g eq (6) of Section 6.3. That is,
price elasticity of demand is culated llow
E
15.8 9.24
50 Q
ATC
MC
P, MC, ATC Profit
8.60
ma
ast f dem usin uation
cal as fo s:
⎥⎦
⎤⎢⎣
⎡−=
//11P
PMRε
.
Substituting the values of MR and P , we get:
⎥⎦/⎤⎡
−=118.156.8Pε
.
ing es:
⎢⎣ /
Rearrang this giv ].// Pε18.8 //[ P156. ε −
=
// ε
8.15//8.5 P1
P
6.8 ε −=⇒
8.15//8.15//6.8 −=⇒ PP εε
8.15//8.15//6.8 −=−⇒ PP εε
203
.8.15//2.7 −=−⇒ Pε
Finally, we get the price elasticity of demand:
.2.2419.22.78.15//
.≈=
−−
=Pε
This implies that the price elasticity of demand for the product of this hypothetical
monopoly is elastic. The value can be interpreted as: As a result of one percent increase
the price of the monopolist’s product, consumers will decrease their consumption by
in
about 2.2 percent, and vice-versa14.
As mentioned earlier, we also know that the monopolist’s price is always greater than the
MC of producing an additional unit of output. The issue is thus to know by how much the
price of the monopolist is markup over its MC ? The markup can be determined using
equation (9) of Section 6.3 as follows:
=
⎥⎦
⎤⎢⎣
⎡−
=
//11
1
P
Markup
ε ⎥⎦⎢⎣ 419.2
=
⎥⎤
⎢⎡− .
11
1
⎥⎥⎤
⎢⎡ −
.1419.2
1
⎦⎢⎣
.419.2
=
⎥⎥⎤
⎢⎡ .
419.1
1
⎦⎢⎣
.419.2
= 84.11=
544303798.0
price, and profit of the mo
Example 2: Unlike the above example, suppose that we now have information only about
the market demand function a hypothetical XYZ monopolist faces for its product and its
total cost function. Suppose the demand and cost functions are PQ 5.060 −= and 2348 QTC += , respectively. The steps involved in order to obtain the short run output,
nopolist are given below.
Solution:
(A) The steps involved to find the short run equilibrium output and price levels are:
14 Note that the accuracy of this value of // Pε can be verified by substituting this value into equation (6)
to obtain or into equation ai 6.8=MR (7) to obt n 6.8=MC .
204
1st: Find the inverse demand function.
PQ 5.060 −=
PQ 5.060 −=−⇒
QQP 21205.05.0
60−=−=⇒
2nd: Find TR.
3rd: Find MR.
PQTR = 22120)2120( QQQQTR −=−=
QdQdTRMR 4120 −==
4th: Find MC.
QdQ
QddQ
dTCMC 6)348( 2
=+
==
5th: Equate MR to
.
6th: Substitute into the inverse demand function to obtain price.
.MC
QQ 64120 =−⇒
QQ 46120 +=⇒
Q10120 =⇒
1=⇒ Q 2
12=Q
P 96)12(21202120 =−=−= Q
and price of the monopolist are 12 and 96
respectively.
) The profit of the monopolist is calculated as:
Therefore, the short run equilibrium output
(B
TCTR −=π
]348[]2120[ 22 QQQ +−−=π .
Substitutin , we get:
+−−=π
g 12=Q
])12(348[])12(2)12(120[ 22
)]144(348[)]144(21440[ +−−=
205
]43248[)]2881440[ +−−=
.7724801152 =−=
(C) In order to show the equilibrium price, output, and profit graphically we need to
follow the following steps.
1st: Find the value of MR and t th ilibr utput, 12=QMC a e equ ium o
QdQdTRMR 4 Q120= −=
dQ=
dTCMC 6=
)12120 72(4 =−=MR 72)12(6 ==M
2nd: Find at Q
C
ATC 12=
QTCATC
23+== 48
.4012480
1243248
12)12(348 2
==+
=+
=ATC
3rd : Graphic solution:
E
96
40
72
12 30 Q
ATCMC
P, MR, MC, ATC
206
Check Your Progress
On the basis on the information given in Example 2 above, answer the questions below.
1. Calculate the price elast and and the markup at the short run equilibrium
o and price of the YZ
2. W price elasticity of demand when MR is 40 and price is
80?
akes the MR zero? What will be the price level and TR at
is output level? How about the elasticity of demand?
6.6 THE LONG RUN EQUILIBRIUM OF A PURE MONOPOLIST
g run, the monopolist wil its plant size or to use the
l nt optimally to produce output that will maximize profit. Hence, if the
opolist earns excess profit in the short run with the existing plant(s), it must
determine weather a plant of different size will earn larger profit in the long run or not.
Since entry is blocked, it is not necessary or a must for a monopolist to operate at optimal
othe ords, the is nothing that induces to install additional plant size so as to
t inimum of LAC (where LAC will be equal to the LMC) and obtain
LMC is the chang in tot sociat d with the change in output when all factors
nt size itself is changed (in the long run). To
understand how the long run m C) and long run average cost (LAC)
e that a monopolist has installed two plant sizes in the short run in order to
meet the current and future demand for its product. Furthermore, assume that the change
anded t a change in price is constant. Given the relevant information in
2 elow, Table 6.3 helps us compute the LMC and LAC.
icity of dem
utput monopolist X .
hat will be the value of the
3. What level of output m
th
In the lon l have time to expand
existing p a
mon
scale. In r w re
operate a the m
normal profit if not its own strategy.
The e al cost as e
including the plant scale vary or when the pla
arginal cost (LM
behave, assum
in quantity dem o
Table 6. b
207
208
Table 6.2: Information for Deriving LMC
Q MR TC1 TC2
0 -
1 34.5 11 14.25
2 33.5 14 15.00
3 32.5 1 9 16.25
4 31.5 26 18.00
Table 6.3: Determination of the LMC from Short Run and Long Run Plants
Q P TC2 SAC1 SAC2 SMC1 SMC2 LMC LAC ProfitTR MR TC1
1 34.5 34.5 - 11.00 14.25 11.00 14.25 - - - 11.00 23.5
2 5 34.0 68.0 33. 14.00 15.00 7.00 7.25 3 0.75 3 7.00 54.0
3 33.5 100.5 32.5 32.50 16.25 6.33 5.42 5 1.25 2.25 5.42 84.25
4 33.0 132.0 31.5 31.50 18.00 6.50 4.50 7 1.75 1.75 4.50 114.0
The problem of the monopolist is which of the two plants should be used in the short and
ng run in order to maximize profit. If the monopolist wants to produce only one unit of
ut.
