Managerial Economics

Meaning

• Managerial economics is defined as the study of economic theories, logic and tools of economic analysis that are used in process of business decision-making.

• In other words economic theories and techniques of economic analysis are applied to analyze business problems, evaluate business opportunities with a view to arrive at appropriate business decision.

.

•Managerial Decision AreasAssessment of Investible fundsSelecting Business areasChoice of ProductDetermining optimum OutputDetermining input-Combination of the product Sales promotion

Application of Economic Concepts

and Theories in Decision Making

Use of Quantitative Methods

•Mathematical tools•Statistical Tools•Econometrics

Application of Economic Concepts, Theories and analytical Tools to find Optimum Solution to Business Problems

Why Economics?

• Biology contributes to medical profession.• Physics to Engineering. • Economics to Managerial profession.Achieve objective of the firmConstraints is limited resources

Application of Economics to Decision Making

I. Determining and defining the objective to be achieved.

II. Collection and analysis of business related data and other information(Economic, social, Political and technological environment.).

III. Inventing the possible courses of action

IV. Select the possible action from the given alternatives.

• II and III are crucial in decision making

Example Launching a product

• Production Related issues and• Sales related issues.

Production Related issues

• Available techniques of Production.• Cost of Production • Supply position of inputs• Price structure of inputs• Cost structure of competitive products• Availability of foreign exchange if inputs are

available.

Sales related issues

• Market size, general market trends and demand prospectus for the product

• Trends in Industry• Competitors• Pricing of product• Pricing strategy of competitors• Degree of competition• Supply position of complementary goods

Scope of Managerial Economics

• Economics applied to the analysis of business problems and decision making.

• Area of business issues to which economic theories can be directly applied are broadly divided into

1. Micro Economics (Operational and internal issues)

2. Macro Economics (Environmental and external issues)

Operational or Internal issues

• What to produce Nature of product or Business• How much to produce Size of firm• How to produce Choice of technology• How to price the commodity• How to promote sales• How to face price competition • How to manage profit and capital• How to manage an inventory

Environmental or External issues• The type of economic system in the country• Trends in GDP, Prices, Saving and Investment Employment,

etc.• Trends in Financial System Banks, Financial and Insurance

companies• Trends in Foreign Trade• Government Economic policies• Social Factors like value system, property rights, customs

and habits.• Socio-economic organization like trade unions, consumer’s

associations, Consumer co-operatives and producers unions.

• Political environment• Degree of Globalization and Influence of MNC’s

Micro Economic Issues

• What to produce• How much to produce• How to produce• How to price the commodity• How to promote sales• How to face competition• How to decide on new investment• How to manage profit and capital• How to manage an inventory

Examples of Economic Theories

• Theory of Demand It deals with the consumer behaviourHow do the consumer decides to buy the

commodityHow do they decide on QuantityWhen do they stop consumingHow consumer behave on Price It helps in making choice in commodity, optimum

level of production and price

Theory of Production and Decision Making

• It explains the relationship between inputs and output.

• Under what conditions the cost increases or decreases

• Helps to decide the optimum size of the firm• Size of total output and amt of capital and

labour to be employed given the objective

Market structure and Pricing theory

• How price is determined.• When price discrimination is desirable,

feasible and profitable.• How advertising will be helpful to increase

sales.• Thus pricing and production decision will help

to determine the optimum size of the firm.

Profit analysis and Management

• Elements of risk is always there even if most efficient techniques are used.

• It guide the firm to measure and manage profit, to make the allowance of risk premium, to calculate the pure return on capital and also future profit.

Theory of Capital and investment decision

• It contribute to deciding choice of project, maintaining capital, capital budgeting, etc

Macro economic Issues

• Trends in Economics: Level of GDPInvestment climateTrends in National Output and employmentPrice trends

• Issues related to Foreign TradeTrends in International TradeTrends in International PricesExchange ratesProspectus in International Market

• Issues related to Government Policies:Monetary PolicyFiscal PolicyForeign Trade PolicyEnvironmental Policy etc

Other Topics related to Managerial Economics

• Mathematical Tools

Economic theories for Decision Making

• Economic concepts (Cost, Price, Demand etc.)• Ascertaining the variables which is relevant.• Relationship between the two or more

variables.

What is Demand ?“ When the desire for a commodity is backed by the

willingness and the ability to spent adequate sums of money, it becomes demand or effective demand in the economic sense of the curve. Only desire for commodity or having money for the same cannot give rise to its demand”

Marshall“ Demand for a product refers the amount of it

which will be bought per unit of time at a particular price”.

03/13/15 group 2 sec c 23

RELATIVE CONCEPT• Demand is the relative concept i.e. it is related

to price and time:1.The demand for rice is 100Kg2.The demand for rice at Rs 5/- per Kg is 100Kg

per day.• Second statement is complete because it

mentions the price and time period, becoz demand varies from time and price.

• The demand refers to the quantity of it purchased at a given price, during a specific time period.

Determinants of Demand1.Price of the product.2.Income and wealth distribution.3.Tastes, habits and preferences.4.Relative prices of other goods

Substitute products. Complementary products.

5.Consumers satisfaction.6.Quantity of money in circulation.7.Utility of the commodity.8.Quality.9.Expectation regarding future price.10.Number consumers, time and place: Transport, communication

and market facilities will increase the consumers

11. Advertisements effects.

12. Growth of population.

13. Level of taxation.

14. Climatic or weather conditions.

15. Special occasions.

16. Technology.

17. Psychology of the consumers:

Bandwagon effect: Demand arises becoz others have it others, Snob effect: Demand arises becoz when it is not commonly

demanded,Demonstration effect: Copying the others.

INDIVIDUAL DEMAND

Price per unit Demand for commodity X

50 10

40 20

30 30

20 40

10 50

05 60

It is the tabular representation of the various quantities of a commodity demanded by an Individual at a different prices during a given period of time

Individual Demand

MARKET DEMAND

Price per Unit Qty Demanded

A B CTotal market

Demand(A + B + C)

50 10 12 15 37

40 20 22 25 67

30 30 32 35 97

20 40 42 45 127

10 50 52 55 157

Demand and Demand Curves (d)

– The market demand curve is the horizontal sum of the demand curves of all individuals.

– Market dd curve is also negatively sloped because 1. Individual dd curves are downward sloping 2. At high prices some buyers will exit the market

MARKET DEMAND

Generalized demand function• The generalized demand function just set forth is expressed in the

most mathematical form.

• Economist and market researchers often expressed generalized demand function in a linear functional form.

• The following equation is an example of a linear form of the generalized demand function:

Qd = a + bP + cM + dPR + eT + fPe + gN

• Where the Variables are (P,M,PR,T,Pe,N).

• And a,b,c,d,e,f and g are parameters.

Generalized demand function

• The intercept “a” shows the value of Qd when the variables P,M,PR,T,Pe,N are all simultaneously equal to zero.

• The other parameter a,b,c,d,e,f and g are called slope parameters.

• They measure the effect on quantity demanded of changing one of the variables while holding rest of it as constant.

• E.g. b measures the change in Qty dd per unit change in price

• i.e b = Qd/ P.

Summary of Generalized demand function

Variable Relation to quantity demanded Sign of Slope parameter

P INVERSE Negative

M Direct for normal goodsInverse for inferior goods

Positive Negative

PR Direct for substitute goodsInverse for the complementary goods

Positive Negative

T Direct Positive

Pe Direct Positive

N Direct Positive

Demand functions

• The relation between price and quantity demanded per period of time, when all other factors that affect demand held constant is called as demand function or simply demand.

• It can be expressed as

Qd = f (P)

illustration

• Generalized demand function isQd = 1800 – 20P + 0.6M – 50PR

• To derive a demand functionsQd = (P)

• The variables M and PR must be assigned fixed value.

• Suppose M = 20000, PR = 250 • Substitute the value in generalized demand

function.

• Qd = 1800 – 20P- 0.6(20000) – 50(250) = 1800 – 20P + 12000 – 12500 = 1300 – 20P• The intercept parameter 1300 is the amount of the

good consumers would demand if price is zero.

• The slope of the demand function is -20 and indicates that a Rs 1 increase in price causes qty dd to decrease by 20 units.

Qd = 1300 – 20 (1) = 1300 -20 = 1280

Determinants of DemandDeterminants of Demand Demand

Increases

Demand decreases Sign of Slope parameter

Income (M)Normal GoodsInferior goods

M risesM Falls

M FallsM rises

C > 0C < 0

Price of related goods (PR)

Substitute goodsComplement good

PR risesPR falls

PR fallsPR rises

d > 0d < 0

Consumer Tastes (T) T rises T falls e > 0

Expected price (Pe) Pe rises Pe Falls f > 0

Number of consumers (N) N rises N Falls g > 0

Demand Schedule

The Law of Demand

“Other factors remaining same (habits, tastes etc.) as price decreases demand increases and vice versa”

Marshall

“Ceteris paribus, higher the price of a commodity, smaller is the quantity demanded and lower the price, larger the quantity demanded.”

Demand Schedule (Hypothetical)

Price of commodity (in Rs) Quantity demanded (unit per week)

5 4 3 2 1

100 200 300 400 500

Quantity demanded (Q)

Q1 Q2

P1

P2

E1

E2

0

D

DPrice(P)

P1 - old price

P2 - new price

Q1 – old quantity demanded

Q2 – new quantity demanded

DD – demand curve

A Linear Demand Curve

Demand Curve

Characteristics of A Typical Demand Curve

Drawn by joining different loci.

Downward sloping.

Reciprocal relationship between price and quantity demanded ( P α 1/Qd )

Linear Non - linear

Assumptions (Other things)a) No change in consumer’s income.b) No change in consumer’s preferences.c) No change in the fashion.d) No change in the price of related goods :

Substitute goods. Complementary goods.

a) No expectation of future price changes or shortages.b) No change in size, age, composition and sex ratio of

the population.c) No change in the range of goods available to the

consumers.

Contd…

h) No change in the distribution of income and wealth.

i) No change in the government policy.

j) No change in weather conditions.

EXCEPTION TO LAW OF DEMAND

• Giffen’s Paradox: Giffen gods are inferior goods. When the price rises the real income of the consumer rises and he will move to a superior goods. This is also called as Giffen’s paradox.

• Qualitative changes: It may increase qty with the increase in the price.

• Price illusion: Higher the price better is the quality.

• Prestige goods: Purchased by the rich people.

• Demonstration effect: Imitating others or Snob appeal

• Fashion:• Necessaries:

Movement along the curveOR

Change in quantity demanded

Extension of demand ‘ With a decrease in price, there is increase in the

quantity demand of the product’.

P1

P2

Q1 Q2

E

E`

D

D

Quantity demanded

Price

Contraction of demand ‘ With a increase in price, there is a decrease in

quantity demanded’.’

Quantity demanded

P2

Q2

P1

Q1

E

E`

Price

SOURCES OF SHIFTS IN THE DEMAND CURVES

• Tastes• Prices of related goods• Income• Demographics• Information• Availability of credit• Changes in expectations

Movement of Demand CurveOR

Change in demand

Increase in demand:

a) More quantity demanded ------ at a given price.b) Same quantity demanded ------ at a higher price.

P1

Q1 Q2

a b

D

D

D`

D`

Q1

P1

P2

D

D

D`

D`a

b

Quantity demanded Quantity demanded

Price

Price

Decrease in demand :

a) Less quantity demanded ---- at same price.

b) Same quantity demanded ---- lower price.

Q2 Q1

P1

a b

Q1

Quantity demanded

P1

D`

bD`

D

D

D`

D

Da

D`

PricePrice

Quantity demanded

P2

Factors And Effects of Change (increase or decrease) in demand

a) Change in income :

Quantity demanded

Price

Increase

Quantity demanded

Price

DecreaseD`

D`

D

D

D

D

D`

D`

b) Change in taste, habit and preference :

D

D

D`

D`

D

D

D`

D`

Quantity demanded

Price

Quantity demanded

Price

Positive Negative

c) Change in fashion and customs :

D

D

D`

D`

D

D

D`

D`

Quantity demanded

Quantity demanded

Price Price

Favorable Unfavorable

g) Change in population :

03/13/15 group 2 sec c 57

Quantity demanded

Quantity demanded

PricePrice

D`

D`

D`

D`

D

D

D

D

Increase Decrease

h) Advertisement and publicity persuasion :

03/13/15 group 2 sec c 58

Quantity demanded

Quantity demanded

Price PriceD

D

D

D

D`

D`

D`

D`

Aggressive Docile

i) Change in value of money :

Quantity demanded

Quantity demanded

Price Price

D`

D`

D`

D`

D

D

D

D

Deflationary Inflationary

( Value of money) ( Value of money)

j) Change in level of taxation :

Quantity demanded

Quantity demanded

D

D`

D`

D`

D

D`D

D

Low High

PricePrice

k) Expectation of future changes in prices :

Quantity demanded

Quantity demanded

D`

D`

D`

D`

D

D

D

D

Rise Fall

Price Price

Shift in DemandPrice Qd = 1300 – 20P

(M = 20000) D0Qd = 1600 – 20P (M = 20500) D1

Qd = 1000 – 20P(M = 19500) D2

65 0 300 0

60 100 400 0

50 300 600 0

40 500 800 200

30 700 1000 400

20 900 1200 600

10 1100 1400 800

Shift in Demand

Determinants of DemandDeterminants of Demand Demand

Increases

Demand decreases Sign of Slope parameter

Income (M)Normal GoodsInferior goods

M risesM Falls

M FallsM rises

C > 0C < 0

Price of related goods (PR)

Substitute goodsComplement good

PR risesPR falls

PR fallsPR rises

d > 0d < 0

Consumer Tastes (T) T rises T falls e > 0

Expected price (Pe) Pe rises Pe Falls f > 0

Number of consumers (N) N rises N Falls g > 0

Supply

• The amount of a good or service offered for sale in a market during a given period of time (e.g a week, a month) is called quantity supplied.

