Combined

1

RUTGERS UNIVERSITY Managerial Economic Analysis

22:223:581:61 Livingston – Beck 251

Professor Sharon Gifford Office hours: Tue. 5:30 – 6:30 Voice: 973-353-1646 (Newark) Levin 217c or by appointment E-mail: [email protected] Course Description: This course is designed to give you a working knowledge of the basic principles of microeconomic theory, with an emphasis on the applications of economics to management decision making. No prior economic training is assumed. Those with recent undergraduate degrees in economics are strongly encouraged to consider substituting an economics elective for this course. Course Materials: Textbook: Managerial Economics and Business Strategy, Fifth Edition, by Michael R. Baye (ISBN 0-07-298389-2), Irwin. The text and Study Guide may be available at the New Jersey and Rutgers Bookstore. However, I strongly recommend that you try to obtain the textbook and Study Guide online before class starts. The bookstores often run out if the book in the first week. Class Notes: Blackboard https://blackboard.newark.rutgers.edu/ . You will need your Rutgers NetID to logon. If you want to have your email forwarded from your Rutgers address, go to http://business.rutgers.edu/students/return.htm. If Blackboard is not accessible go to http://andromeda.rutgers.edu/~sgifford/manecon/. The Powerpoint slides are in the directory "slides". All other material for your class is in the directory "Night class". Prerequisite Topics Calculus: differentiation of linear and power functions, graphing a function, maximizing an objective function. Statistics: regression analysis, t-statistics, R2 . Course Requirements Your grade for the course will be based on two 1-hour in-class exams (20% each), two projects (15% each) and a final exam (20%). The final 10% is based on class participation. Participation credit is earned by being active in class (asking questions, answering questions, telling good jokes, etc.) You can also get participation credit by being active in the Discussion Board on Bb. The projects will be done in groups of up to 4 students. The first project is based on question 10 in chapter 3 of the textbook. Each group will use a different data set, available on the disk that accompanies the text, to run a regression and answer the questions in the text. Each group will hand in one report. The second project will be an industry analysis based on the industry of your choice. Each group will hand in one report.

2

Outline

See Calendar on Bb for dates Week 1 Managerial Economics and Market Forces Ch. 1 and 2 Week 2 Demand Ch. 3 Week 3 Individual Behavior Ch. 4 Week 4 Production and Costs Ch. 5 Week 5 1 hour exam. Chapters 1-5

Organization of the Firm (project 1 due) Ch. 6

Week 6 Nature of Industry Ch. 7 Week 7 Managing Markets Ch. 8 Week 8 Rivalry Ch. 9 Week 9 1 hour exam. Chapters 6-9

Game Theory Ch. 10

Week 10 Pricing Strategy Ch. 11 Week 11 Economics of Information Ch. 12 Week 12 Government in the Marketplace (project 2 due) Ch. 14 Week 13 Review Final Exam Chapters 10, 11, 12 and 14 To prepare for class and the exams, read the assigned chapter(s) before class. Download and print the transparencies and class summaries. Go through the study guide either before or soon after class to test your understanding of the material. Start working on the projects as soon as the material is assigned.