ut for
diffe
and olumn of the third row of
Table 6.3, this will be equal to 2.25, which is TC2 (16.25) less TC1 (14). Furthermore,
lo
output in the long run, then the best choice would be to use plant one. This is
because 21 SACSAC < or 21 TCTC < . If the monopolist wants to produce two units of
output, it should also choose to use the first plant. Since the first plant is chosen to
produce the first and second units, the SMC of the first plant will also be the LMC up to
the second unit of outp
However, the monopolist has to choose plant 2 if it wants to produce 3 units of outp
12 SACSAC < or 12 TCTC < . In this case, the LMC of the monopolist will be the
rence between the total costs of a plant chosen to produce 3 units output (plant 2)
2 units of output (plant 1). As indicated in the eleventh c
208
since the plant 2 is the one to be chosen to produce 4 units of output, the LMC will be
(the SMC of the plant 2). 1.75
who
poin C = The corresponding unit price is P4.
It is thus clear from Figure 6.3 that the monopolist’s point of optimal operation is on the
f
e ewpoint of the society for the monopolist
is not operating at the minimum point of the LAC (envelop) curve. This is because
producing 5 units at point
i
e and implying a normal
(zero) profit. This implies that since there is output restriction or since the monopoly firm
d
l
D
onopolist may prefer to produce at point E3 only if there are firms
p
As indicated in Figure 6.3, the optimal plant of the monopolist in the long run is plant 2
se 2SAC is tangent to the LAC curve and the long run equilibrium is established at
t 2E where SMMR = .2 LMC
alling part of LAC. To the contrary, producing 4 units of output in the long run (or
quilibrium point E ) is not optimal from the vi2
3E where the LAC is at its minimum and where
pSMCLMCLAC === 2 (similar to the case of a competitive firm in the long run) will
ncrease the output of the monopolist and reduce selling price thereby eliminating the
xcess profit that could be enjoyed by producing 4 units of output
oes not produce at its full capacity, price is greater than MC in pure monopoly in the
ong run. This situation, which arises due to restriction of output, is called the
eadweight Loss (DWL) of pure monopoly. This will be discussed in detail under a latter
section.
Nevertheless, the m
lanning to enter into the market and hence the monopolist wants to discourage them or
block entry by reducing price.
209
SAC1
E1
E3
E
ow, we can obtain the monopolist’s price if the
and is given for any level of output. Once the monopolist’s price is
ine the total revenue and the associated profit (or loss) for
ow, we can obtain the monopolist’s price if the
and is given for any level of output. Once the monopolist’s price is
ine the total revenue and the associated profit (or loss) for
2
E
Given the information in the table bel
Given the information in the table bel
price elasticity of demprice elasticity of dem
known, we can also determknown, we can also determ
both the short run and long run. both the short run and long run.
Q MR TC1 TC2
1
E3
E2
Q MR TC1 TC2
0 - - -
1 18 12 17.5
2 12.5 22.8 23.8
3 4 30 26.7
4 3.6 45 30.3
For example, let us calculate the price and short and long run profit (or loss) of the
monopolist if the price elasticity of demand of producing 4 units of output is.6.1 .
SMC2
DD
P1 P2 P3 P4
1 2 3 4 5 Q
LAC
LMCSAC2
MR
SMC1
Figure 6.3: The Long Run Equilibrium of a Pure Monopolist
210
Solution:
1st: Find the unit price of the monopolist when selling 4 units of output .
)( 4P
)//
11(44P
PMRε
−=
)6.1
11(6.3 .4 −= P
)625.01(6.3 −= P 4
P=
)375.0(6.3 4
6.9375.06.3
4
4
=
=
P
P.
2nd: Find the profit of the monopolist when selling 4 units of output. Since, plant 2 is used
to produce 4 units of output we should consider the total cost15 of the second plant to
calculate profit )( 4π .
4244 QQ TCTR −= π )( 42444 QSACPQ −=π
3.304 −= PQπ OR )4
3.306.9(44 −=π
4
==
π 1.83.304.383.30)4(6.9
4
π=−
− 1.8)025.2(44 ==π
3 : Find ,, 23 PP and 1P sequentially
rd
34
3344
34
344 QQ
QPQPQQTRTRMR
−−
=−−
=
34
)3(4.386.3 3−=
P −
)3(1.386.3 3P−=
335.34 P−=−
5.113
5.34==P
3
15 The subscript at the end of the total cost indicates the plant used.
211
2
22332 QPQPTRMR
−==
323
33 QQQQ
TR−−
−
23)2()3(5.114 2
−−
=P
)2(5.344 P−= 2
225.344 P−=−
25.152
5.302 ==P
12
1122
12
122 QQ
QPQPQQTRTRMR
−−− =
−=
12
)1()2(25.155.12 1
−−
=P
15.305.12 P−=−
4 t used to produce each level of
output.
181 =P th: Find profit by considering the total cost of a plan
3233 QQ TCTR −=π
7.26−= PQ3π
8.77.26)3(5.113 = =−π
QTCTR −= 22 Q 21π
5.122 −= PQπ
7.78.22)2(25.152 =−=π
1111 QQ TCTR −=π
121 −= PQπ
612)1(181 =−=π
Ther the ab ve profit figures we can conclude that the short run equilibrium
level of output of the monopolist is 2 units for it yi
efore, from o
elds higher profit as compared to
producing and selling one unit of output (7.7 > 6). In the long run, however, as the profit
212
le ng
an roduce and sell 4
u
vel from producing and selling 4 units of output (8.1) is greater than that of produci
d selling any other level of output (1, or 2, or 3), the monopolist will p
nits of output and thus operates at a point where .6.32 === LMCSMCMR
Check Your Progress
economic profit in the long run? Why or
ndition (rule) of a monopolist the same as the
short run one?
E DISC INATION
ition and ecessary Conditions
iscrimination is the practice of selling a certain product or service of a given
s to different consumers for reasons unrelated to costs. It involves
in diffe nt prices for the same or different quantities of a given quality of a
ers, and/or in different markets based on
t ity of demand.
scrimination is workable when the following three conditions are realized:
power: or at least possess some degree of
opoly power over the commodity or service. That is, it must have some ability to
control the production of the good or service and its price.
ller must be able to segregate buyers into separate classes
li gness or ability to pay for the product or
buyers is based on the difference in elasticity of demand.
st must be able to separate (or segment) the two or more
markets and keep them separate so that it is impossible for one buyer to resale the
1. Can a pure monopolist earn a positive
why not? Discuss.