Concept of Supply

• Supply is defined as the various amounts of goods and services which the sellers are willing and able to sell at any given price during a specific period of time

• It is related to time, place and person• The supply of sugar is 50 kg is not a complete

sentence• The supply of a sugar at price Rs 5/- is 50kg.

Per day is the complete sentence

Factors affecting Supply

• Price• Price of other commodities• Goals of the producer• State of technology• Cost of production• Climate and forces of Nature• Transport facilities• Taxation: Heavy taxes supply will reduce• Expectation regarding future prices

• Self-consumption• Time element: Short period the supply is fixed

and vice

Individual Supply Schedule

Price Per Unit of X Qty. supplied of X

U 5 10

V 10 20

W 15 30

X 20 40

Y 25 50

Z 30 60

Individual supply schedule is a tabular representation of the various quantities of commodity offered for sale by an individual seller at different prices during given period of time

Individual Supply Curve

Market supply schedule

• It is the tabular representation of the various qty. of a commodity offered for sale by all the sellers at different prices during a given period of time. It is the total supply of a commodity by all the sellers at different prices

Market supply schedule

Price( Rs ) Qty. supplied of X Market supply (I + II+ III)

Seller I Seller II Seller III

U 5 10 20 30 60

V 10 20 25 40 85

W 15 30 30 50 110

X 20 40 35 60 135

Y 25 50 40 70 160

Z 30 60 45 80 185

Market supply Curve

Law of Supply

• Others things remaining the same , qty. supplied of a commodity directly varies with its price. i.e. S= f (p)

SUPPLY SCHEDULE

Price Per Unit of X Qty. supplied of X

U 5 10

V 10 20

W 15 30

X 20 40

Y 25 50

Z 30 60

Supply Curve

Assumption • Price of other commodities remains the same• The cost of production remains the same• The method of production remains the same• No change in the availability of goods• No change in transport facilities• No change in weather condition• No change in tax structure and govt. policies• Goals of producer remains the same• No change in expectation about the price• No natural calamities and no self consumption

Exceptions to the law of supply • Backward bending supply curve

Wage rate ( Rs.) Hours of work Daily Income (Rs.)

5 8 40

7 10 70

10 12 120

12 10 120

• Fixed income groups: If person expects the income of Rs.20 he will save 500 Rs at 4% rate of interest and at 5% rate he will save Rs. 400 Rs.

• Expectation regarding future prices• Need for cash by the seller • Rare collection the supply is permanently

fixed whatever the price.• Self consumption

Movements or variation in Supply

• When there is change in supply exclusively due to change in Price

Shift in supplyWhen there is a change in supply due to change in factors other than the Price

Generalized supply function• It shows how the different variables jointly determine the

quantity supplied.• The generalized supply function is expressed

mathematically as

Qs = g(P, Pi, Pr, T, Pe, F)

Qs = Qty of goods and service offered for sale P = Price of goods or service. Pi = Price of inputs Pr = Price of goods that are related to production. T = Level of available technology. Pr = Expected price of the producer F = No. of firms in the industry

Generalized supply function

• As in case of demand, economists often find itself to express the generalised supply function in linear functional form:

Qs = h + kP + lPi+ mPr + nT + rPe + sF• Where P, Pi, Pr, T, Pe, F is a variables affecting

the supply, h is the intercept parameter, and k, l, m, n, r, and s are the slope parameters.

Relation to Generalised demand functionVariable Relation to Quantity

suppliedSign of slope parameter

P Direct K = is Positive

Pi Inverse L = is Negative

Pr Inverse for substitute in production (Wheat and Corn)Direct for complement in production(Oil and Gas)

m = is Negative

m = is Positive

T Direct n = is Positive

Pe Inverse r = is Negative

F Direct S = is Positive

Supply function• Supply function is derived from generalised supply function.• A supply function shows the relation between supply and price.

Qs = g(P, Pi, Pr, T, Pe, F) = g (P) Illustration

Qs = 50 + 10P – 8pi + 5F• Suppose the price of the input is Rs. 50 and there are 90 firms then

the supply function will be

Qs = 50 + 10P -8(50) + 5(90) = 100 + 10P

• The supply schedule with equation can be drawn and is given in next slide

Qs = 100 +10P

Price Quantity Supplied schedule

65 750

60 700

50 600

40 500

30 400

20 300

10 200

Shift in Supply Price Qs = 100 + 10P

Pi = 50, F = 90Qs = 250 + 10PPi = 31.25, F = 90

Qs = -200 + 10PPi = 50, F = 30

65 750 900 450

60 700 850 400

50 600 750 300

40 500 650 200

30 400 550 100

20 300 450 0

10 200 350 0

Shift in Supply Determinants of supply

Supply Increases Supply Decreases Sign of Slope parameter

Price of inputs (Pi) Pi falls Pi rises I < 0

Price of goods related in Production (Pr)Substitute goodComplement good

Pr fallsPr rises

Pr risesPr falls

M < 0M > 0

State of technology (T)

T rises T falls n > 0

Expected Price (Pe) Pe falls Pe rises r < 0

Number of firms or productive capacity in Industry (F)

F rises F falls S > 0

Market Equilibrium

• Demand and supply provide an analytical framework for the analysis of the behaviour of buyers and sellers in markets.

• Demand shows how buyers respond to changes in price and other variables that determine quantities, buyers are willing to purchase.

• Supply shows how sellers respond to changes in price and other variables that determine quantities offered for sale.

• The interaction of buyers and sellers in the market place leads to market equilibrium.

Market Equilibrium

• Market equilibrium is a situation which at the prevailing price, consumers can buy all of a good they wish and producers can sell all of good they wish.

Market Equilibrium Price Qs = 100 + 10P

S0Qd = 1300 – 20P D0

Excess supply ( +) Excess Demand ( -)

65 750 0 +750

60 700 100 +600

50 600 300 +300

40 500 500 0

30 400 700 -300

20 300 900 -600

10 200 1100 -900

Qd = Qs1300 – 20 P = 100 + 10PSolving this equation for the equilibrium price,1200 = 30PP = 40

Market Equilibrium

Market Equilibrium• At Market clearing price of 40

Qd = 1300 – (20 * 40) = 500Qs = 100 + (10 * 40) = 500

• If the price is Rs 50 there is a surplus of 300 units. Using the demand and supply. equations, when P = 50,

• Therefore, When price is Rs 50.

Qd = 1300 – (20 * 50) = 300Qs = 100 + (10 * 50) = 600

There fore when the price is Rs 50Qs – Qd = 600 – 300 = 300

Changes in Market EquilibriumDemand Shifts (Supply remains constant)

Supply Shifts (Demand Remains constant)

Simultaneous Shift in Demand and Supply

Simultaneous Shift in Demand and Supply

Predicting the Direction of change in Airfares (Qualitative analysis)

• Suppose you manage a travel department for a U.S. corporation and your sales force makes heavy use of air travel to call on customers.

• The president of the corporation to reduce travel expenditures for 2004.

• You need to predict what will happen in future price of airfares in 2004.

• The wall street journal recently came with the news.

A number of new, small airlines have recently entered the industry and others are expected to enter in 2004.

Video-conferencing is becoming a popular, cost effective alternative to business travel for many U.S. corporation. The trend will cut the price on teleconferencing rates.

Direction of change in Airfares: Qualitative Analysis

ELASTICITY OF DEMAND

• The degree of responsiveness of Qty. demanded of a commodity to a change in its price is known as elasticity of demand.

• Ed = % change in qty. dd /% change in determinant

• Elastic: Small change in price brings big change in demand

• Inelastic: Big change in price brings small change in demand

Kinds of Elasticity

• Price Elasticity• Income Elasticity• Cross Elasticity• Arc Elasticity

PRICE EASTICITY OF DEMAND

• IT is the degree of responsiveness of qty. demanded of a commodity to a change in its price.

• Ed = % change in qty. dd /% change in P• Ed = proportionate change in qty. dd

/Proportionate change in P• Ed = Q / Q = Q / Q * P / P P / P

Definition: Elasticity of Demand

Price elasticity of demand is defined as the percentage change in quantity demanded divided by the percentage change in price.

Equation:

Elasticity of Demand =

% change in Qd

% change in Price

ExampleSuppose Mongini’s cake is originally priced at Rs. 10 and the amount sold is 50 cakes per week. If the price is increased to Rs. 11, then 40 cakes are sold per week. What is the price elasticity of demand?

% Change in Price = [(11-10)/10]*100 = 10%

% Change in Quantity Demanded = [(40-50)/50]*100 = 20 % (ignoring the negative sign)

Elasticity = 20/10 = 2

Even a very small change in price has lead a high-proportional fall in quantity demanded.

TYPES OF PRICE ELASTICITY OF DEMAND

TYPES OF PRICE ELASTICITY OF DEMAND

The Farmer’s Dilemma• For many crops, a strange situation arises a bad crop year

results in a good year for farm incomes, and a good crop year results in a bad year for farm incomes. How can this be?

• Price elasticity gives us the answer:– Bad crop year: supply decreases, prices for farm products rise, but

quantity demanded doesn’t fall very much. The quantity demanded of farm products is not very responsive to changes in prices

– Good crop year: supply increases, prices for farm products fall, but quantity demanded doesn’t increase very much. The quantity demanded of farm products is not very responsive to changes in prices

• It is easy to show this with a graph. But first we need yet another concept: Total Revenue = Price x Quantity

Measurement of price elasticity of demand

• Percentage Method

• Total outlay Method

• Geometric Method

Percentage Method or Ratio Method

• It is the ratio of % change in Demand to a % change in Price.

• Ed = % Q OR Q * P = P * Q

• % P Q P Q P • Unit elastic Ed =1• Relatively Elastic Ed >1 • Relatively Inelastic Ed <1

Total Outlay Method or Revenue Or Expenditure Method

Price (Rs) QTY. DD (units) Total Outlay (Rs) Elasticity

50 5 250 Relatively elastic Ed > 140 10 400

30 20 600 Unit Elastic Ed = 1

20 30 600

10 40 400 Relatively inelastic Ed < 15 50 250

Geometric Method Or Exact Method

• Ed = Lower segment of demand curve

Upper segment of demand curve

Ed at pt A = D’A/DA = 1

Ed at pt B = D’B/DB = 1/3 < 1

Ed at pt C = D’C/DC =9/3 > 1

Other concepts of Elasticity of Demand

• Income Elasticity of Demand = Q * Y

Y Q

Ed = % change in qty. dd /% change in Y• Cross Elasticity of Demand = Q x * P y

P y Q x

Arc elasticity of Demand =

Q x P

Q1+ Q2 P1+ P2

Factors Influencing Elasticity

• Nature of commodity: Necessary or luxurious goods

• Availability of substitutes:

• Number of Uses of a commodity: Multipurpose elastic and vice-versa.• Income:

• Proportion of Expenditure: A small prop. Of exp demand is elastic.

• Time period:

• Height of Price and Range of Price change: Very low or very High price demand is inelastic; Diamonds

or salt but moderately priced goods have elastic demand.

• Urgent or postponement:

• Durability of commodity: Short run Inelastic , but long run elastic Perishable goods is

elastic.

• Habits and customs:

• Complementary goods: Inelastic

• Recurring Demand: Relatively elastic

• Demonstration effect:

Significance of elasticity of Demand• Useful to Producer and monopolist:

• Useful to the govt.

• Factor pricing:

• Importance to trade unionist:

• International Trade:

• Useful to policy Makers: Prices of agricultural goods , Fiscal and monetary policies etc.

THEORY OF PRODUCTION

• The fundamental questions that managers are faced with are

How can production optimized or cost minimize?

How does output respond to change in quantity of inputs?

How does technology matter in reducing the cost of production?

How can the least- cost combination of inputs be achieved?

Given the technology, what happens to the rate of return when more plants are added to the firm?

Input and output• An input is simply anything which the firm buys for in its

production or other processes.

• Inputs are classified as

1) Fixed inputs: A fixed input is one whose supply is inelastic in the short-run. In technical sense, a fixed factor is one that remains fixed (or constant) for a certain level of output.