Managerial Economics Prof. Sharon Gifford

1

Lecture 1 Managerial Economics and Market Forces

The objective of this course is to teach students how to use microeconomic models as a tool for making good business decisions. A manager of a firm must understand how to allocate the firm’s scarce resources in order to achieve the firm’s goal. In general, a firm’s goal is to maximize the value of the firm. The firm’s value depends on the profits that are generated over time. The appropriate way to measure the value of the firm is to calculate the present value of the stream of profits that the firm will receive in the future. If the firm’s profits grow at a constant rate over time, then maximizing the value of the firm is equivalent to maximizing current profits. Clearly, the assumption of a constant growth rate in profits is extreme. To maximize current profits, the manager must understand marginal analysis. This mathematical tool considers how profits are affected by the choice of the quantity of the product produced. To calculate the effect of an increase in the quantity produced, marginal analysis reveals that this is measured by the difference between marginal revenue and marginal cost. Increasing output by one unit generates an addition to revenue, called marginal revenue, and an addition to costs, called marginal costs. If marginal revenue is greater than marginal cost, then profit increases with the additional output. Profit is maximized only when the additional revenue just offsets the additional costs. Demand and supply represent market forces. Demand is the willingness of consumers to pay for a product. Supply is the willingness of firms to produce a product. The law of demand states that more will be purchased only if the price is decreased. Equivalently, if the price falls, a greater quantity will be demanded. When the price of the product changes, this is a movement along a stationary demand curve. The demand can be shifted by changes in factors other than the price. For example, if a good is normal, then an increase in consumer income increases demand for the good. For an inferior good, an increase in income reduces demand. Both of these effects shift the demand curve. Other factors that shift demand are prices of complementary and substitute goods and advertising and other sources of product information. If some consumers pay less than the maximum they are willing to pay, then the difference represents a surplus of value over price. The sum of all these surplus values is called consumer surplus. The supply of a product is determined by a firm’s costs. The law of supply states that an increase in the price of the product will result in an increase in the quantity supplied. Equivalently, to generate a greater quantity supplied, a higher price must be offered. Changes in price and the quantity supplied are movements along a stationary supply curve. Changes in other determinants of supply will shift the supply curve. For example, an increase in input prices increases costs and so increases the minimum price required by firms to supply a given quantity of the product. This is a decrease in supply. At the same price, firms will supply less. Other factors that affect supply are technology, the number of firms and taxes. If some units are sold at a price higher than the minimum required by the firm, then this difference represents a surplus for the firm. The sum of all surpluses in a market is called producer surplus.


2

An equilibrium is a situation in which no one has an incentive to change his or her decision given the decisions of others. A market equilibrium is a price at which the quantity demanded is equal to the quantity supplied. Those consumers who are willing to pay this price can buy as much of the good as they want. Those unwilling to pay this price will not buy any. Firms willing to sell at this price will sell all they want to at this price. Those unwilling to sell at this price will sell nothing. Some government policies prevent the market equilibrium price from being achieved. A price ceiling, such as rent control, is less than the market equilibrium price and results in a shortage. The quantity demanded is greater than the quantity supplied. Some customers who are willing to pay the price ceiling are unable to buy as much as they want. The product is restricted to those with the lowest search costs. The costs of search for an available unit of the good will pay two prices: the monetary price and a nonpecuniary price that is equal to the opportunity cost of their time spent searching. The total surplus, consumer and producer, is less than at the market equilibrium price. A price floor, such as a minimum wage, is above the market equilibrium price and results in a surplus of the product. The quantity of labor supplied is greater than the quantity demanded. Some workers willing to sell at the price floor will not be able to sell. Again, the total consumer and producer surplus is less than at the market equilibrium price. Comparative statics is the analysis of the effect shifts in supply and/or demand on the equilibrium price and quantity. Understanding these effects allows managers to predict changes in market prices. An increase in demand results in a higher price and quantity. A decrease in supply results in a higher price and lower quantity. However, if both supply and demand change simultaneously, the effect on price and quantity may be indeterminate.

Managerial Economic Analysis

1

2/26/2008 Managerial Economic Analysis Prof. Sharon Gifford Rutgers University 1

Chapter 1: Fundamentals of Managerial Economics

Goals and Constraints

Goal: maximize profitsMarket RivalryTime Value of MoneyMaximizing Profits


How are managers like economists?

• Hiring?• Purchase?• Advertising?


How are managers like central planners?

• assign tasks

• motivate effort

• reward performance


How are managers like entrepreneurs?

• product characteristics

• pricing policy

• performance

• planning


Goals and Constraints

• What is the manager’s goal?over timeunder uncertaintyrisk considerations

• What constrains managers?financial constraintsmarket constraintsmanagement constraints


What is the Invisible Hand

• How does greed serve consumers?

• What are opportunity costs?