2. Is the long run profit-maximizing co
6.7 PRIC RIM
6.7.1 Defin N
Price d
quality at different price
charg g re
product or service to different class of buy
elas ic
Price di
(A) Monopoly The seller must be a monopolist
mon
(B) Market segregation: The se
where each group has a different wil n
service. This segregation of
(C) No resale: The monopoli
product to another.
213
6.7.2 Types of Price Discrimination
nsider three types of price discriminations. These are: first,
ird degree price discriminations.
egree (perfec price discrimination: This means that the monopolist sells
t at different prices and prices may differ from person to person.
e ns th t the m opolist sells each unit of output to that individual who values it
lling to pay for it. This turns out that
ut.
ce discrimination monopolist must produce an
al s
Economists usually co
second, and th
First d t)
different units of outpu
This m a a on
most highly at the maximum price that he/she is wi
perfect price discrimination produces an efficient level of outp
To prove this, note that a perfectly pri
t )( MCP =output level where price is equal to the margin co . If price is grater than
n it would mean that there is someone who is willing to pay more than what
to n unit of output; so, why not produce that extra unit and sell to
o
on is an idealized concept as the word “perfect”
ency, we refer to the situation where all the
aking someone better off without making others worse off have already
out. There are few real life ex ples of perfect price discrimination. A
t fferent prices to his/her patients based on their ability
o pay f the closest examples of perfect price discrimination. Other examples
ntial prices to different classes or ranks of train
air transportation (the payment for economic and business
ople fly in the same airplane); cinema hall; football
atch etc. Fo ple, the prices can be differentiated as first class or rank ticket-Birr
watch a football match in a stadium; a
l through train.
the MC, the
it costs produce a extra
that pers n?
However, perfect price discriminati
might suggest. But it is interesting theoretically since it gives us an example of a
resource allocation mechanism (other than perfectly competitive market) where Pareto
efficiency is achieved. By Pareto effici
possibilities of m
been carried am
small own doctor who charges di
t is one o
include, the prevailing differe
transportation; international
class are different though two pe
m r exam
60, second rank-Birr 40; and third rank-Birr 30 to
movie in a cinema hall, or to trave
214
Second degree (non-linear) price discrimination: This means that a monopolist sells
; but every individual who buys the same
goods consumed or depending how much is bought but not across people like first
ost common examples of this type of price
ination are the practice of charging diffe ption at different
bands (blocks) and bulk discounts in public utilities.
or example, the price of electricity often depends on how much is consumed. Suppose
r charges consumers a progressive rate across bands say for the first
H each at a ice of 0.2730 cents; for the next 50 KWH each at 0.2921 cents; and
KWH each at 0.4508 cents. In this case, the payment/ bill of the household
who consumed 200 KWH a month is:
different units of output for different prices
amount of output pays the same price. In other words, price differs across the quantity of
degree price discrimination. The m
discrim rent prices for consum
F
an electricity supplie
50KW pr
the next 100
[ ])4508.0100()2921.050()2730.050( xxx ++= Bill
335.7308.45605.146.13 =++ =
The above example indicates that the price charged by the hypothetical electricity
hence the decision to consume more
er.
ed by such type of monopolist is
sive because price per u es as consumption increases from one block to
another. In this case, consumers who purchase large quantities of the monopolist’s
product or service may face a price equal to MC at some level of purchase.
, since there is consumption at a price greater than
MC (at least for some consumers), there are some ways to make som mers in the
market better off without making others worse off. That is, not all the possibilities to
supplier is progressive in a sense price per unit increases as consumption increases from
one band to another. That is, any output or service consumed within the next higher
consumption band will cost higher price and
depends on the willingness and ability to pay of the consum
Contrary to the example above, sometimes monopolists offer discounts for bulk
purchases, in most cases across blocks. The price charg
regres nit decreas
From the viewpoint of social welfare
e consu
215
maximize social welfare are exhausted. Hence, second degree (non-linear) price
discrimination is Pareto inefficient.
Third degree price discrimination: This occurs when a monopolist charges different
prices for the same commodity in different markets; but every unit of output sold in a
given market is sold at the same price. For this to happen markets must be kept separate
(no resale) and the elasticity of demand of these two or more markets must be different.
Third degree price discrimination is the most common form of price discrimination. An
example of charging different prices in different markets is found in international trade
when a nation sells its commodity abroad at a lower price than in its domestic market.
g the domestic
and less elastic.
price discrimination is: “How does a monopolist determine
trate this with an example, assume that a monopolist sells its product only in two
monopolist is:
This is referred to as dumping. The reason for dumping is that the demand for a
monopolist product is more elastic abroad because substitutes are available from other
nations whereas there can be import restriction in domestic market makin
dem
The key issue of third degree
the optimal price to charge in each market?” The answer is based on the
conditions/assumptions that consumers in each market are not able to resale the good in
another market, and that there are different elasticities of demand in the two (or more)
markets.
To illus
markets. Furthermore, let )( 11 qp and )( 22 qp be the inverse demand functions of market
1(domestic) and market 2 (abroad), respectively. In addition, let )( 21 qqc + be the cost of
producing the output. Thus, the profit maximization problem of the
Max )()()( 21222111 qqcqqpqq21,qq
p +−+ ---------------------------------------- (1)
The optimal solution m
qMR ------------- (2a)
– Equilibrium in market 2 ------------------------- (2b)
ust have:
)( qqMC += – Equilibrium in market 1 -------------)( 2111
)()( 2122 qqMCqMR +=
216
Equations 2a and 2b say that the MC of producing an additional unit of output must be
qual to the MR in each market. If the MR in market 1 exceeds MC, it pays to expand
utput sale in market 1 and vice versa. Using the standard elasticity of demand formula
r MR, we can write the profit maximization condition as:
e
o
fo
)(/)(/
11)( 211
11 qqMCq
qpP
+=⎥⎦
⎤⎢⎣
⎡−
ε
)(/)(/
11)( 212
22 qqMCq
qpP
+=⎥⎦
⎤⎢⎣
⎡−
ε
hese two conditions imply that: ⎥⎦
⎤⎢⎣
⎡−=
⎤⎡−
/)(/11)(11)(
2qqpqp
Pε T ⎥
⎦⎢⎣ /)(/ 22
111 qPε
⎥⎦
⎢⎣−
/)(/1
1
22
qPε
⎤⎡⎦⎣=⇒
1)()( 211
qpqp P ----
⎥⎤
⎢⎡−
11/)(/ qε
--------------------------------------------------------- (3)
If price in the first market is greater than price in the second market )( 21 pp > , then each
ust be greater than 1 and thus we must have: side of equation (3) m
⎥⎥⎦
⎤
⎢⎢⎣
⎡−<⎥
⎦
⎤⎢⎣
⎡−
)(/11
/)(/11
21 qq pP εε------------------------------------------------ (4)
his implies that,
T
)(/
11> -------------------------------------------------- (5
/)(/ 21 qq pP εε)
Therefore, /)(/)1q(/ pp 2qεε < ------------------ ------ ------ ---------- (6)
Equation (6) says that th lower elastic dem (price insensitive)
must have the higher pri ile t ce s e m wil lower price. The
validity of this argument i ate the of a rical example below.