2) Variable inputs: A variable input is defined as one whose supply in the short-run is elastic, e.g., labour and raw material, etc. all the users of such factors can employ a larger quantity in the short-run as well as in the long-run.

Short-run and Long-run Production The short-run refers to a period of time in which the supply of certain

inputs (e.g. plant, building, machinery etc.) is fixed or inelastic.

In the short-run therefore, production of a commodity can be increased by increasing the use of only variable inputs like labour and raw materials.

Variable Input: labor force, Fixed Input: machinery, plant size, raw materials.

Long-run refers to a period of time in which the supply of all the inputs is elastic, but not enough to permit a change in technology.

That is, in the long-run, all the inputs are variable.

Corresponds to the planning stage

Production Function

• The total amount of output produced by a firm is a function of the levels of input usage by the firm.

• Relation Between Input and Output – the maximum amount of output that can be obtained per period of time given the factor inputs is captured by the production function.

• Describes purely Technological Relationship.

• Flow Concept.

Production Function

• A real-life production function is generally very complex.

Q = f(LB, L, K, M, T, t)

• Where LB = land and building L= labour, K= capital, M= raw materials, T= technology and t= time.

• The economists have however reduced the number of input variables used in a production function to only two, viz., capital(K) and labour(L), for the sake of convenience and simplicity in the analysis of input-output relations.

Production Function

• Also, technology (T) of production remains constant over a period of time.

• That is why, in most production functions, only labour and capital are include

• As such, the general form of its production function for coal mining firm may be expressed as

Qc = f (K, L)

• Where Qc = the quantity of coal produced per time unit,K = capital, and L = labour.

Production Function• The short-run production function or what may also be

termed as ‘single variable input production function’, can be expressed as

• Q = f (K, L) where K is a constant …(1a)

• For example, suppose a production function is expressed as

Q = bL• Where b = gives constant returns to labour.

Total, Average and Marginal Product

• Total Product: Total Output Produced during some period of time by all factors of Production employed during that Period.

• Total Product (TP) function – In the Short Run captures relationship between the amount of labor and the level of output, ceteris paribus

Total Product

Quantity of Labour

Total Product

0 05 5010 12015 18020 22025 25030 27035 27540 27545 270

Variation of Output (One fixed, one variable factor), with Capital fixed at say 5

Units

Average Product

• AP is merely the Total product per Unit of the Variable Factor

AP = TP / L

Average ProductQuantity of

LabourTotal

ProductAverage Product

0 0 …5 50 10.0010 120 12.0015 180 12.0020 220 11.0025 250 10.0030 270 9.0035 275 7.8640 275 6.8845 270 6.00

Marginal Product (MP)• The additional output that results from the

use of an additional unit of a variable input, holding other inputs constant.

• Measured as the ratio of the change in output (TP) to the change in the quantity of labor (or other variable input) used

• MP = ∆ in Output / ∆ in Labour

Marginal ProductQuantity of

LabourTotal

ProductChange

in TPMarginal Product

0 0 … …5 50 50 10

10 120 70 1415 180 60 1220 220 40 825 250 30 630 270 20 435 275 5 140 275 0 045 270 -5 -1

Marginal Product (Continued)

• Note that the MP is positive when an increase in labor results in an increase in output;

• A negative MP occurs when output falls when additional labor is used.

Production Function

• In the long -term production function, both K and L are included and the function takes the following form.

Q = f (K, L) …(1b)

• Consider, for example, the Cobb-Douglas production function-the most famous and widely used production function – given in the form of an equation as

Q = …(1.2)

• (where K= capital, L= Labour, and A , a and b, are parameters and b =1 – a).

• α and β are the output elasticities of capital and labor, respectively.

• These values are constants determined by available technology.

• Output elasticity measures the responsiveness of output to a change in levels of either labor or capital used in production, ceteris paribus.

• For example if α = 0.45, a 1% increase in capital usage would lead to approximately a 0.45% increase in output.

Production Function• Production function (1.2) gives the general form of Cobb-

Douglas production function.

• The numerical values of parameters A, a and b, can be estimated by using actual factory data on production, capital and labour.

• Suppose numerical values of parameters are estimated as A=50, a=0.5 and b=0.5.

• Once numerical values are known, the Cobb-Douglas production function can be expressed in its specific form as follows.

Production Function• This production function can be used to obtain

the maximum quantity (Q) that can be produced with different combinations of capital (K) and Labour (L).

• The maximum quantity of output that can be produced from different combinations of K and L can be worked out by using the following formula.

Production Function

• For example, suppose K = 2 and L = 5. Then

• And if K = 5 and L = 5, then

• Similarly, by assigning different numerical values to K and L, the resulting output can be worked out for different combinations of K and L and a tabular form of production function can be prepared.

Similarly, by assigning different numerical values to K and L, the resulting output can be worked out for different combinations of K and L and a tabular form of production function can be prepared.

• It is important to note that the four combinations of K and L • 10K + 1L• 5K + 5L• 2K + 5L and• 1K + 10L produces the same output

Production with one variable input

• The law of diminishing returns states that when more and more units of a variable input are used with a given quantity of fixed inputs,

• The total output may initially increase or increasing rate, but it will eventually increase at increasing rate.

• That is, marginal increase in total output decreases eventually when additional units of a variable factor are used, given quantity of fixed factors.

Assumptions:

• The law of diminishing returns is based on the following assumptions:

Labor is the only variable input, capital remaining constant;

Labour is homogeneous;

Input prices are given.

• To illustrate the law of diminishing returns, we assume

i) That a firm (say, the coal mining firm in our earlier example) as a set of mining machinery as its capital (K) fixed in the short-run and

ii) It can employ only more mine workers to increase its coal production.

• Thus, the short run production function for the firm will take the following form.

constant),Qc Kf(L=

Let us assume also that the labour output relationship in coal production is given by a hypothetical production function of the following form.

constantL,Q 3c K10 15L L 2 ++−=

• Given the production function, we may substitute different numerical values of L in the function and work out a series of Qc i.e.

• The quantity of coal that is produced with different number of workers.

• For example, if L = 5, then by substitution, we get

• Qc= -53 + 15 x 52 + 10 x 5 = -125 + 375 + 50 = 300

• What we need now is to work out marginal productivity of labour (MPL) to find the trend in the contribution of the marginal labour and average productivity of labour (APL) to find the average contribution of labour.

• Marginal Productivity of Labour (MPL) can be obtained by differentiating the production function.

• Thus,

• can be written as10303 2 ++−=

∂∂= LL

L

QMPL

constantL),(Q 3c K10 15L L 2 ++−=

• Alternatively, where labour can be increased at least by one unit (MPL) can be obtained as

MPL = TPL - TPL-1

• Average Productivity of Labour (APL) can be obtained by dividing the production function by L. Thus,

10151015 2

23

++−=++−= LLL

LLLAPL

No of Workers (N)

Total Product (TPL) (tones)

Marginal Product* (MPL)

Average product (APL)

Stages of production(based on

MPL)

1 2 3 4 5

123456

2472138216300384

244866788484

243646546064

IIncreasing

returns

78910

462528576600

78664824

66666460

IIDiminishing

Returns

1112

594552

-6-42

5446

IIINegative returns

SHORT-RUN THEORY OF PRODUCTIONSHORT-RUN THEORY OF PRODUCTION

• Long-run and short-run production: – fixed and variable factors

• The law of diminishing returns

• The short-run production function:– total physical product (TPP)– average physical product (APP)– marginal physical product (MPP)– the graphical relationship between TPP, APP and MPP

Wheat production per year from a particular farm (tonnes)Wheat production per year from a particular farm (tonnes)

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Wheat production per year from a particular farm

Number of farm workers

Tonn

es o

f whe

at p

rodu

ced

per y

ear

Number of workers 012345678

TPP 0 310243640424240

Wheat production per year from a particular farm

0

10

20

30

40

0 1 2 3 4 5 6 7 8Number of farm workers

Tonn

es o

f whe

at p

rodu

ced

per y

ear

TPP

Wheat production per year from a particular farm

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Number of farm workers

Tonn

es o

f whe

at p

rodu

ced

per y

ear

TPP

a

b

Diminishing returnsset in here

Wheat production per year from a particular farm

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Number of farm workers

Tonn

es o

f whe

at p

rodu

ced

per y

ear

TPP

a

b

d

Maximum output

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Wheat production per year from a particular farm

Number offarm workers (L)

Tonn

es o

f whe

at p

er y

ear

TPP

-2

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8

Tonn

es o

f whe

at p

er y

ear

Number offarm workers (L)

∆TPP = 7

∆L = 1

MPP = ∆TPP / ∆L = 7

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Wheat production per year from a particular farm

Tonn

es o

f whe

at p

er y

ear

TPP

-2

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8

Tonn

es o

f whe

at p

er y

ear

MPP

Number offarm workers (L)

Number offarm workers (L)

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Wheat production per year from a particular farm

Tonn

es o

f whe

at p

er y

ear

TPP

-2

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8

Tonn

es o

f whe

at p

er y

ear

APP

MPP

APP = TPP / L

Number offarm workers (L)

Number offarm workers (L)

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Wheat production per year from a particular farm

Tonn

es o

f whe

at p

er y

ear

TPP

-2

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8

Tonn

es o

f whe

at p

er y

ear

APP

MPP

b

Diminishing returnsset in here

Number offarm workers (L)

Number offarm workers (L)

b

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Wheat production per year from a particular farm

Tonn

es o

f whe

at p

er y

ear

TPP

-2

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8

Tonn

es o

f whe

at p

er y

ear

APP

MPP

b

d

d

Number offarm workers (L)

Number offarm workers (L)

Maximumoutputb

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Wheat production per year from a particular farm

Tonn

es o

f whe

at p

er y

ear

TPP

-2

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8

Tonn

es o

f whe

at p

er y

ear

APP

MPP

b

b

d

d

Number offarm workers (L)

Number offarm workers (L)

Slope = TPP / L= APP

c

c

Iso-quants

An iso-quant is a curve or line that has various combinations of inputs that yield the same amount of output.

Production function

•Here we will assume output is made with the inputs capital and labor. K = amount of capital used and L = amount of labor.

•The production function is written in general as Q = F(K, L) – sometimes we put a y instead of Q, where Q = output, and F and the parentheses are general symbols that mean output is a function of capital and labor.

•The output, Q, from the production function is the maximum output that can be obtained form the inputs.

•On the next screen we will see some isoquants.

Note: on a given curve L and K change while Q is fixed.

ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS

• Iso-quants– their shape

– diminishing marginal rate of substitution

– isoquants and returns to scale

– isoquants and marginal returns

• Iso-costs– slope and position of the isocost

– shifts in the isocost

Unitsof K402010 6 4

Unitsof L 512203050

Point ondiagramabcde

a

Units of labour (L)

Uni

ts o

f cap

ital (

K)An isoquant

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45 50

Unitsof K402010 6 4

Unitsof L 512203050

Point ondiagramabcde

a

b

Units of labour (L)

Uni

ts o

f cap

ital (

K)An isoquant

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45 50

An isoquant

Unitsof K402010 6 4

Unitsof L 512203050

Point ondiagramabcde

a

b

c

de

Units of labour (L)

Uni

ts o

f cap

ital (

K)

0

5

10

15

20

25

30

35

40

45

0 5 10 15 20 25 30 35 40 45 50

MRTS

• The slope of the isoquant defines the substitutability between two factors of inputs (capital and labor).

• This is known as the marginal rate of technical substitution (MRTS) and is presented mathematically as:

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20 22

Uni

ts o

f cap

ital (

K)

Units of labour (L)

g

h∆K = 2

∆L = 1

isoquant

MRS = 2 MRS = ∆K / ∆L

Diminishing marginal rate of factor substitution

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12 14 16 18 20

Uni

ts o

f cap

ital (

K)

Units of labour (L)

g

h

j

k

∆K = 2

∆L = 1

∆K = 1

∆L = 1

Diminishing marginal rate of factor substitution

isoquant

MRS = 2

MRS = 1

MRS = ∆K / ∆L

0

10

20

30

0 10 20

An isoquant mapU

nits

of c

apita

l (K)

Units of labour (L)

I1

0

10

20

30

0 10 20

I2

Uni

ts o

f cap

ital (

K)

Units of labour (L)

An isoquant map

I1

0

10

20

30

0 10 20

I2

I3

Uni

ts o

f cap

ital (

K)

Units of labour (L)

An isoquant map

I1

0

10

20

30

0 10 20

I2

I3

I4

Uni

ts o

f cap

ital (

K)

Units of labour (L)

An isoquant map

I1

0

10

20

30

0 10 20

I1

I2

I3

I4

I5

Uni

ts o

f cap

ital (

K)

Units of labour (L)

An isoquant map

• Assume that there are two resources, Labor (L) and Capital (K).

• The money payments to these resources are Wages (W) and Rent (R).

• An isocost line is similar to the budget line. It’s a set of points with the same cost, C. Let’s plot K on the y axis and L on the x axis.

WL + RK = C; solve for K by first subtracting WL from both sides.RK = C - WL; next divide both sides by R.K = C/R – (W/R)L; note that C/R is the y intercept and W/R is the slope.