• How does self interest contribute to the

general welfare?


2


Rivalry and Benefits of Trade

• What determines “the price”?• Who benefits from trade, buyer or seller?• Is all trade voluntary?• How do sellers get customers to buy?• How do consumers get sellers to offer

goods and services?


Time Value of Money• Why do you care if you have to wait for

revenues?• What is the opportunity cost of waiting?• If you invest $100 today at 10% interest,

how much money do you have in one year.

• Receiving this in one year is equivalent to receiving $100 today.


Present Value (PV) and FutureValues (FV)

• If PV is received now, then in one year, FV = PV + iPV = (1+i)PVor PV = FV/(1+i)

• Higher interest rates reduce PV.• In 5 years

FV = PV(1+i)5 or PV = FV/(1+i)5


A sequence of incomes

Three payments over three years has a present value of

PV = FV1/(1+i) + FV2/(1+i)2 + FV3/(1+i)3

• In general,

PV = ��t FVt/(1+i)t


Uses of Net Present Value• Net present value of a project with initial

costs C0NPV = PV −−−− C0.

• The value of a firm is the present value of future profits ππππt

PVfirm = ��t ππππt/(1+i)

• How do we measure these future profits?


A NAÏVE way to estimate the value of the firm.

Assume that the growth of profits is constant, thenππππt+1 = (1+g)ππππt for t = 0,…,∞∞∞∞, and

PVfirm = ��t ππππt/(1+i)t = ��t ππππ0(1+g)t/(1+i)t

= ππππ0 [(1+i)/(i−−−−g)]. Maximizing the value of the firm is the same as

maximizing current profits.


3


Simple Profit Maximization

• What is the simplest way to define profits?

• What do profits depend on?

• What if quantity (Q) produced and sold?ππππ(Q) = TR(Q) −−−− TC(Q).


Marginal This and That

• What do you get if you sell one moreunit?

MR(Q+1) = TR(Q+1) −−−− TR(Q) = ∆∆∆∆TR

• What does it cost to produce one more

unit?

MC(Q+1) = TC(Q+1) −−−− TC(Q) = ∆∆∆∆TC


Marginal Profit

• ∆π∆π∆π∆π(Q+1) = ππππ(Q+1) – ππππ(Q) = ∆∆∆∆TR −−−− ∆∆∆∆TC =

MR(Q+1) −−−− MC(Q+1).

• Should you produce more or less?

• If MR(Q+1) > MC(Q+1) then ∆π∆π∆π∆π(Q+1) > 0.

• If MR(Q+1) < MC(Q+1) then ∆π∆π∆π∆π(Q+1) < 0.


Calculus

• > 0 if MR(Q) > MC(Q)• < 0 if MR(Q) < MC(Q)• = 0 if MR(Q) = MC(Q)• How do we know if profits are

maximized?

�� QMCQMRdQ

dTCdQ

dTRdQd −=−=π


What is a derivative?

π(Q)

Slope = dπ/dQ = 0

Q*

$


How do you take a derivative?

f(x) = m⋅xn

df(x)/dx = m⋅n⋅xn-1

f(x) = 5x – 10x2

df(x)/dx = 5 − 20x


4


Example: TR(Q) = 10Q − 2Q2 TC(Q) = 2 + Q2

π(Q) = TR(Q) −TC(Q) = 10Q − 2Q2 − 2 − Q2

= 10Q − 3Q2 − 2

Set dπ/dQ = 10 − 6Q = 0

Solve for Q: 10 = 6QQ = 10/6 = 5/3

At Q = 5/3, profits are maximized.


Next• What are demand and supply?• What is the difference between demand and

quantity demanded?• What is the difference between supply and

quantity supplied?• What makes demand or supply change?• Whar makes the quantity demanded or

supplied change?