Example: Supp e the d fun s a olis s in et 1 and market 2
are and pq pect Furthermore, assume that its cost
function is . With this information at hand let us:
------ ------ ------
e market with a ity of and
ce wh he pri ensitiv arket l have
s illustr d with help nume
os emand ction monop t face mark
1 1 55 pq −= 2 , res2 270 −= ively.
205 += QTC
217
1) determine pq h i pro he m olist;
2) calculate the profit of the mon t fro ling duct in the two markets;
3) determine price ities man e tw rkets; and
4) show the outputs and prices of the two m s us bac ack diagram
1q 2p t, and ,, 12 at maxim ze the fit of t onop
opolis m sel its pro
the elastic of de d in th o ma
arket ing the k-to-b
Solution:
From the given cost function, the common marginal cost is: 5==dQ
dTCMC .
1. Outputs and prices of the monopolist
(a) For market 1
1st: Find the inverse demand function.
: Find
11 55 pq −=
11 55 qp −=
2nd: Find 111 qpTR =
111 55(TR −= )
21155 qq −=
1
11 dq
dTRMR = 3rd
255 qMR −= 11
4th: Equate MR to MC.
MR MC=1
1 =q
1 −=q
555 − 2 2− 555
502 1 −=− q
252
501 =q
bstitute in the inverse demand function.
=−
(b) For market 2
=
5th: Su 251 =q
55 11 =−= qp 302555
218
1 : Findst the inverse demand function
p−
22 270 pq −=
70q =− 22 2
22
2 5.03522
70 q qp −=−=
2nd: Find TR.
3rd: Find MR.
222 qpTR = 222 )5.035( qqTR −=
=35q2-0.5q22
2
2dTR= 2 dq
MR
4th: Equate MR to MC.
5th: on.
2. The profit of the monopolist:
a et. Thus, total profit will be
= )( 21
22 35 qMR −=
M MCR =2
535 2 =− q
3552 −=− q
302 =q
Substitute 30=q in the inverse demand functi2
22 5.035 qp −=
)30(5.0352 −=p
=−=p 2015352
From the above solution the monopolist will sell 25 units of output in market 1 and 30 in
market 2. The price of a unit of output in market 1 is Birr 30 while it is Birr 20 in the
second m rk
TCTRTR −+π
[ ])205()( 2211 +−+= Qpqpq
Since 21 qqQ += the profit equation is also
219
[ ])20)(5()( 212211 ++−+= qqpqp qπ
[ ])20)3025(5()2030()3025( ++−+= xx
)20)55(5(600750 +−+=
20275(1350 +−=
3.
)
10552951350 =−=
Price elasticity of demand
Market 1
11 55 pq −=
Slope: 11
1 −=dpdq
1
1
1
11 //
qpx
dpdq
p =ε
25301// 1 xp −=ε
2.12 .125
// 1 −−=pε30
==
Market 2
22 270 qq −=
22
2 −=dpdq Slope:
2
222 // pxdq
p =ε 2 qdp
30202// 2 xp −=ε
33.133.13040//
.
2 =−=−=pε
220
The above result tells us that demand is more elastic in market 2 as compared to market
1. Therefore, as described in equation 4 to 6 earlier in this section, the monopolist charges
lower price in market 2 compared to market 1.
4. Back to back diagram
The relationship between output and prices in the two markets can be represented using
what is known as the Back to back diagram as follows.
o ive to price changes16.
P
q2q1
DD2MR2
DD1
MC = 5
P2=20
P1=30
MR1
q1 q2=30 =25
Market 1 Market 2
Figure 6.4: The Back to Back Diagram of Third Degree Price Discrimination
From the above figure, it is clear that the market with lower elasticity of demand
(market1) has higher price. This implies that the monopolist will charge high price in the
market in which quantity purchased is less resp ns
16 pp For further reading on this topic, see Koutsoyiannis, A. (1998). “Modern Microeconomics”. 2nd edition,
197.
221
6.8 A MULTI-PLANT MONOPOLIST
o far it has been assumed that a monopolist owns and produces by means of only one
stall more than one plant and
conditions may differ from one plant to another. Such a monopolist is called a
the allocation of production
plant 2 in the case of two plants).
opolist’s profit maximization rule is equating MR MC. However, we have only
e function and many marginal cost functions for a multi-plant
The marginal cost function of plant 1
Common or the multi-plant marginal cost function
commo
produce, and also find how much should be produced by each plant.
S
plant. Nevertheless, it is also possible for a monopolist to in
hence cost
multi-plant monopolist. The problem of such a monopolist is
among the different plants (say, between plant 1 and
The mon
one marginal revenu
monopolist. For the case of a monopolist with two plants, we have:
=1MC
=MC The marginal cost function of plant 2 2
=MC
The profit maximization rule of this multi-plant monopolist is depicted in Figure 6.5.
Example: Given the price and MC figures of two plants for each level of output,
determine the MR, the n MC, and the total output a multi-plant monopolist should
MR
MCMC1 MC2
DD
O q1 q2 Q O Q* = q1+q2 Q
Each Plant Multi-plant Figure 6.5: Short Run Equilibrium of a Multi-Plant Monopolist
222
Table 6.4: The Short Run Equilibrium of a Multi-Plant Monopolist
Q P MR MC1 MC2 MC
1 5.00 5.00 1.92 2.04 1.92
2 4.50 4.00 2.00 2.14 2.00
3 4.10 3.30 2.08 2.24 2.04
4 3.80 2.90 2.16 2.34 2.08
5 3.55 2.55 2.24 2.44 2.14
6 3.35 2.35 2.32 2.54 2.16
7 3.20 2.30 2.40 2.64 2.24
8 3.08 2.24 2.48 2.74 2.24
9 2.98 2.18 2.56 2.84 2.32
10 2.89 2.08 2.64 2.94 2.34
The common MC is obtained by arran ging the MC figures in ascending order. The profit
al to the common MC. Once the total
output to produce is determined, the monopolist will produce 5 units using plant 1 and 3
is maximized when MR = MC1 = MC2 = MC.