A Cost Function: Two Resources

C/R

C/W

Absolute value of slope equalsThe relative price of Labor, W/R.

K (machines rented)

Labor hours used in production

An isocost line

Bundles of: Labor Machine rental with C = Rs30 (Rs6 per labor hour) (Rs3 per machine hour)

a 0 10

b 1 8

c 2 6

d 3 4

e 4 2

f 5 0

A Numerical Example

Points a through f lie on the isocost line for C = Rs30/hour.

The Isocost Line

0 1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

Labor, L (worker-hours employed)

Cap

ital,

K (

mac

hine

s re

nted

)

a

b

c

d

e

f

The Isocost Line

• Wage-rental ratio– With K on the y axis and L on the x axis, the slope of any

isocost line equals W/R, the wage-rental ratio. It is also the relative price of labor.

• The y-intercept shows the number of units of K that could be rented for Rs.C.

• The x-intercept shows the number of units of L that could be hired for Rs.C.

Changes in One Resource Price

0 1 2 3 4 5 6 7 8 9 10

Cap

ital,

K (

mac

hine

s re

nted

)

2

4

6

8

10

Labor, L (worker-hours employed)

a

f

Cost = Rs30; R = Rs3/machineThe money wage, W = ...

…Rs6

…Rs10

A Change in W

h

Changes in Cost

0 1 2 3 4 5 6 7 8 9 10

Cap

ital,

K (

mac

hine

s re

nted

)

2

4

6

8

10

Labor, L (worker-hours employed)

g

h

A Change in Cost; every pointbetween g and h costs Rs18.

W = Rs6; R = Rs3;C = Rs30

Cost Minimization

0 1 2 3 4 5 6 7 8 9 10

Cap

ital,

K (

mac

hine

s re

nted

)

2

4

6

8

10

Labor, L (worker-hours employed)

a

equ.W = Rs6; R = Rs3;C = Rs30

Choose the recipe where thedesired isoquant is tangent tothe lowest isocost.

C = Rs18

12

C = Rs36

Conclusion: Buy resources such that the last dollar spent on K adds the same amount to output as the last dollar spent on L.

• The |slope| of the isocost line = W/R.

• The |slope| of the isoquant = MPL/MPK

– This will be demonstrated on the board.

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40

An isocost

Units of labour (L)

Uni

ts o

f cap

ital (

K)

Assumptions

PK = Rs20 000 W = Rs10 000TC = Rs300 000

TC = Rs300 000

a

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40

Units of labour (L)

Uni

ts o

f cap

ital (

K)

TC = Rs300 000

a

b

Assumptions

PK = Rs20 000 W = Rs10 000TC = Rs300 000

An isocost

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40

Units of labour (L)

Uni

ts o

f cap

ital (

K)

TC = Rs300 000

a

b

c

Assumptions

PK = Rs20 000 W = Rs10 000TC = Rs300 000

An isocost

0

5

10

15

20

25

30

0 5 10 15 20 25 30 35 40

Units of labour (L)

Uni

ts o

f cap

ital (

K)

TC = Rs300 000

a

b

c

d

Assumptions

PK = Rs20 000 W = Rs10 000TC = Rs300 000

An isocost

ISOQUANT- ISOCOST ANALYSISISOQUANT- ISOCOST ANALYSIS

• Least-cost combination of factors for a given output

– point of tangency

– comparison with marginal productivity approach

• Highest output for a given cost of production

0

5

10

15

20

25

30

35

0 10 20 30 40 50

Finding the least-cost method of production

Units of labour (L)

Uni

ts o

f cap

ital (

K)

Assumptions

PK = Rs20 000W = Rs10 000

TC = Rs200 000

TC = Rs300 000

TC = Rs400 000

TC = Rs500 000

0

5

10

15

20

25

30

35

0 10 20 30 40 50

Units of labour (L)

Uni

ts o

f cap

ital (

K)Finding the least-cost method of production

TPP1

0

5

10

15

20

25

30

35

0 10 20 30 40 50

Units of labour (L)

Uni

ts o

f cap

ital (

K)Finding the least-cost method of production

TC = Rs400 000r

TPP1

0

5

10

15

20

25

30

35

0 10 20 30 40 50

Units of labour (L)

Uni

ts o

f cap

ital (

K)Finding the least-cost method of production

TC = Rs400 000

TC = Rs500 000s

r

tTPP1

Finding the maximum output for a given total cost

TPP1

TPP2

TPP3

TPP4

TPP5

Uni

ts o

f cap

ital (

K)

Units of labour (L)

O

O

Isocost

Uni

ts o

f cap

ital (

K)

Units of labour (L)

TPP1

TPP2

TPP3

TPP4

TPP5

Finding the maximum output for a given total cost

O

r

v

Uni

ts o

f cap

ital (

K)

Units of labour (L)

TPP1

TPP2

TPP3

TPP4

TPP5

Finding the maximum output for a given total cost

O

s

u

Uni

ts o

f cap

ital (

K)

Units of labour (L)

TPP1

TPP2

TPP3

TPP4

TPP5

r

v

Finding the maximum output for a given total cost

O

t

Uni

ts o

f cap

ital (

K)

Units of labour (L)

TPP1

TPP2

TPP3

TPP4

TPP5

r

v

s

u

Finding the maximum output for a given total cost

O

K1

L1

Uni

ts o

f cap

ital (

K)

Units of labour (L)

TPP1

TPP2

TPP3

TPP4

TPP5

r

v

s

u

t

Finding the maximum output for a given total cost

Properties of Iso-Quant

• An isoquant has a negative slope in the economic region and in the economic range of isoquant.

• Economic region is also known as the product maximizing region.

• The negative slope of the isoquant implies substitutability between the inputs.

• It means that if one of the inputs is reduced, the other input has to be so increased that the total output remains unaffected.

• Isoquants are convex to the origin Convexity of isoquants implies two things.

I) substitution between the two inputs, and

II) diminishing marginal rate of technical substitution (MRTS) between the inputs in the economic region.

III)The MRTS is defined as, = slope of the isoquant.

IV)MRTS is the rate at which a marginal unit of labour can substitute a marginal unit of capital (moving downward on the isoquant) without affecting the total output.

ΔL

ΔKMRTSLK

−=

• This rate is indicated by the slope of the isoquant.

• The MRTS decreases for two reason:

i) no factor is a perfect substitute for another, and

ii)inputs are subject to diminishing marginal returns.

Therefore, more and more units of an input are needed to replace each successive unit of the other input.

• the corresponding units of L substituting K go (in fig.) on increasing i.e.

• As a result, MRTS = goes on decreasing i.e.,

•

321 ΔΔΔ LLL <<

321 ΔKΔKΔK ==

L

K

∆∆

• Isoquants are non-intersecting and non-tangential. This implies that in terms of output.

L1

Q2 = 200

Q1 = 200

L2

O

K

M

Capital (K)

Labour (L)

Fig. Intersecting Isoquants

J

(K)KL(L)OL(K)JL(L)OL 2222 +=+

• Since OL2 is common to both the sides, it means,

J L2 (K) = K L2 (K)

But it can be seen in fig that J L2 < K L2(K)but the intersection of the two isoquants means that JL2 and KL2 are equal in terms of isoquants will not intersect or be tangent to each other.

Upper isoquants represent higher level

of output.

b

a

IQ2 = 200

IQ1 = 200

XO

Quality of K

Quality of L

Fig. Comparison of Output at Two Isoquaqnts

c

Economic region

Q1

Upper ridge line

Lower ridge line

f

g

h

a

b

c

d

Q3

Q2

Q4

Capital (K)

Labour (L)

o

Economic region is that area of production plane in which substitution between two inputs is technically feasible without affecting the output.

This area is marked by locating the points on the isoquants at which MRTS = 0.

A zero MRTS implies that further substitution between inputs is technically not feasible.

It also determines the minimum quantity of an input that must be used to production a given output.

Beyond this point, an additional employment of one input will necessitates employing additional units of the other input.

• By joining the resulting points a, b, c and d we get a line called the upper ridge line, Od, similarly by joining the points e, f, f and h we get the lower ridge line, Oh.

• The ridge lines are locus of points on the isoquants where the marginal products (MP) of the inputs are equal to zero.

• The upper ridge line implies that MP of capital is zero along the line, Od. The lower ridge line implies that MP of labour is zero along the line, Oh.

• The area between the two ridge lines, Od, and Oh, is called ‘Economic Region’ or technically efficient region of production.

Upper ridge line

Lower ridge line

f

g

h

a

b

c

d

Q3

Q2

Q4

Capital (K)

Labour (L)

o

The laws of returns to scale

• The laws of returns to scale explain the behavior of output in response to a proportional and simultaneous change in inputs, increasing inputs proportionately and simultaneously is, in fact, an expansion of the scale of production.

Three technical possibilities

• Total output may increase more than proportionately.

• Total output may increase proportionately and

• Total output may increase less than proportionately

kinds of returns to scale

• Increasing returns to scale;

• Constant returns to scale, and

• Diminishing returns to scale.

Increasing returns to scale• When inputs, K and L are increased at a

certain proportion and output increase more than proportionately, it exhibits increasing returns to scale.

• The increasing returns to scale is illustrated in fig.

Increasing returns to scale

Product lines

Q = 50

Q = 25

Q = 10

B

C

c

b

a

4K

3K

2K

1K

1L 2L 3L 4L Labour (L)

Fig. Increasing Returns to Scale

The movement from point a to b on the line OB means doubling the inputs.

It can be seen in fig that input combination increases from 1K + 1L to 2K + 2L.

As a result of doubling the inputs, output is more than doubled; it increases from 10 to 25 units e.g. an increase of 150%.

Similarly, the movement from point b to point c indicates 50% increase in inputs as a result of which the output increases from 25 units to 50 units i.e. by 100%. O

Capital (K)

Economies of scale

• The scale of production has an very important bearing on the cost of production.

• It is the manufacturer’s common experience that larger the scale of production, the lower generally is the average cost of production.

• That is why the entrepreneur is tempted to enlarge the scale of production so that he benefit from the resulting economies of scale.

• There are two types of Internal and External Economies.

Internal Economies of Scale• These are those economies in production, those in

production costs, which accrue to the firm itself when it expands its output or enlarges its scale of production.

• The internal economies arise within a firm as a result of its own expansion of the industry.

• The internal economies are simply due to the increase in the scale of production.

• They arise from the use of the methods which small firms do not find it worthwhile to employ.

Three reasons for increasing returns to scale

• Technical and managerial indivisibilities: Certain inputs, particularly mechanical equipments and

managers, used in the process of production are available in a given size.

Such inputs cannot be divided into parts to suit small scale of production.

Because of indivisibility of machinery and managers, given the state of technology, they have to be employed in a minimum quantity even if scale of production is much less than the capacity output.

Therefore, when scale of production is expanded by increasing all the inputs, the productivity of indivisible factors increases exponentially because of technological advantage. This results in increasing returns to scale.

Internal Economies• Labour Economies: Division of Labour, this will increase the

efficiency, saves time and promote skill information.

• Technical economies: Modern machinery.

• Marketing Economies: Buying inputs at large qty when it expands the output. Small firms are deprived of these benefits.

The cost of marketing the product is also reduced providing thereby the economies of large scale transportation.

Per unit advertisement cost is reduced.

• Higher degree of specialization (Managerial economies) The use of specialized labour suitable to a particular job and

of a composite machinery increases productivity of both labour and capital per unit of inputs.

• Financial economies: The finance will be available at competitive rate and at easy terms. Can also raise money from the market, because of its goodwill.

• Risk Bearing Economies: Can diversify the risk by selling products in different parts of the world.

• Dimensional relationsFor example, when the length and breadth of a

room (15’ x 10’ =- 150 Sq. ft.) are doubled then the size of the room is more than doubled; it increases to 30’ x 20’ = 600 sq. ft.

In accordance with this dimensional relationship, when the labour and capital are doubled, the output is more than doubled and so on.

External Economies

• These are those economies which accrue to each member firm as a result of the expansion of the industry as a whole.

External Economies• Availability of raw-material and machineries at lower price: Expansion of

the industry may results in the availability of inputs like raw-material and other equipments at lower prices.

• Technical external economies: Since the growth of industry enables the firm to use the new technical know-how employing thereby improved machinery and other inputs.

• Development of Skill labour: By training and development of the industry.

• The growth of subsidiary industry: Will supply the raw-material.

• Transport and marketing facilities:

• Information Service: Will disseminate information, technical knowledge and R and D

Constant returns to scale

• When the increase in output is proportionate to the increase in inputs it exhibits constant returns to scale.

Fig. Constant Return to Scale

Capital (K)

1011 ⇒+ LK

2022 ⇒+ LK

3033 ⇒+ LK

Product lines

Q = 30

Q = 20

Q = 10

B

c

b

a

4K

3K

2K

1K

1L 2L 3L 4L Labour (L)

Decreasing Return to Scale

• When economies of scale reach their limits and diseconomies are yet to begin, returns to scale become constant.