1

Lecture 2 Demand Analysis, Estimation and Individual Behavior

Demand analysis uses an estimated demand equation to answer many questions about how the quantity demanded of a good depends on a variety of factors. In general, consumer demand depends on the price of the good, consumer income, the prices of related goods and the information available to the consumer about the good. The reasons for these relationships are explored further below when we consider individual behavior. The problem of estimating the demand equation will also be considered below. But first, we will analyze the information available from a demand equation. Managers are very concerned with accurate predictions of future demand for their product. Managers must often plan production ahead of time, before they know what actual demand is. However, managers may have some information about how they expect of the aspects of their markets to behave. For example, economists may predict increasing consumer income because of a booming economy. Or managers may know that a competitor is advertising a reduction in price. To determine the effect of these predicted changes, managers need to know how sensitive the demand for their product is to these changes. This sensitivity is called elasticity. Elasticity indicates the percentage change in the quantity demanded for a percentage change in some other variable, such as income or prices. Own-price elasticity measures the percentage change in the quantity demanded for a percentage change in the price of the good’s own price. This price elasticity determines whether demand is elastic or inelastic. If demand is elastic, then the percentage change in quantity is greater than the percentage change in price, implying that a decrease in the price will increase the quantity so much that revenues increase. If demand is inelastic, then lowering the price will reduce revenues because the increase in quantity is not sufficient to compensate for the lower price. Demand tends to be more elastic if there are available substitutes and if the time horizon is longer. Cross-price elasticity measures the effect on the quantity demanded of a change in the price of some other price. If cross-price elasticity is positive, then the two goods are substitutes: a decrease in the price of a substitute decreases the quantity demanded of the good in question. If the cross-price elasticity is negative, then the two goods are complements. Notice that the sign of the cross-price elasticity is important. Income elasticity measures the percentage change in the quantity demanded for a percentage change in consumer income. If income elasticity is positive, then the good is said to be normal: and increase in income increases the quantity demanded. If the income elasticity is negative, then the good is said to be inferior. This means that people buy less of this good when their income increases. If the income elasticity is zero, then the good is a necessity. To estimate the demand or product, regression analysis is used along with data on the relevant variables. Regression techniques essentially fit a line to the data. This line may be straight (linear) or not (nonlinear). The goal of regression techniques is to minimize the unexplained errors, the difference between the actual observations and the forecasted quantities from the fitted equation. The computer printout of regression results contain information about how well the equation fits the data and whether or not the independent variables have explanatory power.


2

The measure of the explanatory power of an independent variable is the number of standard deviations that the estimated coefficient on that variable is from zero. The t-statistic measures this. We know from statistical theory that the probability that the estimated coefficient is more than two standard deviations from zero when the true coefficient is zero is less than 5%. Therefore, if the absolute value of the t-statistic is greater than 2, then we can be 95% confident that the true coefficient is not zero, implying that the independent variable has explanatory power. Although the t-statistic gives information about the explanatory power of individual variables, we are also concerned with the explanatory power of the equation as a whole. This is measured by the coefficient of determination, R2. This measures the percentage of he total deviation in the data that is explained by the equation. If R2 is close to one, then most of the deviation in the data is explained. However, this can be the case for only if the data is closely packed along the estimated line. If the data is widely spread out, then not line will fit the data closely. Therefore, there is no particular value of R2 for which we can say we have a good fit. However, R2 can be used to compare the goodness of fit of two different specifications of the equation, as long as the equations contain the same number of independent variables. If one equation has more variables than the other does, then the adjusted R2 must be used. The relationships between the quantity demanded and the other variables are made clearer by the theory of consumer behavior. Consumers are assumed to have rational preferences over goods. This means that consumers can compare all bundles of goods, prefer more to less, and are consistent in these comparisons. In addition, consumers are assumed to have a decreasing willingness to trade away a good as they have less of it. These assumptions are described by a diagram of indifference curves. An indifference curve connects all bundles of goods that the consumer considers to be equivalent. Consumers want to be on the highest indifference curve possible, but their choice is limited by the budget constraint. This constrain says that consumers cannot spend more money than they have. The bundle of goods that is on the highest indifference curve without violating the budget constraint is the consumer’s equilibrium bundle. At this bundle, the consumer if just willing to trade one good for some of another at the terms of trade prescribed by the prices of the good. This implies that observing the prices at which consumers are just willing to trade reveals information about consumer preferences. By observing changes in quantities purchased at different prices, we can collect data on the demand for the good. Since a demand equation is estimated from the observations of prices and quantities, the estimated demand measures the willingness of consumers to trade for the good. Therefore, preferences themselves are revealed by the demand equation.