Mathematical Example:
maximizing level of output the multi-plant monopolist will produce is 8 units of output. It
is at this level of output that the MR will be equ
units using plant 2. This is because profit
Suppose a monopolist faces a linear demand function PQ 2200 −= for its product. Let, the
cost functions of the two plants be: 11 10qTC
= and 222 25.0 qTC = , respectively. Given the
above information, find 1q , 2q ,
P and the profit of the multi-plant monopolist.
223
Solu
1 : Find the inverse demand function, TR, and MR:
Inverse demand function
tion:
st
PQ 2200 −=
QP 5.0100 −= ;
here Q = q
W
PQ 2200 −=−
1 +q2
Total revenue
PQTR =
QQTR )5.0100( −=
25.0100 QQ
Marginal revenue
−=
dQ
MR =
Q−= 100
2
dTR
nd: Find the marginal cost of the two plants; 1MC and 2MC
10)10(
1
1
1
11 ===
dqqd
dqdTCMC
22
22
2
22 5.0)25.0( q
dqqd
dqdTCMC ===
3rd: Equate the MR to the two MCs ( 11MCMR = and 2MCMR = )
1MCMR =
10100 =−Q
10)2 =q
10100 21 =−− qq -------------------------------------------------------------
(100 1 +− q
(1)
2MCMR =
25.0100 qQ =−
221 5.0)(100 qqq =+−
224
------------------------------------------------------- (2)
tions in step 3 using simultaneous equation procedures to obtain
the output levels to be produced by each plant.
221 5.0100 qqq =−−
4th: Solve the two equa
⎩⎨⎧
−×=−−=−−
)1](5.0100[10100
221
21
qqqqq
⎨⎧
−=++−⇒ 21
5.010010100
qqqqq =−−
⎩ 221
05.010 2 =−⇒ q
205.02
10==⇒ q .
Substituting this output level into one of the two equations we found under step 3, we get the
utput that should be produced using plant 1. Let us substitut into the first
e
e 202 =qoptimal o
quation17.
10100 21 =−− qq
1020100 1 =−− q
80 − 101 =q
7010801 =−=q th l arket price by substituting 90702021 =+=+= qqQ5 : Calcu ate the m into the inverse
d one. emand function derived from the market demand in step
QP 5.0100 −=
)90(5.0100 −=P
5545100 =−=P
6th: Finally, calculate the profit of the multi-plant monopolist using the total revenue – total cost
approach. It can be calculated in two ways: either by substituting total output into the
to ining total revenue by multiplying price and total outpu as
)(Q
t )(Qtal revenue function or obta
follows:
)( 21 TCTCTR +−=π
17 Afte ether substituting them into both equations will satisfy the
equ xt step! r obtaining q1 and q2 you should check wh
ality. Do this before proceeding to the ne
225
0 221 qq +
2+−
50 +−
)25.01()5.0100( 2QQ −−=
])90(5.0)90(100[ 2−= ])20(25.0)70(10[
409000[ −= ]100700[]
[ ] 418004950 =−= 50
OR
)( TCTCPQ +− 21=π
221 qq +=
6.9 THE SOCIAL COST OF MONOPOLY
Is the existence of a monopolist evil? The answer to this question depends on the pricing
decision of the monopolist. If the monopolist charges a single price, the answer is
“YES”! If the monopolist charges different prices based on the willingness to pay (WTP)
[or if the monopolist sells each unit at the maximum price consumers are willing to pay],
i.e., if the monopolist can exercise the first degree price discrimination, the answer to the
above question would be “NO”! That is, a monopolist exercising the first degree price
discrimination produces a Pareto efficient outcome as it expands output to the level
where P = MC. If the monopolist exercises the second or the third degree price
discrimination (block pricing, bulk discount, market segregation based on differences in
price elasticity of dem e is Pareto inefficient though the inefficiency is
m onopolist charging a single price is evil; that of
a second or third degree price discriminator is less evil; and that of a first degree price
discriminator is consistent with social welfare maximization (just like a perfect
competitor).
e that a remarkable outcome of a perfectly competitive
market is an efficient resource allocation, which results in a maximum social welfare and
maximum employment. This is because the equilibrium of a competitive firm is at the
)25.010()9055( −×
])20(25.0)70(10[4950 2+−=
4150=
and), the outcom
inimal. To sum up, the existence of a m
We have seen in Chapter Fiv
226
equality of price and the MC of producing the good which implies that the marginal
utility of goods consumed is also equal to the price charged. Hence, if
cation efficiency) and
)(MU )( p
MCP = (i.e., allo PMU = (i.e., maximization of consumers’
welfare), then 18.
A t is through
using t nsumers’ surplus (CS) and producers’ surplus (PS).
Consu e difference between what consumers are willing to pay for
different levels of quantity demanded (proportional DD curve; see in the figure
below at they actually paid to consume amount of output (prorata DD
curve; see
the perceived DD curve and above the equilibrium price or (prorata DD curve) or simply
by area
willin ay a price higher than the equilibrium price or it is the savings of the
c
CS E CS E
Linear Demand and Supply Curves Non-Linear Demand and Supply Curves
PMCMU ==
n alternative way to understand the efficiency of the competitive marke
he concepts of co
mers’ surplus is th
PDD
)19 and wh EQ
ADD in the figure below). In Figure 6.6, it is shown by the area to the left of
1EPPE . In other words, it represents money not spent by consumers who have the
gness to p
onsumers from buying EQ at equilibrium price EP .
P1 P1
PS PS
D
18 ack to Chapter Two on how the equality of P = MU is derived based on the ordinalist argument.
perceived demand curve can be linear or non-linear. Because determining CS and PS from non-nowledge in integral calculus, which is discussion of consumers and producers
surpluses using linear demand and supply functions for the mathematical example in this section.