• For example, doubling of coal mining plant may not double the coal deposits.

• Similarly doubling the fishing fleet may not double the fish output because availability of fish may decrease in the ocean when fishing is carried out on an increased scale.

Product lines

Labour (L)

Fig. Decreasing Return to Scale Scale

Q = 24

Q = 18

Q = 10

B

C

4K

3K

2K

1K

1L 2L 3L 4L

Capital (K)

Decreasing Return to Scale

c

b

a

INTERNAL DISECONOMIES

• Large scale production firms faces a problem of management and control over the production unit.

• Lack of proper coordination and supervision of different departments.

• So growth of the firm beyond the limit will bring more problems.

• The increase in the scale of output beyond its optimum size creates the managerial structure inflexible and cumbersome which ultimately reduces efficiency of the management

External Diseconomies

• Constraints in the Supply of raw-material.

• Demand for labour will increase due to growth of industry.

• Instabilities of demand for the product

Economies of Scope

• When the cost efficiencies in production allow the firm to produce a variety of products rather than a single product in large volume, it can be referred to the Economies of Scope.

• This allows product diversification in the same scale of plant and with the same technology.

Returns to Scale (Summary)• Increasing returns to scale

– When the % change in output > % change in inputs

• E.g. a 30% rise in factor inputs leads to a 50% rise in output

– Long run average total cost will be falling

• Decreasing returns to scale – When the % change in output < % change in inputs

• E.g when a 60% rise in factor inputs raises output by only 20%

– Long run average total cost will be rising

• Constant returns to scale – When the % change in output = % change in inputs

– E.g when a 10% increase in all factor inputs leads to a 10% rise in total output

– Long run average total cost will be constant

Consumer Surplus

• The concept was formulated by Dupuit in 1844 to measure the social benefits of Public goods such as canals, bridges, national highways etc,

• Marshall further popularized the concept

• The concept was based on cardinal measurability and interpersonal comparison of utility

Concept or Defination

• It is simply the difference between ‘the price that one is willing to pay’ and the ‘price one actually pays pays’ for a particular product.

• It is also used in policy formulation by government and price policy purchased by the monopolistic seller of a product.

• People generally get more utility from the consumption of goods than the price they actually pay for them.

• This extra satisfaction which the consumer obtains from buying a good is called as consumer surplus.

• The amount of money which a person is willing to pay for a good indicates the amount of utility he derives from that good.

• Marginal utility of a unit of a good determines the price a consumer will be prepared to pay for that unit.

• The total utility which a person gets from a good is given by the sum of marginal utilities ( ∑ MU) of the units of a good purchased.

• The total price the consumer actually pays is equal to the price per unit of the good multiplied by the number of units of it purchased.

• Consumer’s surplus = ∑ MU – (Price * No. of units of a commodity purchased.)

Consumer Surplus and DMU• The concept of consumer surplus is derived from the law of

diminishing marginal utility.

• As the consumer purchase more units of a good its MU diminishes and the consumer’s willingness to pay for additional units of commodity declines.

• The consumer is in equilibrium when MU from a commodity becomes equal too its price.

• That is consumer purchases the number of units of commodity at which MU equals price.

• This means willingness to pay and actually pays are equal but rest previous units there is a consumer surplus.

• But for the previous units customer’s willingness to is greater than the price he actually pays for them.

• Because the price of all units are same.

Consumer Surplus• It measures extra utility or satisfaction which a

consumer obtains from the consumption of a certain amount of a commodity over and above the utility of its market value.

• The total utility obtained from consuming water is immense while its market value is negligible.

• It is due to the occurrence of DMU that a consumer gets total utility from the consumption of a commodity greater than its market value

• Marshall tried to obtain the monetary measure of this surplus, i.e. how many rupees this surplus of utility is worth to consumer.

• It is the monetary value of this surplus that Marshall called Consumer surplus.

Determine Monetary value of Surplus

• Total utility of money in terms of money that consumer expects to get from consumption of a certain amount of commodity.

• The total market value of the amount of commodity consumed by him.

• It is easy to find out market value i.e. P*Q

Marginal Utility and Consumer Surplus

No. of Units

Marginal Utility

Price Net Marginal Benefit

1 20 12 82 18 12 63 16 12 44 14 12 25 12 12 06 10 12 -2

Consumer Surplus (from 5 Units) =

20

The consumer surplusof purchasing 5 units is the sum of thesurplus derived from each one individually.

Consumer Surplus 8 + 6 + 4 + 2 + 0 + -2 = 20

Consumer Surplus - Example

Price of X

Price (Rs)

2 3 4 5 6

13

0 1

14

10

12

14

16

18

20

Market Price

Will not buy more than 5 because surplus from additional units is negative

Consumer SurplusThe stepladder demand curve can be converted into a

straight-line demand curve by making the units of the good smaller.

Consumer surplus measures the total net benefit to consumers =

total benefits from consumption (-)the total expenses.

Thus, consumer surplus is area under the demand curve and above the price.

Note that the area under the demand curve up to the level of consumption measures the total benefits.

Demand Curve

ConsumerSurplus

Consumer Surplus

Price of X

Price (Rs.)

2 3 4 5 60 1

ActualExpenditure

12

20

Market Price

Consumer Surplus and Market Price

A lower market price will usually increase consumer surplus.

A higher market price will usually reduce consumer surplus.

Consumer surplus will be smaller when the demand curve is more elastic and larger when the demand curve is inelastic.

How the Price Affects Consumer Surplus?

Initialconsumer

surplus

Quantity

Consumer Surplus at Price P2 vs. at Price P1

Price

0

Demand

A

BC

D EF

P1

Q1

P2

Q2

Consumer surplusto new consumers

Additional consumersurplus to initial consumers

Consumer Surplus

Price

Quantity

D

Po

Qo

Maximum Willingness to Pay for Qo

What is paid

Consumer Surplus

Original Consumer Surplus

Change in Consumer Surplus: Price Increase

Quantity

New Consumer Surplus

Loss in Surplus: Consumers paying more

Loss in Surplus: Consumers buying less

Price

D

Po

Qo

P1

Q1

PRODUCER SURPLUS

• The revenue that producers obtain from a good over and above the price paid.

• This is the difference between the minimum supply price that sellers are willing to accept and the price that they actually receive.

• A related notion from the demand side of the market is consumer surplus.

• Producers' surplus is the extra revenue received when selling a good.

• The supply price is less than the price actually received.

• Most producers under most circumstances receive some surplus of revenue.

• Even competitive markets overflowing with efficiency generate an ample amount of producer surplus.

Producer Surplus

• The amount a seller is paid , minus the seller’s cost.

• It is the area above the supply curve, and below the equilibrium price.

Minimum Amount Needed to Supply Qo

Producer Surplus

Price

Quantity

Po

Qo

What is paid

Producer Surplus

S

Consumer and Producer Surplus

Price

Quantity

Po

Qo

S

Producer Surplus

Consumer Surplus

D

The magic of perfectly competitive markets

• At equilibrium, both consumer and producer surplus are at their maximum

• Any interference with the equilibrium price in perfectly competitive markets will reduce total consumer and producer surplus

Cost

• By "Cost of Production" is meant the total sum of money required for the production of a specific quantity of output. In the word of Gulhrie and Wallace:

• "In Economics, cost of production has a special meaning.

• It is all of the payments or expenditures necessary to obtain the factors of production of land, labor, capital and management required to produce a commodity.

• It represents money costs which we want to incur in order to acquire the factors of production".

Cost of Production

• The following elements are included in the cost of production:

(a) Purchase of raw machinery, (b) Installation of plant and machinery,(c) Wages of labor, (d) Rent of Building,(e) Interest on capital, (f) Wear and tear of the machinery and building, (g) Advertisement expenses, (h) Insurance charges, (i) Payment of taxes,(j) In the cost of production, the imputed value of the factor of

production owned by the firm itself is also added,(k) The normal profit of the entrepreneur is also included In the cost of

production.

FIXED, VARIABLE, AND INCREMENTAL COSTS

• Fixed costs: unaffected by changes in activity level over a feasible range of operations for the capacity or capability available.

• Typical fixed costs include:

insurance and taxes on facilitiesgeneral management and administrative salaries license fees interest costs on borrowed capital.

• Fixed costs will be affected When: large changes in usage of resources occurplant expansion or shutdown is involved

FIXED, VARIABLE AND INCREMENTAL COSTS

• Variable costs: associated with an operation that vary in total with the quantity of output or other measures of activity level.

• Example of variable costs include :

Costs of material and labor used in a product or service.

FIXED,VARIABLE AND INCREMENTAL COSTS

• Incremental cost: additional cost that results from increasing output of a system by one (or more) units.

• Incremental cost is often associated with “go / no go” decisions that involve a limited change in output or activity level.

• A very simple example of incremental cost would be a factory producing widgets where it takes one employee an hour to produce one widget.

• the incremental cost of a widget would include the wages for an hour in addition to the cost of materials used in production of a widget.

• A more exact figure could comprise added costs, like electricity consumed if the factory had to stay open for a longer duration, or the cost for shipping the additional widget to a consumer.

SUNK COST AND OPPORTUNITY COST

• A sunk cost is one that has occurred in the past and has no relevance to estimates of future costs and revenues related to an alternative course of action;

• Example : Product Research• Companies spend money each year for research and development as

they work to come up with new products and services.

• While the nature of research varies from business to business,

• It's recognized as a sunk cost, since once the money is spent on conducting a focus group or administering a survey, it's gone.

Opportunity cost

• An opportunity cost is the cost of the best rejected ( i.e., foregone ) opportunity and is hidden or implied;

What is opportunity cost?

• Andy had $65.00 to spend at the toy store. The basketball net cost $50.00, so he had to buy that instead of the skateboard, which cost $75.00.

• Sara had enough money for either the rabbit or the bike. She decided to buy the bike because then she could ride bikes with her friends after school.

• Opportunity cost is

the process of choosing one good or service over another. The item that you don’t pick is the opportunity cost. The rabbit is Sara’s opportunity cost and the skateboard is Andy’s opportunity cost.

Opportunity Costs

Purchases

Social Cost

• Building a new railway $100 million• Creating pollution nearby (e.g. cutting trees,

noises) $5 million• Social cost of building highway• = private cost + external cost • = $105 million

Historical Costs and Replacement Costs.

• Historical cost or original costs of an asset refers to the original price paid by the management to purchase it in the past.

• Whereas replacement costs refers to the cost that a firm incurs to replace or acquire the same asset now.

• The distinction between the historical cost and the replacement cost result from the changes of prices over time.

• In conventional financial accounts, the value of an asset is shown at their historical costs but in decision-making the firm needs to adjust them to reflect price level changes.

• Example: If a firm acquires a machine for $20,000 in the year 1990 and the same machine costs $40,000 now. The amount $20,000 is the historical cost and the amount $40,000 is the replacement cost.

Money Cost• Money Cost of production is the actual monetary

expenditure made by company in the production process.

• Money cost thus includes all the business expenses which involve outlay of money to support business operations.

• For example the monetary expenditure on purchase of raw material, payment of wages and salaries, payment of rent and other charges of business etc can be termed as Money Cost.

Real Cost

• Real Cost of production or business operation on the other hand includes all such expenses/costs of business which may or may not involve actual monetary expenditure.

• For example if owner of a business venture uses his personal land and building for running the business venture and

• He/she does not charge any rent for the same then such head will not be considered/included while computing the Money Cost but this head will be part of Real Cost computation.

Accounting Cost

• Accounting Cost includes all such business expenses that are recorded in the book of accounts of a business firm as acceptable business expenses.

• Such expenses include expenses like Cost of Raw Material, Wages and Salaries, Various Direct and Indirect business Overheads, Depreciation, Taxes etc.

• When such business expenses or accounting expenses are deducted from the Sales income of any firm the accounting profit is obtained.

• Such Accounting/Business expenses or costs are also termed as Explicit Costs.

• Accounting Cost: Various allowed business expenses.

• Such as Cost of Raw Material, Salaries and Wages, Electricity Bill, Telephone Charges, Various Administrative Expenses, Selling and Distribution Expenses, Production Overhead Expenses, Other Indirect Overhead Expenses etc.

• Accounting Profit = Sales Income - Accounting Cost

Economic Cost• Economic Cost on the other hand includes all the

accounting expenses as well as the Opportunity cost of a business firm.

• Economic Cost and Economic Profit is thus calculated as follows:

• Economic Cost = Accounting Cost (Explicit Costs) + Opportunity Cost.

• Economic Profit = Total Revenues - (Accounting Cost +

Opportunity Cost)

Private Cost and Social Cost• The actual expenses of individuals/ firms which are borne

or paid out by the individual or a firm can be termed as Private Cost.

• Thus for a business firm this may include expenses like Cost of Raw Material, Salaries and Wages, Rent, Various Overhead Expenses etc.

• On the other hand Private Cost for an individual will be his or her private expenses such as expense on food, rent of house, expenses on clothing, expenses on travel, expenses on entertainment etc.