1


Chapter 2 Demand and Supply• Demand reflects customers’ willingness to pay for

a product.• Supply reflects firms’ willingness to sell a

product.• Together, these determine the equilibrium price

and quantity sold.• Changes in demand and supply result in changes

in price and quantity.


Demand

• Why does demand depend on tastes?

• Why does demand depend on productqualities?

• Why does demand depend on availablesubstitute and complementary goods?

• Why does demand depend on income?

• Why does demand depend on information?


Demand Curve• At what price will any quantity will sell,

holding all else constant?• What quantity can be sold at any price,

holding all else constant?

10 20 Q

P = 10 – 0.5 Q10P

5 D


Law of Demand

• What happens if the price decreases?

• This is a movement along a stationary

demand curve.

• What if any other factor changes?

• This shifts the demand curve.


A decrease in price increases the quantity demanded.

Q0 Q1

P0

P1


Change in Demand

• Increase in income increases demand for a normal good.

P

DD'

Q

2


Complements and Substitutes

• What happens if the price of a substitute increases?

• What happens if the price of a complement increases?

• If advertising increases, this may increase demand.

• Are these are all shifts in demand or changes in the quantity demanded?


Estimating a Demand Function• Considers all of these effects:

Q = α0 + α1 Px + α2 Py + α3 M + α4 A

• Px price of the good x

• Py price of another good y• M measure of consumer income• A advertising expenditures• Where do I get one of these?


Q = α0 + α1 Px + α2 Py + α3 M + α4 A

Why do we expect thatα1 < 0 law of demand

< 0 for complementsα2

> 0 for substitutes

< 0 for inferior goodsα3

> 0 for normal goods2/26/2008 Managerial Economic Analysis Prof. Sharon Gifford Rutgers University 10

Get curve from equation:

Qdx = 12,000 − 3 Px + 4 Py − 1 M + 2 A

If Py = 15, M = 10,000, A = 2,000 then the equation for the demand curve is Qd

x = 6,060 −3 Px or Px = 2,020 − 1/3 Qd

x.


Consumer Surplus

• Not every customer pays the most they are willing to pay.

• Consumer surplus is the difference between what the consumer is willing to pay and the actual price.


If a consumer is willing to pay 4 for a firstunit, 3 for a second and 2 for a third:

P

432

1 2 3 Q

3


Calculating Consumer Surplus

• If P = 2, consumer surplus is (4 + 3 + 2) − (2 + 2 + 2) = 3.

• At P = 2, the firm’s revenue is $6.• Consumer is willing to pay $9 for all

three.• The firm could increase its revenue by

selling a bundle of 3 for $9.


Supply

• What does supply depend on?• Supply curve: minimum price at which any

quantity will be supplied, holding all else constant.

• Law of supply: if price increases more will be supplied.

• Is this is a movement along a stationary supply curve or a shift in supply?


Changes in Supply

• If input prices increase, supply shifts up (back). This is a decrease in supply.

S0

S1P

Q


• A decrease in price decreases the quantity supplied.

P0P1

S0

Q1 Q0


Supply Function

Qsx = β0 + βx Px + β2 Pr

Px price of the good x Pr price of input good r We expect: βx > 0 βr < 0.


Equation for supply curve:If Qs

x = 200 + 3 Px − 6 Pr and Pr = 100, then the equation for the supply curve is Qs

x = 3 Px − 400 or Px = 1/3 Qs

x + 400/3 .

4


Producer Surplus

• Not every unit is sold “at cost”.