Refer b19 The
linear demand and supply functions requires some advanced kbeyond the scope of the course, we restrict ourselves to the
DDP
PEDDA
P
QE
MC=SS
QE
MC=SS
DDP
P
PE
227
Figure 6.6: Consumers’ Surplus and Producers’ Surplus
The MC of producing a good rep quating the MC or the supply
curve that passes through point E to demand (as in the above graphs) gives the producers’
surp m
pric
firms
different quantities of output). Put differently, it is the money that suppliers receive solely
beca
produce that unit. In Figure 6.6, it is shown by the area
These perfectly competitive market, the social cost of
onopoly arises due to the fact that a monopolist operates inefficiently as compared to
that price under monopol is greater than price
nder perfect competition or and the monopolist’s optimum level of
o
becau
resents the supply curve. E
lus (PS). Producers’ surplus is the area above the MC curve but below the equilibriu
e ( EP ). The PS indicates the difference between the market price (what competitive
arge per unit) and the MC (what competitive firms actually incur for producing ch
use of selling each unit of output (below QE) at a price above what they incur to
.EDPE
being the CS and PS in a
m
y )( MPperfect competition in the sense
)( CP CM PP >u
utput )( MQ is less than output under perfect competition )( CQ or CM QQ < . This is
se unlike the competitive firms that equate MCP = in order to determine
output and price, which in turn always makesequilibrium MRP = , a monopolist
mines its equilibrium output and price by equating MR MC= and hence its price is deter
gr
As a result, som
the m
surpl
(DWL)
eater than both marginal revenue and marginal cost.20
e part of the CS and PS in a perfectly competitive market are lost when
arket is monopolized by a single firm. These losses in consumers’ and producers’
uses due to monopoly power are known as the social cost or the Dead Weight Loss
of monopoly. Consider the graph below.
20 Note that P > MC implies that the value of the good measured in terms of market price is greater than the
social cost measured in terms of MC.
228
The a
comp se. As
th
area
that w by
A B EC
EM
Figure 6.7: The social Cost (Dead Weight Loss) of Monopoly
bove graph shows the change in the CS and PS when the market is changed from
etitive to monopoly or from monopoly to competitive. Consider the first ca
e market changes from perfect competition to monopoly, the CS goes down by
MCC APE [area CABE since they lose some surplus from the reduction in the units
ere used to be sold under perfect competition MC Q
P
Q − ; and area MC BAPP since
mers are now getting all the units they buy at a higher price]. Alternatively, we can
der what happens when a monopolist is replaced by a perfectly competitive firm. As
arket changes from monopoly to perfect competition, goes up by
MCC APE [area MC BAPP since consumers are now getting all the units they used to
nder mon poly at a lower price; and area CABE since they now gain some surplus
al units )( MC QQ − that are now sold in the market]. Let us continue our
ssion with the first approach – where a perfect competitor is replaced by a pure
consu
consi
the m the CS
area
buy u o
from the addition
discu
monopolist.
P
MC P F PM PC
DDC=MRC=MC
DDM
MRM
QM QC Q
D
229
The PS, on the other hand, goes up by area due to the higher price on the units
at were already being sold; and goes down by due to the loss from the decline
elling
MC BAPP
CM BEEth
)( MC QQ −in the level output as the firm is not s now.
ers to the monopolist, and hence one
de of t rket (the producer) is made better off while the other side (consumers) is
d
How BE and represent the Dead Weight Loss (DWL) due to
monopolist’s price than paying the completive price. The DWL due to monopoly like
at of the DWL due to tax increase measures the value of the lost output by valuing each
e that people are willing to pay for a unit. In other words, as
e move from competitive to monopoly output, the sum of the distance between the
lost
(are .
Clearly, an economy is performing well when it generates much to the consumer surplus
is s em.
Nu
ndency of moving from competitive to monopoly output. If the
emand and total cost functions are Q = 100 – 2P and TC = 14Q + 2Q2 respectively,
C. Calculate the CS and PS under competitive and monopoly market structures.
The area MC BAPP is just a transfer from the consum
si he ma
ma e worse off; but, the total surplus does not change as a result of this transfer.
ever, the areas A C CM BEE
monopoly behavior.
The DWL provides a measure of how much worse off people are paying the
th
unit of lost output at a pric
w
demand curve and the MC curve generates (gives) the value of the
output )( MC QQ − due to monopoly behavior. The total area between the two curves
a CM EAE ) is the DWL when moving from competitive to monopoly output
and an inefficient situation is one in which the maximum amount of consumers’ surplus
queezed out of the syst
merical Example:
Assume that there is a te
d
A. Determine PC, QC, PM, and QM.
B. Show the equilibrium Q and P you obtained in (A) above graphically.
230
D. Calculate the part of CS transferred to the monopolist due to inefficiency
monopoly
of
.
Solution
A. E
(i
50 –
36 = 4.5Q
Q
E. Calculate the social cost (net loss or DWL) of monopoly.
:
quilibrium Q and P:
) In perfectly competitive market:
P = MC
0.5Q = 14 + 4Q
50 – 14 = 4Q + 0.5Q
C = 8 PC 0 – 0.5Q OR PC = 14 + 4Q
– 0. )
= 5
= 50 5(8) = 14 + 4(8
= 50 – 4 = 14 + 32
PC = 46 PC = 46
(ii) In monopoly market:
TR = P.Q
= (50 – 0.5Q).Q
= 50Q – 0.5Q2
QTRR −=∂
= 50 Q∂
M
QTCMC 414 +=∂
= Q∂
Equate MR MC: MR = MC
50 – 14 = 4Q + Q
6
Q
to
50 – Q = 14 + 4Q
3 = 5Q
M = 36/5 = 7.2 PM
= 50 – 0.5(7.2)
= 50 – 0.5Q
231
= 50 – 3.6
PM = 46.4
B. Graphical presentation of the results under (A)
C.
i)
Consumers’ and producers’ surplus:
( Under perfect competition:
.16)8)(4(21
==⇒ CS
)8)(4650(21
−=CS
.128)8)(32(21
2
==⇒ PS
)8)(1446(1−=PS
( ii) Under monopoly:
.96.12)2.7)(6.3(
21
==⇒ CS
)2.7)(4.4650(2
−=CS
1
232
6.12992.2568.103
)2.7)(6.3()2.7)(8.28(21
)2.7)(8.424.46()2.7)(148.42(21PS −+−=
=+=
+=⇒ PS
⇒ PS
D The amount of surplus transferred from consumers to the monopolist: .
= (46.4 – 46
.