Social Cost• Social Cost on the other hand includes Private Cost and also such

costs which are not borne by the firm but by the society at large.

• Such Cost (that is cost not borne or paid out by the firm) is also known as External Cost.

• Another example of external cost can be the cost of providing the basic infrastructure facilities like good roads, sewage system or network, street lights etc.

Cost Concepts

I. Total Costs (TC)I. Total Costs (TC)

— whatever total cost is for any level of output

— sum of all costs

Two Sub-Components:Two Sub-Components:

(A)Total Fixed Costs — TFC (Overhead Costs)

— do not vary with output

— come from fixed inputs

(B) Total Variable Costs — TVC

— vary with output

— come from variable inputs

Note: TC = TFC + TVC

Understanding Fixed, Variable, Total cost

Number of Units Produced

Fixed Cost

Variable Cost

Total Cost

1 10 5 15

2 10 10 20

3 10 17 27

4 10 30 40

5 10 45 55

Cost Concepts

Cost(Rs)Cost(Rs)

Output (or TP or Output (or TP or Q)Q)

Graph of Total Cost Concepts

TC

TVC

TFC

(TFC)

0

10

20

30

40

0 1 2 3 4 5 6 7 8

Wheat production per year from a particular farm

Tonn

es o

f whe

at p

er y

ear

TPP

-2

0

2

4

6

8

10

12

14

0 1 2 3 4 5 6 7 8

Tonn

es o

f whe

at p

er y

ear

APP

MPP

b

b

d

d

Number offarm workers (L)

Number offarm workers (L)

Slope = TPP / L= APP

c

c

Cost Concepts

II. Average Total Costs (ATC) II. Average Total Costs (ATC) – Total Cost Per Unit of Output

Two Sub-Components:Two Sub-Components:

Q

TCATC =

(A) Average Fixed Cost: Q

TFCAFC =

(B) Average Variable Cost: Q

TVCAVC =

TwoAverageCosts!!

Note: ATC = AFC + AVC

Cost Concepts

III. Marginal Costs (MC) :III. Marginal Costs (MC) : Increase in Total Cost that results from an increase in output

Q

TCMC

∆∆=

The Short Run Cost Function

• Add ATC = AFC + AVC to the table

The Short Run Cost Function

• ATC = AFC + AVC

Cost Concepts

Cost(Rs)Cost(Rs)

OutputOutput

Graph of Average & Marginal Cost Concepts

AVC

AFC

ATCMC

Q2Q1

Cost Concepts

(1) When marginal is below average (1) When marginal is below average →→ average is falling. average is falling.

(2) When marginal is above average (2) When marginal is above average →→ average is rising. average is rising.

(3) When marginal is equal average (3) When marginal is equal average →→ average is at its lowest average is at its lowest

point.point.

Note : There is a certain correspondence between productNote : There is a certain correspondence between productconcepts and cost concepts.concepts and cost concepts.

Summary of Relationship Between Marginal Cost & Average Cost

When AVC is at its minimum, AP will be at its maximum.When AVC is at its minimum, AP will be at its maximum.

When MC is at a minimum, MP will be at its maximum.When MC is at a minimum, MP will be at its maximum.

(See diagram in book.)(See diagram in book.)

285

The Short Run Cost Function• Production cost graph or map is

The Short Run Cost Function

• Important Map Observations– AFC declines steadily over the range of

production. Why?

– In general, ATC is u-shaped. Why?

– MC intersects the minimum point (q*) on ATC. Why?

The Short Run Cost Function

• A change in input prices will shift the cost curves.

– If fixed input costs are reduced then ATC will shift downward. AVC and MC will remain unaffected.

Computer Chip Case

The Short Run Cost Function

• A change in input prices will shift the cost curves.

– If variable input costs are reduced then MC, AVC, and AC will all shift downward.

Airline Industry Case

Long-Run Average Cost Curve(No distinction between fixed and variable in Long-Run)

Total Costs per Total Costs per Unit(Rs)Unit(Rs)

(LRAC)(LRAC)

Q (Output)Q (Output)

Plots the relationship between the lowest attainable Average Cost and output when both capital (or plant size) and labor can be varied.

LRAC

0

C1

Q1

C2

Q2

Attainable Attainable CostsCosts

Unattainable Unattainable CostsCosts

Relationship Between SATC & LRAC

Short-Run & Long-Run Costs

Average Average Costs per Costs per Unit (Rs) Unit (Rs)

Q (Output)Q (Output)0

SATC

1

SATC

2

SATC

3

LRAC

LMC

SMC

1

Relationship Between SATC & LRAC

Short-Run & Long-Run Costs

Average Average Costs per Costs per Unit (Rs)Unit (Rs)

Q (Output)Q (Output)0

LRAC

X

Xmin

X

X = minimum pointX = minimum point

Long-Run Average Cost Curve

Slope of LRAC

Costs per Costs per UnitUnit

Q Q (Output)(Output)

LRAC

0 Qm

0 to Qm: Economies of Scale Qm Rightward: Diseconomies of Scale

* Q* Qmm is the most efficient point – doubly efficient: is the most efficient point – doubly efficient:

(1) It represents the lowest possible costs for its production level (like all points on LRAC curve).

(2) It is the output level that has absolutely lowest costs of all output levels.

Other Possible Shapes for LRAC

Constant Returns to Scale : LRAC curve is horizontal

Average Average Cost per Cost per Unit (Rs)Unit (Rs)

Q Q (Output)(Output)

LRAC

0

Average Average Cost per Cost per Unit (Rs)Unit (Rs)

Q Q (Output)(Output)

LRAC

0

OROR

Doubling Input spending always leads to a doubling of

output.

Other Possible Shapes for LRAC

Continually Decreasing Costs

Average Average Cost per Cost per Unit (Rs)Unit (Rs)

Q Q (Output)(Output)

LRAC

0

Decreasing Cost!!!

Minimum Efficient Scale

Definition :

The smallest quantity of output at which long-run average cost reaches its lowest level.

A Perfectly Competitive Market

• For a market to be perfectly competitive, six conditions must be met:

1. Both buyers and sellers are price takers – a price taker is a firm or individual who takes the price determined by market supply and demand as given

2. The number of firms is large – any one firm’s output compared to the market output is imperceptible and what one firm does has no influence on other firms

• A perfectly competitive market is a market in which economic forces operate unimpeded

A Perfectly Competitive Market

3. There are no barriers to entry – barriers to entry are social, political, or economic impediments that prevent firms from entering a market.

3. Firms’ products are identical – this requirement means that each firm’s output is indistinguishable from any other firm’s output

4. There is complete information – all consumers know all about the market such as prices, products, and available technology

5. Selling firms are profit-maximizing entrepreneurial firms – firms must seek maximum profit and only profit

Total Revenue of a Competitive Firm

• Total revenue for a firm is the selling price times the quantity sold.

TR = P TR = P ×× Q Q

Average Revenue of a Competitive Firm

• Average revenue is the revenue per unit sold – P = AR.– This is simply because all units sold are sold at the

same price.

A v e r a g e R e v e n u e =T o t a l r e v e n u e

Q u a n t i t y

P r i c e Q u a n t i t y

Q u a n t i t y

P r i c e

= ×

=

Marginal Revenue of a Competitive Firm

• Marginal Revenue is the increase (Δ) in total revenue when an additional unit is sold.

MRMR = = ∆∆TRTR / / ∆∆QQ

Revenue of a Perfectly Competitive Firm

• Total Revenue: The amount of money received when the firm sells the product, i.e.,– Total Revenue = Price of the product × Quantity of the product sold

– TR = P × Q

• Since the firm is a price taker under perfect competition, it sells each additional unit of the product for the same price.

• Average Revenue = Total Revenue/Quantity sold– AR = TR/Q = P

• Marginal Revenue = Additional revenue earned from selling an additional unit of the product.– MR = ∂TR/∂Q = P

• Thus, for a competitive firm AR = P = MR

Total Revenue: P×Q

TP = Q P TR AR MR

0 3 0 0 0

10 3 30 3 3

25 3 75 3 3

50 3 150 3 3

70 3 210 3 3

85 3 255 3 3

95 3 285 3 3

100 3 300 3 3

101 3 303 3 3

95 3 285 3 3

85 3 255 3 3

The Revenue of a Competitive Firm

• In perfect competition, marginal revenue equals price: P = MR.

• We saw earlier that P = AR • Therefore, for all firms in perfect competition,

P = AR = MR

9.4 Profit Maximization (SR): TR and TC approach

What Is Perfect Competition?

– Figure illustrates a firm’s revenue concepts.– Part (a) shows that market demand and market

supply determine the market price that the firm must take.

What Is Perfect Competition?

– A perfectly competitive firm’s goal is to make maximum economic profit, given the constraints it faces.

– So the firm must decide:– 1. How to produce at minimum cost– 2. What quantity to produce– 3. Whether to enter or exit a market– We start by looking at the firm’s output decision.

Profit Maximization by the Competitive Firm: Approach I: Total Profit = TR – TC

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

0.00 20.00 40.00 60.00 80.00 100.00 120.00

Output

TC, TR, & Profit

TC TR

L TP = Q TR TC Profit

0 0 0 80 -80

1 10 30 105 -75

2 25 75 130 -55

3 50 150 155 -5

4 70 210 180 30

5 85 255 205 50

6 95 285 235 50

7 100 300 255 45

8 101 303 280 23

9 95 285 305 -20

10 85 255 330 -75

On the Diagram, the profit maximizing level of output is the level where the vertical difference between the TR and TC is the largest.

With P = Rs 3/unit, profits are maximized by producing 95 units of output.

The Firm’s Output Decision

• Profit-Maximizing Output– A perfectly competitive firm chooses the output

that maximizes its economic profit.– One way to find the profit-maximizing output is to

look at the firm’s the total revenue and total cost curves.

– Figure on the next slide looks at these curves along with the firm’s total profit curve.

The Firm’s Output Decision

– Part (a) shows the total revenue, TR, curve.

Part (a) also shows the total cost curve, TC, which is like the one in previous Slides.

Total revenue minus total cost is economic profit (or loss), shown by the curve EP in part (b).

The Firm’s Output Decision

– At low output levels, the firm incurs an economic loss—it can’t cover its fixed costs.

At intermediate output levels, the firm makes an economic profit.

The Firm’s Output Decision

– At high output levels, the firm again incurs an economic loss—now the firm faces steeply rising costs because of diminishing returns.

The firm maximizes its economic profit when it produces 9 sweaters a day.

Max Profit

Max Output

Profit Maximization by the Competitive Firm: Approach I: Total Profit = TR – TC

Input (L) TP (Q) AP (Q/L) MP TC TR Profit

0 0 0.00 80 0 -80

1 10 10.00 10 105 30 -75

2 25 12.50 15 130 75 -55

3 50 16.67 25 155 150 -5

4 70 17.50 20 180 210 30

5 85 17.00 15 205 255 50

6 95 15.83 10 235 285 50

7 100 14.29 5 255 300 45

8 101 12.63 1 280 303 23

9 95 10.55 -6 305 285 -20

10 85 8.50 -10 330 255 -75

Stag

e I

Stag

e II

Stag

e III

Profit Maximization by the Competitive Firm: Approach II: MR = MC

• Most managers do not make decisions looking at TR and TC. Most decisions are made at the “margin.”

• The output level that will maximize profit is determined by comparing the amount that each additional unit of output adds to TR and TC.

• Recall, Marginal Cost (MC) represents additional cost from producing an additional unit of output; and Marginal Revenue (MR) represents addition to TR from selling (producing) an additional (one more) unit of output, which is equal to the price of that output.

• Thus, MC and MR can be used to determine profit maximizing level of output.

Profit Maximization by the Competitive Firm: Approach II: MR = MC

• The firm will continue to expand production until MR is equal to MC, i.e., profit is maximized when MR = MC.

• With P being Rs 3/unit, profits are maximized by producing 95 units of output.

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0.00 20.00 40.00 60.00 80.00 100.00 120.00

Output

MR, MC, & Profit

MR MC

L Q TR MR TC MC Profit

0 0 0 80 -80

1 10 30 3 105 2.50 -75

2 25 75 3 130 1.67 -55

3 50 150 3 155 1.00 -5

4 70 210 3 180 1.25 30

5 85 255 3 205 1.67 50

6 95 285 3 235 3.00 55

7 100 300 3 255 5.00 45

8 101 303 3 280 25.0 23

9 95 285 3 305 -4.17 -20

10 85 255 3 330 -2.50 -75

The Firm’s Output Decision

• Marginal Analysis and Supply Decision– The firm can use marginal analysis to determine the

profit-maximizing output. – Because marginal revenue is constant and marginal

cost eventually increases as output increases, profit is maximized by producing the output at which marginal revenue, MR, equals marginal cost, MC.

– Figure on the next slide shows the marginal analysis that determines the profit-maximizing output.

The Firm’s Output Decision

– At high output levels, the firm again incurs an economic loss—now the firm faces steeply rising costs because of diminishing returns.

The firm maximizes its economic profit when it produces 9 sweaters a day.