• Producer surplus is the difference between

the actual price and the minimum price at

which the good would be supplied.


Graph of Producer Surplus

PS = [400 − 400/3]800/2 = (266.67)400 = 106,668.

Gains from trade are CS + PS.

P400

PS

S

800 Q

400/3


Market Equilibrium

• An equilibrium is a situation in which no

one has an incentive to do something

different, given the actions of others.

• A market equilibrium is a price Pe at which

supply equals demand:

QS = QD = Qe.


At PH > Pe, QSx > QD

x. This is a surplus.

At PL < Pe, QSx < QD

x. This is a shortage.

P

PH

Pe

PL

Q

S

D

surplus

shortage


Calculating the Equilibrium PriceIf demand is

QD = 10 − 2P and supply is

QS = 2 + 2P then set

QD = 10 − 2P = QS = 2 + 2P

and solve for Pe = 2 and Qe = 2 + 2Pe = 6.


Comparative Statics

• Changes in supply and/or demand result in changes in the equilibrium P and Q.

• Changes in supply or demand are caused by changes in things other than price.

5


An increase in income for a normal good

P

P1

P0

Q0 Q1 Q

D0

D1

S

For a normal good, increased incomeincreases demand, which results in a higherprice and larger quantity.


An increase in materials costs

P

P1

P0

Q1 Q0 Q

D

S0S1

An increase in costs decreases supply, resultingin a higher price and lower quantity.


Excel Worksheets• Click here to

Practice calculating demand and supply on “Demand” and “Supply” sheets

Shift demand and supply curvesDetermine market equilibrium on “market” sheetCalculate CS and PS on “Surplus” sheet.


Price Ceilings

A price ceiling is a government policy thatsets price PC < Pe.

Only QS is traded, buyers willing to pay P(QS). Example: rent control.

P(QS)Pe

PC

S

D

QS Qe QD


Example: Rent Control• The shortage implies that goods are

allocated to those with lowest “waiting-in-line” costs.

• P(QS) > Pe includes cost-of-waiting and is full economic price paid.

• Those with a low opportunity cost of waiting benefit from the price ceiling.

• At QS there is less consumer and producer surplus than at Qe.


Price Floors

• A price floor is a minimum price which can be charged or paid.

PF

Pe

QD Qe QS

D

S

6


Example: minimum wage

• Only QD is traded and there is a surplus of job seekers.

• The surplus implies that workers are allocated to those firms with the lowest “search” costs.

• At QD there is less consumer and producer surplus than at Qe.


Conclusion• If both supply and demand shift, the results

may be ambiguous.• The key to this analysis is whether a change

in a firm’s environment affects demand or supply or both.

• For next week: Demand analysis and estimation.

• Be sure to study Chapter 3 for next week.• Introduce yourself on the Discussion Board


1

Lecture 3 Individual Behavior

The relationships between the quantity demanded and the other variables are made clearer by the theory of consumer behavior. Consumers are assumed to have rational preferences over goods. This means that consumers can compare all bundles of goods, prefer more to less, and are consistent in these comparisons. In addition, consumers are assumed to have a decreasing willingness to trade away a good as they have less of it. These assumptions are described by a diagram of indifference curves. An indifference curve connects all bundles of goods that the consumer considers to be equivalent. Consumers want to be on the highest indifference curve possible, but their choice is limited by the budget constraint. This constrain says that consumers cannot spend more money than they have. The bundle of goods that is on the highest indifference curve without violating the budget constraint is the consumer’s equilibrium bundle. At this bundle, the consumer if just willing to trade one good for some of another at the terms of trade prescribed by the prices of the good. This implies that observing the prices at which consumers are just willing to trade reveals information about consumer preferences. By observing changes in quantities purchased at different prices, we can collect data on the demand for the good. Since a demand equation is estimated from the observations of prices and quantities, the estimated demand measures the willingness of consumers to trade for the good. Therefore, preferences themselves are revealed by the demand equation.

1


Chapter 3:

Demand Analysis


Regression Analysis

• Regression analysis estimates the demand

equation.