Method (i)
(PM – PC) x QM
) x 7.2
= 0.4 x 7.2 = 2.88
E DWL due to monopoly
of
the triangle shaded is:
The DWL is represented by the shaded area in the figure under (B) above. The area
44.1)8.0)(6.3(21
)2.78)(8.424.46(21
−=DWL
==⇒
−
DWL
Method (ii)
Alternatively, DWL is the (negative) net change in consumers’ and producers’
surpluses.
Changes in CS = CS under monopoly – CS under perfect competition. That is,
(LOSS!)
Changes in PS = PS under monopoly – PS under perfect competition. That is,
(GAIN!)
e (NCh) in consumers’ and producers surpluses is:
The net change is negative – indicating an overall loss to the economy:
Method (iii)
04.31696.12 −=−=∆CS
6.11286.129 =−=∆PS
Thus, the net chang
44.16.104.3 −=+−=⇒
∆+∆=NCh
PSCSNCh
44.1=⇒ DWL
DWL Lost rs toProduceerednot transf PSCS +=
))(at (21))((
2 MPDWL =1
CMCCC QQQMCPQQP −−+−− M M
233
)2.78)(8.4246(1)2. +2
78)(464.46(21
−−−−=DWL
44.128.116.0
)8.0)(2.3(21)8.0)(4.0(
21
=+=⇒
+=
DWL
DWL
nceptually, all the three ods are the same.
Co meth
Check Yo
What are the necessary conditions fo pr ination?
Is there any relationship between the pr
price discrimination charges and nd in the segregated
markets? Discuss.
Differentiate between the concepts of discrimi ulti-plant
monopolist.
How do you compare the social welfare ects of perfectly competitive and
monopoly market structures?
LESSON SUMMARY
produ ven in then we have an
perfect market structure s the opposite of perfect
petition. Unlike a com a price maker. As a result, a
nopolist faces a downw
Economies of scale or decreasing average costs are the m ources of imperfect
competition in pure monopoly. When the minimum efficient size of plant is larger
relative to the national or onal market, the cost conditions of the monopolist
rs to entry hence monopoly power es. In addition to
eclining costs, other fo leading to market imperfections such as legal
ur Progress
r the practicability of
ices a monopolist engaged in third degree
the price elasticities of dem
ice discrim1.
2.
a
price nation and m3.
asp4.
6.10
When a single firm ces all the output in a gi
called monopoly, which i
petitive firm a monopolist is
ard sloping demand curve.
dustry
exact im
com
mo
ajor s
regi
produce barrie and emerg
d rces
234
restrictions in the form of patents or government regulat
/competition.
There is a spectrum betw and na
urs when av r succ utput so
at the industry requires a cient firm. Few industries come close to
n today - perh like telephone, water, electricity etc.
onopolist's dema y derive its total revenue. From the
hedule or urve of total easily derive its marginal revenue – the
extra revenue resulting fro it of output. For a monopolist,
enue will fa
ions are also barriers to
entry
een perfect competition
erage costs are falling fo
tural monopoly. Natural
monopoly occ essive units of o
th single most effi
aps local utilities this conditio
From a m nd curve, we can easil
sc c revenue, we can
m the sale of an extra un
marginal rev ll short of price ( PMR < ) because of the loss on all
s of output th en it is forced to drop price in order to
utput
ind ma re the last unit it sells brings in
e just equal to R
previous unit at will result wh
sell an extra unit of o
A monopolist will f
.
ximum profit position whe
its extra cost. This same Mextra revenu MC= result can be shown
the interse ves. Regardless of whether a
pl ist the equality of marginal
al cost .
o st may sell given quality to different
consumers at different pric ts. Such a practice is called
ination. The three necessary conditions that must be fulfilled for price
iscrimination to take place are: (a) monopoly power; (b) market segmentation; and
there should no be resa ne market to another. The basis for
ce discrimination are c o pay (first degree or perfect price
rimination); quantity of output consumed (second or non-linear price
crimination); and elastic gree price discrimination).
Exercise of monopoly pow omic waste when price rises above
is bec es where
graphically by ction of MR and MC cur
ant or multi-plant monopol
must hold at the equilibrium
its product or service of a
es for reasons unrelated to cos
monopolist is a single
revenue and margin
A monop li
price discrim
d
(c) le of products from o
pri onsumers’ ability t
disc
dis ity of demand (third de
er also leads to econ
marginal cost. This ause a monopolist produc MR equal and
tly produces les uals price (less than the point
f allocatio efficiency). I onopolist does not produce the optimal
level of output where the s s y ) is equal to the value of
ers or ial welfare (as measured by
MC
consequen s output than where MC eq
n other words, a mo n
ocial cost (as mea ured b MC
the good to consum soc MUP = ). Rather, the
235
236
monopolist is keeping its output a little in short supply. It does not produce up to the
point of MCP = because to do so would require lowering price to all consumers,
which would make the monopolist lose some profit. So, society does not get as
much of the monopolist’s output as it wants in terms of the good’s marginal cost
and marginal value to consumers. The losses in consumers' and producers' surpluses
due to monopoly power are known as the social cost or the Dead weight Losses
(DWL) of monopoly.
6.11 REVIEW QUESTIONS
I. True or False Questions with Justification(s).
1. The lower the value of the MR of a monopolist the higher will be the degree of its
monopoly power.
2. The lower the value of the price elasticity of demand for a monopolist product the
higher will be the markup.
3. We can derive the short run supply curve for a monopolist, provided that the
minimum AVC is known.
II. Discussion Questions
1. How many price discriminations are there under pure monopoly? What are they?
2. Does the difference in payment by spectators for the same movie or football match in
a stadium represent an example of price discrimination? Why or why not?
3. Why is that it is meaningless to ask what price will a monopolist charge for its
product?
4. What kind of economic and technological conditions are conducive to the emergence
of monopoly power?
5. Why a monopolist is better off with price discrimination than without? Under what
conditions is it feasible for a monopolist to practice price discrimination?
237
III: Workout Questions
1. Suppose a hypothetical monopolist facing a linear demand function operates at an
output level where the elasticity of demand is negative 3. If the government imposes
a quantity tax of Birr 6 per unit, how much will be the new selling price of the
monopolist?
2. Given the demand function a single plant monopolist faces and its cost function as: 310 −= PQ and QTC 2= , respectively,
A. Determine the short run optimal output, price, and profit of this monopolist.
B. Calculate elasticity and mark up price at the equilibrium output and price.
C. Show your results in (A) and (B) graphically using the marginal approach.
D. Based on your graph in (C), do you think there is a room for entry into the
market in which this existing monopoly operates? Why or why not?