The Firm’s Output Decision

– If MR > MC, economic profit increases if output increases.

If MR < MC, economic profit decreases if output increases.

If MR = MC, economic profit decreases if output changes in either direction, so economic profit is maximized.

Determining Profits Graphically: A Firm with Profit

AVC

MC

Q

P

ATC

Find output where MC = MR, this is the profit

maximizing Q

P = D = MR

MC = MR

Qprofit max

Find profit per unit where the profit max Q intersects ATC

ATC at Qprofit max

P

ATCProfits

Since P>ATC at the profit maximizing quantity, this firm is earning profits

Determining Profits Graphically: A Firm with Zero Profit or Losses

AVC

MC

Q

P

ATC

MC = MR

Qprofit max

ATC at Qprofit max

P =ATC

P = D = MR

Since P=ATC at the profit maximizing quantity,

this firm is earning zero profit or loss

Find output where MC = MR, this is the profit

maximizing Q

Find profit per unit where the profit max Q intersects ATC

Determining Profits Graphically: A Firm with Losses

AVC

MC

Q

P

ATC

MC = MR

Qprofit max

ATC at Qprofit max

P

ATC P = D = MR

Since P<ATC at the profit maximizing quantity,

this firm is earning losses

Find output where MC = MR, this is the profit

maximizing Q

Find profit per unit where the profit max Q intersects ATC

Losses

Determining Profits Graphically: The Shutdown Decision

AVC

MC

Q

P

ATC

Qprofit max

PShutdown

P = D = MR

• The shutdown point is the point below which the firm will be better off if it shuts down than it will if it stays in business

• If P>min of AVC, then the firm will still produce, but earn a loss

• If P<min of AVC, the firm will shut down

• If a firm shuts down, it still has to pay its fixed costs

Short-Run Market Supply and Demand

• The market (industry) supply curve is the horizontal sum of all the firms’ marginal cost curves

• While the firm’s demand curve is perfectly elastic, the industry’s demand curve is downward sloping

• The market supply curve takes into account any changes in input prices that might occur

ATCProfits

Short-Run Market Supply and Demand Graph

P

Q

Market Supply

P

Market Demand

P

Q

P P = D = MR

MC

ATC

Qprofit max

Market Firm

Long-Run Competitive Equilibrium

• Profits create incentives for new firms to enter, market supply will increase, and the price will fall until zero profits are made

• At long run equilibrium, economic profits are zero

• The existence of losses will cause firms to leave the industry, market supply will decrease, and the price will increase until losses are zero

Long-Run Competitive Equilibrium

• Normal profit is the amount the owners would have received in their next best alternative

• Zero profit does not mean that the entrepreneur does not get anything for his efforts

• Economic profits are profits above normal profits

Long-Run Competitive Equilibrium Graph

P

Q

P = D = MR

MC

SRATC

LRATC

At long-run equilibrium, economic profits are zero

SR Profits

Market Response to an Increase in Demand Graph

P

Q

S0(SR)

P0

D0

P

Q

P0

MC

ATC

Q0,2

Market Firm

S1(SR)

D1

P1

1

P11 1

Q1

2

2 2

Q0 Q1 Q2

1

1 22

S(LR)

Long-Run Market Supply

• If the long-run industry supply curve is upward sloping, the market is an increasing-cost industry

• If the long-run industry supply curve is perfectly elastic, the market is a constant-cost industry

• If the long-run industry supply curve is downward sloping, the market is a decreasing-cost industry

• In the short run, the price does more of the adjusting, and in the long run, more of the adjustment is done by quantity

Monopoly• Only one seller of a particular product

Characteristics of Monopoly

• Single Producer• No close substitute• Inelastic demand curve• Price Maker• Barriers to entry Legal restrictions or barriers to entry of other

firms Control over key raw material• Examples: Public utilities – telephones and

electricity etc.

Total Revenue

Price Quantity Total Revenue

6 0 0

5 1 5

4 2 8

3 3 9

2 4 8

1 5 5

0 6 0

Can you work out the demand, total revenue and marginal revenue functions from this information?

TR

PriceQ

Q

TR

Demand and Total Revenue

AR = D

0

0

63

3 6

9

6

3

Graph B

Graph A

D

TR

P,MR

Q

Q

Marginal Revenue

Q2MR

AR = D

AB

C

0

0Q1

A

C

Graph B

Graph A

X

TR

Profit Maximizing Output Decisionunder Monopoly in the Short-run

The Total Curves Approach

Profit maximization output decision rule for a monopolist depends on two considerations.

• One, whether there is any output level at which TR exceeds the TVC. If not, the profit maximizing strategy is to shut down.

• If there are output levels at which TR > TVC, the monopolist will produce where the vertical distance between TR and TC is at its maximum.

$TR

TC

TVC

Q

Profit Maximizing Output Decisionunder Monopoly in the Short-run

The Total Curves Approach

• In this case, the vertical distance between TR and TC is at maximum at the Q* level of output.

– Note that at Q* units of output, TR and TC curves have the same slope, i.e., MR = MC. (This is called the Necessary Condition of profit maximization)

– Further, the slope of MC exceeds that of the MR (MC has a positive slope and MR has a negative slope). (This is called the Sufficient Condition of profit maximization)

$TR

TC

TVC

QQ*

Output and Price Determination

LO2

Steps for Graphically Determining the Profit-Maximizing Output, Profit-Maximizing Price, and Economic Profits (if Any) in Pure Monopoly

Step 1 Determine the profit-maximizing output by finding where MR=MC.

Step 2Determine the profit-maximizing price by extending a vertical line upward from the output determined in step 1 to the pure monopolist’s demand curve.

Step 3Determine the pure monopolist’s economic profit by using one of two methods:

Method 1. Find profit per unit by subtracting the average total cost of the profit-maximizing output from the profit-maximizing price. Then multiply the difference by the profit-maximizing output to determine economic profit (if any).

Method 2. Find total cost by multiplying the average total cost of the profit-maximizing output by that output. Find total revenue by multiplying the profit-maximizing output by the profit-maximizing price. Then subtract total cost from total revenue to determine the economic profit (if any).

10-337

Finding Pm and Qm

Price

Quantity of output

Market Demand

MR

MC

Pm

Qm

MC = MR

Cost data will determinea monopolist’s profit.

$200

175

150

125

25

100

75

50

Pric

e, C

osts

, and

Rev

enue

1 2 3 4 5 6 7 8 9 10Quantity

Output and Price Determination

LO2

0

D

MR

ATC

MC

MR=MCA=$94

EconomicProfit

Pm=$122

10-339

Misconceptions of Monopoly Pricing

• Not highest price

• Total profit

• Possibility of losses

LO2 10-340

Misconceptions of Monopoly Pricing

LO2

0

D

MR

ATC

MC

MR=MC

Loss

AVCPm

Qm

V

A

10-341

Price Discrimination It refers to discrimination of price for different

consumers on the basis of their income or purchasing power, geographical location, age, sex, colour, marital status, quantity purchased, time of purchase etc. for eg:-

• Physicians and hospitals• Merchandise sellers• Railways and Airlines• Cinema shows or musical concerts• Domestic and foreign markets

Necessary conditions• Different Markets must be separable for a seller

• The Elasticity of demand must be different in different markets

• There must be imperfect competition in the market

• Profit maximizing output should be larger than the quantity demanded in a single market or section of consumers

First Degree of Price DiscriminationCosts / Revenue

Output / Sales

S

DQ

P

0

Second Degree of Price Discrimination

Costs / Revenue

Output / Sales

S

DQ

P

0

P3

P2

P1

Q3Q2Q1

Third Degree of Price Discrimination

Costs / Revenue

Output / SalesOutput / SalesOutput / Sales

QA QBQ0 00

MRB

ARA

MRAARB

Market A

MC

MR

AR=D

Total MarketMarket B

PA

PB

Four Market Models

LO1

Characteristics of the Four Basic Market Models

CharacteristicPure

CompetitionMonopolistic Competition Oligopoly Monopoly

Number of firms A very large number

Many Few One

Type of product Standardized Differentiated Standardized or differentiated

Unique; no close subs.

Control over price None Some, but within rather narrow limits

Limited by mutual inter-dependence; considerable with collusion

Considerable

Conditions of entry

Very easy, no obstacles

Relatively easy Significant obstacles Blocked

Nonprice competition

None Considerable emphasis on advertising, brand names, trademarks

Typically a great deal, particularly with product differentiation

Mostly public relation advertising

Examples Agriculture Retail trade, dresses, shoes Steel, auto, farm implements

Local utilities

DEMAND FORECASTING• Demand forecasting means estimation of the

demand for the good in the forecast period.

• It is a process of estimating a future event by casting forward past data.

• The past data are systematically combined in a predetermined way to obtain the estimate of future demand.

Why demand forecasting?

• Planning and scheduling production• Acquiring inputs• Making provision for finances• Formulating pricing strategy• Planning advertisement

Criteria for selecting a good forecasting method

1. Accuracy: Different methods of forecasting yield accurate results under different circumstances. An appropriate choice of method will ensure more accurate results.

2. Reliability: A time tested method increases the reliability of that method. If a particular method was used to give reliable result in the past then the same method can be reused for forecasting future.

3. Economical: Although complete enumeration method of forecasting demand would perhaps yield more accurate result yet it would be a very expensive method.

The team conducting forecast cannot afford to discuss the economic aspect of forecasting and therefore should select the least expensive of the methods which would give some reliable forecasts.

Criteria for selecting a good forecasting method

4. Data availability: Forecasting is made on the basis of the availability of primary or secondary data and therefore the required data should be easily available preferably in the required form.

5. Flexibility: As the managerial economist is faced with a number of uncontrollable variables, flexibility in using would be a necessary condition for a good forecast.

6. Durability: The forecast that are made should be valid in the long run because there is a certain time lag in conducting the forecasts and the period when the product is likely to enter the market.

7. Simplicity: Depending upon the objective the researcher should apply a simple and straightforward method of forecasting

• Consumer Surveys: It involves gathering of information about consumer

behavior from a sample of consumers which is analyzed and then further projected onto the population.

Surveys are conducted to assess consumers perception of various aspects, such as new variations in products, variations in prices of the product and related products, new variations in services provided etc.

The drawback of this method is that the consumer has to respond to hypothetical situations.

Complete Enumeration Method

• Complete Enumeration Survey covers all the consumers. It resembles the Census Data Collection which considers the entire population.

• In this case all the consumers are covered and information is obtained from all regarding the prospective demand for the product under consideration.

• In this method the consumer is asked about the future plan of purchasing product in question.

• For Example if majority of households in a city report the quantity (q) and they are willing to purchase a commodity then the total probable demand (DP) may be calculated as

•

Advantages

(a) Quite accurate as it surveys all the consumers of a product

(b) It is simple to use

(c) It is not affected by personal bias

(d) It is based on collected data

Disadvantages

(a) It is costly

(b) It is time consuming

(c) It is difficult and practically impossible to survey all the consumers

(d) Useful only for products with limited consumers

Sample Survey:• In case of the sample survey method, few

consumers are selected to represent the entire population of the consumers of the commodity consumed.

• The total demand for the product in the market is then projected on the basis of the opinion collected from the sample.

• The most important advantage of this method is that it is less expensive and less tedious compared to the method of complete enumeration.

• On the basis of information collected the probable demand is estimated through the following formula

• D = Probable demand Forecast• H = census number of households from the relevant

market• = number of household reporting demand for the

product• = number of household surveyed.

• = Average expected consumption by the reporting household ( = total qty reported to be consumed by the reporting household / no. of households)

Sample Survey Method

Instead of surveying all the consumers of a commodity, only a few consumers are selected and their views on the probable demand are collected

Population

Sample

Advantages

(a) It is simple and does not cost much

(b) Since only a few consumers are to be approached, the methods works quickly

(c) The risk of handling a large number of data is reduced

(d) It gives excellent results, if used carefully

Disadvantages

(a) The conclusions are based on the view of only a few consumers and not all of them

(b) The sample may not be a true representation of the entire population

End –Use Method

• A given product may have different end uses. For example: milk may have different end uses such as milk powder, chocolates, sweet -meats like ‘barfi’ etc.

• Therefore the end users of milk are identified. • A survey is planned of the end users and the estimated

demands from all segments of end users are added. • This method of demand forecasting is easy to manage

if the number of end-users is limited.• In this method the investigator expects the end- users

to provide correct information well in advance of their respective production schedules.

• Advantages:(a)The method yields accurate predictions(b)It provides sector wise demand forecast for

different industries• Disadvantages:(a)It requires complex and diverse calculation(b)It is costlier as compared to other survey

methods and is more time consuming(c)Industry data may not be readily available

Opinion Poll Method

• It aims at collecting opinions of those who are supposed to possess knowledge of the market, e.g sales representative, sales executives, professional marketing experts and consultants,

• The opinion poll methods include:Expert opinion methodDelphi methodMarket studies and experiments

Expert Opinion

• The expert opinion method, also known as “EXPERT CONSENSUS METHOD”, is being widely used for demand forecasting.