3. Advanced: Suppose a multi-monopolist has marginal cost functions
11 220 qMC += , and
22 510 qMC += .
Where, 1MC is the marginal cost of the first plant and 2MC is the marginal cost of
the second plant. Besides, 1q and 2q represent output to be produced using the first
and second plants, respectively. If the monopolist is maximizing its short run profit
by producing 5 units of output in the first plant, then:
A. What is the monopolist's profit maximizing level of output in the second plant?
Show the steps how you have determined 2q .
B. Prepare a schedule similar to 6.3 for both marginal costs for 1 up to 10 output
levels and show how you determine the total short run output of the monopolist.
4. Assume that a monopolist has identified two markets such that the inverse demand
functions for its product in the two markets are:
11 292 qP −= , and
22 70 qP −= .
Its total cost function is: 2240100 QQTC ++= ; Where 21 qqQ += .
238
A. How much output will the monopolist sell and what price will it charge in the
two markets with price discrimination and without price discrimination?
B. Show the short run optimal outputs and prices in the two markets with price
discrimination using back-to-back diagram.
C. Find the amount of profit the monopolists will earn with price discrimination.
What is total profit if the monopolist does not discriminate between the two
markets?
D. Based on the profit figures you obtained in “C” above, are you then convinced
that a monopolist is always better off with price discrimination than without?
Why or why not?
E. In which market is the elasticity of demand higher? What is its implication?
F. Calculate the mark up at the short run equilibrium when the monopolist
discriminates. In which market is it higher? Why?
G. Show that a monopolist charges a price higher than its marginal cost in the
two markets.
5. Assuming that the monopolist in Question 4 above has evolved from perfect
competition to monopoly.
A. What is the restricted amount of output due to monopoly power?
B. Calculate the consumers’ and producers’ surplus under perfect competition
and monopoly.
C. What is the surplus transferred from consumers to the monopolist?
D. Calculate the net social cost (or Dead weight loss-DWL) due to monopoly
power or behavior.
E. Show first, the output and price levels under perfect competition graphically
and then shade or label with number (i) consumers’ and monopoly surplus; (ii)
surplus transferred to the monopolist; and (iii) the net DWL.
6. If the marginal cost functions of a monopolist were those given for the two plants in
Question 3, but if it faces the total market demand function in Question 4,
A. How much output should the multi-plant monopolist produce in each plant?
B. What will be the price the monopolist charges?
C. Calculate the monopolist’s profit assuming that TFC of each plant is 30 Birr.
239
REFERENCES
Dwivedi, D.N. (1997). Microeconomic Theory. 3P
rdP ed. Vikas Publishing House Pvt
Ltd, New Delhi.
Ferguson, C.E. and Gould J.P. (1989). Microeconomic Theory. 6th ed. Irwin
Publications.
Henderson, M. and Quandt E. (1980). Microeconomic Theory: A Mathematical
Approach. 3P
rdP edition. McGraw Hill.
Koutsoyiannis, A. (1981). Modern Microeconomics. 2nd edition. St Martins Pr.
Mansfield, E. (1988). Microeconomics: Theory and Applications. Shorter sixth
edition. W.W. Norton & Company: New York, London.
Pindyck, R. S. and D.L. Rubinfeld (1991). Microeconomics. 8th ed. Macmillan.
Salvatore, D. (2003). Microeconomics: Theory and Applications. 4th ed. Oxford
University Press, New York.
Varian, Hal R. (2002). Intermediate Microeconomics: A Modern Approach. 6th ed.
W.W. Norton and Company.
240
ANSWERS TO SELECTED REVIEW QUESTIONS
CHAPTER ONE
Part I
1. a
2. d
3. e
4. d
5. c
6. a
7. a
8. d
Part II
1. True
2. False
CHAPTER TWO
Part I
1. c
2. d
3. c
4. c
5. b
6. d
7. d
8. d
9. c
10. a
11. a
12. a
Part II
1. True
2. True
3. False
4. False
5. False
Part III
4.
a. Expected income =
Birr 12,000; Expected
utility =10.8 utils.
b. She is risk-averse.
Because, the expected
utility from gambling
(10.8) < the utility from
the safe source of
income (11).
5. X* = 320; Y* = 80
6. 31−=d
pε . Demand
is price inelastic at the
point.
7.
a. Birr 400.
b. 1600 utils.
c. She is indifferent
between buying and not
buying the share. This is
because the expected
utility from the gamble
(= 1600) is exactly the
same as her current
utility from the safe
source (U = 4m = 4*400
= 1600).
d. risk-neutral
CHAPTER THREE
Part I
1. b
2. c
3. d
4. c
5. a
6. a
7. b
8. a
9. c
10. b
11. b
12. d
13. c
14. a
241
CHAPTER FOUR
Part I
1. b
2. d
3. b
4. a
5. d
6. c
7. d
8. b
9. d
10. a
11. d
12. b
13. a
14. d
15. a
CHAPTER FIVE
Part II
1. (B) Q* = 25.
(E) PS = ?
(F) ∞=// dpε
2.
3. (A) Q* = 200;
Π* = 600.
(B) MC = 1 + 0.04Q;
ATC = (200/Q) + 1
+ 0.02Q;
AVC = 1 + 0.02Q.
At equilibrium, MC* = 9;
ATC* = 6; AVC* = 5.
(C) PS = 800
2.373;8.26.3100200
≈≈⇒±=
QQQ
CHAPTER SIX
Part I
1. True
2. True
3. False
Part III
1.
2. (A) Q* = 10/27; P* =
3; Π* = 10/27
(B) ;3// =dpε
Markup = 3/2 = 1.5
3.
4.
(A) *With price
discrimination: q1 = 6;
p1 = 80; q2 = 1; p2 = 69.
* Without price
discrimination:
Q = 7; P = 72.67.
(B) *With price
discrimination: Π* =171
* Without price
discrimination:
Π* = 130.67
(F) Markup in market 1
= 20/17; Markup in
market 2 = 69/68. It is
higher in market 1
because consumers in
market 1 are less
sensitive to price
changes.
5. (A) output declines by
1 unit (from 8 to 7).
(B) *Under perfect
competition:
CS = 21.33; PS = 128
*Under monopoly:
CS =16.33; PS = 130.67.
(C) CS transferred to
producer = 4.67.
(D) DWL = 2.33
6.
(A) q1 = 410/29 = 14.14;
q2 = 222/29 = 7.66
(B) P = 5464/87 = 62.8.
(C) Π = 602.68