• This method utilizes the findings of market research and the opinions of management executives, consultants, and trade association officials, trade journal editors and sector analysts. When done by

• An expert, qualitative techniques provide reasonably good forecasts for a short term because of the expert’s familiarity with the issues and the problems involved.

Expert Opinion• Salesmen are required to estimate expected sales in their territories.

Salesmen being the closest to the customers, have most intimate feel of the market.

• The estimates of individual salesmen are consolidated to find out the total estimated sales.

• These estimates are reviewed to eliminate the bias of optimism or pessimism.

• Thereafter they are further revised in the light of factors proposed change in prices, product design, advertising budget, expected change in competition, changes in purchasing power, income distribution, employment, population etc.

• The final forecast will emerge after all these factors are taken into account.

• The method is known as collective opinion as it takes advantage of the collective wisdom of salesmen, departmental heads like production manager, sales manager, marketing manager, managerial economist and top executives, as well as dealers and distributors.

Advantages: 1. The method is simple and does not involve the use of

statistical techniques.2. The forecasts are based on first-hand knowledge of salesmen

and others directly connected with sales.3. The method is useful in predicting sales of new products.

Here, salesmen will have to depend more on their judgementthan in the case of existing products.

Disadvantages:1. It is subjective. Salesmen may underestimate the forecast if it

is to be used to decide their quotas.2. This method can only be used for short-term forecasting.3. Focus of salesmen is centered round the present trend, and they

don’t think about the future. They may even lack the breadth of vision for looking into the future.

Delphi Method

• This is a variant of the opinion poll or survey method.

• In Delphi Method, an attempt is made to arrive at a consensus of opinion.

• The participants are supplied with responses to previous questions from others in the group by a leader.

• The leader provides each expert with opportunity to react to the information given by others, including reasons advanced, without disclosing the source.

• The Delphi method is primarily used to forecast the demand for “NEW PRODUCTS”.

Advantages & Disadvantages of Delphi Method:Delphi method has some exclusive advantages: a) It facilitates anonymity of the respondent’s identity. This enables

respondents to be frank and forthright in giving their views. b) It facilitates posing the problem to the experts at one time and have their

response – nearly as good as pooling the panelists together. In one case 620 experts from different background such as policy-makers, technologists, scientists, economists, administrators and advisers were consulted.

However, Delphi method presumes these two conditions: 1) panelists must be rich in their expertise, having wide knowledge of the subject and are sincere and earnest in their disposition towards the participants.

2) The conductors are objective in their job, possess skill to conceptualize the problems for discussion to generate considerable thinking, stimulate dialogue among panelists and make inferential analysis of the numerous views of the participants.

Experimental Approaches Experimental Approaches Customer Surveys are sometimes conducted

over the telephone or on street corners, at shopping malls, and so forth.

The new product is displayed or described, and potential customers are asked whether they would be interested in purchasing the item.

While this approach can help to isolate attractive or unattractive product features, experience has shown that "intent to purchase" as measured in this way is difficult to translate into a meaningful demand forecast. This falls short of being a true “demand experiment”.

Consumer Panels

• Consumer Panels are also used in the early phases of product development.

• Here a small group of potential customers are brought together in a room where they can use the product and discuss it among themselves.

• Panel members are often paid a nominal amount for their participation.

• Like surveys, these procedures are more useful for analyzing product attributes than for estimating demand, and they do not constitute true “demand experiments” because no purchases take place

Market Experiment

• Market Experiment can help to overcome the survey problems as they generate data before introducing a product or implementing a policy.

• Market Experiments are two types:-

1) Test marketing:-

2) Controlled experiments:-

Test marketing

• In this case, a test area is selected, which should be a representative of the whole market in which the new product is to be launched.

• A test area may include several cities and towns, or a particular region of a country or even a sample of consumers.

• More than one test area can be selected if the firm wants to assess the effects on demand due to various alternative marketing mix.

• Advertising or packaging can be done in various market areas. Then the demand for the product can be compared at different levels of price and advertising expenditure.

• In this way, consumer’s response to change in price or advertising can be judged.

Test Marketing• Test Marketing is often employed after new product

development but prior to a full-scale national launch of a new brand or product.

• The idea is to choose a relatively small, reasonably isolated, yet somehow demographically "typical" market area.

• The total marketing plan for the item, including advertising, promotions, and distribution tactics, is "rolled out" and implemented in the test market, and measurements of product awareness, market penetration, and market share are made.

DRAWBACKS OF THE MARKET EXPERIMENT

1) The test experiments are that they are very costly and much time consuming.

2) If in a test market prices are raised, consumer may switch to the competitor’s products.

3) It may be difficult to regain lost customers even if the price is reduced to the previous level. Moreover, it is often difficult to select an area, which accurately represents the potential market.

Controlled experiments

• Controlled experiments are conducted to the test demand for a new product launched or to test the demands for various brands of a product.

• They are selected consumers.

DRAWBACKS OF THE CONTROLLED EXPERIMENTS

1) The consumers may be biased in the process of selection of a sample of consumers on which experiments is to be performed.

2)The selected consumers may not respond accurately If they come to know that they are a part of an experiment being conducted and their behavior is being recorded.

Statistical Method

• Statistical method is used for long run forecasting.• Statistical & mathematical techniques are used to

forecast demand.• Statistical methods has been used to explain time-

series & cross-section data for estimating long-term demand.

• Statistical methods are considered to be superior techniques of demand estimation.

• The important statistical methods are –1. Trend Projection method/time series2. Barometric methods3. Econometric method

1. Trend project method

• Trend project method are also called as time series method – therefore, it is also known as time series analysis.

• The data relating to sales over a period of time is known as time series data (10 – 20 yrs).

• On the basis of the past trend in demand, forecasting the future demand trend is possible.

• Trend project method classified into 3 types –1. Graphical method

2. Fitting trend equation/least square method &

3. Box – Jenkins method

1. Graphical Method Annual data on sales are plotted on a graph paper & a line

is drawn through the plotted points. This method is very simple & less expensive.

2. Fitting Trend Equation A trend line (curve) is fitting to the time-series sales data

with the aid of statistical techniques.

3. Box Jenkins Method This method of forecasting is used only for short-term

predictions. This method is suitable for forecasting demand with only

stationary time series sales data. Stationary time-series is one which does not reveal a log

term trend.

Graphical method: The past data will be plotted on a graph

The identified trend will be extended further in the same pattern to ascertain the demand in the forecast period

In the figure trend 1 is linear, trend 2 is non-linear

Dem

and

Trend 2

2. Barometric Method Barometric method is an improvement over trend

projection method. Under barometric method, present events are

used to predict the directions of change in future. This method done with the help of economic &

statistical indicators. This method is also known as Economic Indicators

Methods. Under barometric method, present events are used to predict the directions of change in future.

Barometric Technique The Bhuj earthquake in January 2001, lead to a massive destruction of property & buildings in Gujrat.This necessitated construction of buildings to rehabilitate the people of affected areas.The construction was followed by a spurt in the demand for cement, fans, tube lights, etc.Thus, construction of buildings leads to the demand for cement.Here, construction of buildings is the leading indicator or the barometer

TREND PROJECTION METHOD

• Based on analysis of past sales patterns• Shows effective demand for the product for a

specified time period• The trend can be estimated by using the Least

Square Method

A producer of soaps decides to forecast the next years sales of his product.The data for the last five years is as follows:

YEARSYEARS SALES IN Rs.LAKHSSALES IN Rs.LAKHS

19961996 4545

19971997 5252

19981998 4848

19991999 5555

20002000 6060

The data is plotted on a graph:

• The equation for the straight line trend is

Y = a + bxa-intercept

b-shows impact of independent variable

The Y intercept and the slope of the line are found by making substitutions in the following normal equations:

∑Y = na + b ∑ x

∑XY = a ∑x + b ∑x2

Substituting the above values in the normal equations:260=5a +15b (Eq.3)

813=15a + 55b (Eq.4)solving the two equations,

a = 42.1 , b = 3.3

YEARSYEARS SALES Rs. SALES Rs. LAKHS (Y)LAKHS (Y)

XX XX22 XYXY

19961996 4545 11 11 4545

19971997 5252 22 44 104104

19981998 4848 33 99 144144

19991999 5555 44 1616 220220

20002000 6060 55 2525 300300

N=5N=5 ∑∑Y=260Y=260 ∑∑X=15X=15 ∑∑XX22=55=55 ∑∑XY=813XY=813

Therefore, the equation for the straight line trend is

Y=42.1 + 3.3XUsing this equation we can find the trend values for

the previous years and estimate the sales for the year 2001 as follows:

Thus, the forecast sales for year 2001 is Rs.61.9 lakhs.

Y 1996 =Y 1996 = 42.1+3.3(1) =42.1+3.3(1) = 45.445.4

Y 1997 =Y 1997 = 42.1+3.3(2) =42.1+3.3(2) = 48.748.7

Y 1998 =Y 1998 = 42.1+3.3(3) =42.1+3.3(3) = 52.052.0

Y 1999 =Y 1999 = 42.1+3.3(4) =42.1+3.3(4) = 55.355.3

Y 2000 =Y 2000 = 42.1+3.3(5) =42.1+3.3(5) = 58.658.6

Y 2001 =Y 2001 = 42.1+3.3(6) =42.1+3.3(6) = 61.961.9

Estimation of Trend by the Method of Least Squares

Q. The annual sales of a company are as follows:Year 1991 1992 1993 1994 1995Sales ‘000 45 56 58 46 75

Using the method of least squares, fit a st. line trend and estimate the annual sales of 1997.

Year Sales

y

1990 = 0Time-

Deviationx

x2 xy Estimated Trend’000Y=45 + 5x

1991 45 1 1 45 50

1992 56 2 4 112 55

1993 78 3 9 234 60

1994 46 4 16 184 65

1995 75 5 25 375 70

n = 5 Σ y = 300 Σ x = 15 Σ x2 = 55 Σ xy = 950

n = 5 Σ y = 300 Σ x = 15 Σ x2 = 55 Σ xy = 950

Σ y = n.a. + b Σ x …1Σxy = a Σx + b Σx2 …. 2

Substituting the computed valueswe have,300 = 5a + 15b ….3 (x 3)950 = 15a + 55b …. 4Multiplying (3) by 3 we have900 = 15a + 45b950 = 15a + 55b Therefore, 10b = 50, b = 5Substituting b = 5 in (3)300 = 5a + 15(5)300 = 5a + 755a = 225 a = 45

St. line equation is Y = a + bxSubstituting the values of a and b,Y = 45 + 5xTherefore,Y1991 (x=1) = 45 + 5(1) = 50Y1992 (x=2) = 45 + 5(2) = 55Y1993 (x=3) = 45 + 5(3) = 60Y1994 (x=4) = 45 + 5(4) = 65Y1995 (x=5) = 45 + 5(5) = 70Y1996 (x=6) = 45 + 5(6) = 75Forecast for the year 1997Y1997 (x=7) = 45 + 5(7) = 80i.e. Rs.80,000/-

Use of Economic IndicatorsThe use of this approach bases demand forecasting on certain

economic indicators following these steps:

1. See whether a relationship exists between demand for the product and the economic indicator.

2. Establish the relationship through the method of least squares and derive the regression equation. Assuming the relationship to be linear, the equation will be Y = a + bx

3. Once the regression equation is derived, the value of

Y i.e. demand can be estimated for any given value of x.

Draw back: Finding an appropriate economic indicator may be difficult.

For new products it is inappropriate as no past data exists.

Illustration: Suppose a company manufacturing tractors finds that a relationship exists between sale of tractors and Farm Income Index published by CSO. Table below shows the number of tractors sold and

the corresponding farm income index 1988 through 1992. Regression equation is calculated as follows:

Year Farm Income

Index (x)

Sales ofTractor

s(y)

X1 = x/10 Y1 = y/10 x1y1 x12

1988 100 110 10 11 110 100

1989 110 130 11 13 143 121

1990 140 150 14 15 210 196

1991 150 160 15 16 240 225

1992 200 180 20 18 360 400

n = 5 ΣX1=70

ΣY1 =73 ΣX1y1=1063 ΣX12=1042

The equations to be solved simultaneously are:

Σy1 = n.a. + b Σ x1 …….(1)

Σx1y1 = a Σx1 + bΣ x12……(2)

Substituting the various values, we get,

73 = 5a + 70b (x14)…(3)1063 =70a + 1042b1022 =70a + 980b 62b = 41 b = 41/62 = 0.66

Substituting the value of b in (3) 73 = 5a + 70 (0.66) = 5a + 46.2 5a = 73 – 46.2 = 26.8 a = 26.8/5 = 5.36 a = 5.36 b = 0.66

y1 = 5.36 + 0.66x1

Y/10 = 5.36 + 0.66 (X/10)

Y = 10(5.36) + 0.66(x/10)10 = 53.6 + 0.66xIf the index of farm income becomes 210, sale of tractors will beY = 53.6 + 0.66(210) = 53.6 + 138.6 = 192 tractors.