• Used to forecast effects of anticipated

changes in prices, income, advertising, etc.

on demand.


Elasticities• effect of an independent variable X on

quantity Q: for any explanatory variable x

X/XQ/Q

X%Q%

EQX ∆∆=

∆∆=

%∆Q = EQX × %∆X

QX

dXdQ

X/dXQ/dQ

E QX ⋅==


Price Elasticity

Linear demand: QX = 22,000 − 2.5PX + 4PY − 1M + 1.5A Own price elasticity depends on Px/QX:

EQP

PQ

PQQXPX

X

X

X

X

X

X

= ∂∂

⋅ = − <2 5 0.


Price Elasticity and MR

� �

� �

�

= = ∆ ∆ =

< = ∆ ∆ <

> = ∆ ∆ >

0 MR Q TR/ : elastic unitary

1

0 MR

Q TR/ : inelastic

1

0 MR

Q TR/ : elastic

1

E X X P Q

elastic

unitary elastic

inelastic

MR QD

P


Cross-price Elasticity

QX = 22,000 − 2.5PX + 4PY − 1M + 1.5A

� �

� �

�

=

<

>

t independen 0

s complement 0

s substitute 0

E Y X P Q

X

Y

X

Y

Y

XYPXQ Q

P4

QP

PQ

E =⋅∂∂=

2


0QM

1QM

MQ

EXX

XMXQ <−=⋅

∂∂=

��

��

�

=

<

>

necessity 0

inferior 0

normal 0

E MXQ

Income elasticity

• Advertising elasticity: XAXQ QA 51E ��=


Nonlinear Demand

Taking natural logarithms:

AMYX AMPcPQ YXXββββ=

ln ln ln ln ln lnX X X Y Y M AQ c P P M A= +β +β +β +β

Elasticities are the coefficients: EQX = βX EQY = βY EQM = βM EQA = βA


Regression Analysis• Finds the equation that best fits the data.• May be linear

P

P’

Q’ Q(P’) Q

•

•

•••

•

•


• Or nonlinear

P

P’

Q’ Q(P’) Q

•

•

•••

•

•


Sum of Squared Errors (SSE)• The deviations of observed Q’ from

predicted Q(P’) are residual errors.• Squaring and summing these errors gives

the (SSE).• Least Squares Regression chooses the

coefficients β0 and βX for the equation which minimize the SSE.

QX = β0 + βXPX


Interpretation of Results• t-statistics: number of standard deviations σb that

the estimated coefficient is from zero (H0).

02σ σ σ 2σ b

bb

0btσ−=�

3


Goodness of Fit• R2 measures how much of the deviation in

the data is explained by the equation.• The total deviation is measured by the total

sum of squared errors TSS: deviations of observed values Q’ from the mean .

• The coefficient of determination is the proportion of the total deviation explained by the regression.

Q


TSSSSETSS

R 2 −=

• Note that 0 ≤ R2 ≤ 1. The closer R2 is to 1, the more explanatory power the equation has.

• R2 may be low because the TSS is large.

P

Q’ Q

•

• •

•

•

Q

error


Using R2

• R2 can be used to compare the results of two

different specifications of the equation, if

the have the same independent variables.

• If the two equations have a different number

of independent variables, then the adjusted

R2 is used.


Estimating Nonlinear Equations• The data must be converted by taking the

natural log of each variable.• A linear regression techniques can then be

used on the logged data.

ln ln ln ln ln lnX X X Y Y M AQ c P P M A= +β +β +β +β


Forcasting• To forecast with a nonlinear specification,

the value of the independent variables must

be entered in their logged form.

• The result is a value for lnQ. To get Q, take

the antilog:

Q = elnQ

If lnQ = 6.215, then Q = e6.215 = 500.2/26/2008 Managerial Economic Analysis Prof. Sharon Gifford Rutgers University 18

Auction of Airwaves• Data to access data go, to the CD or Bb.• Click Tools, Data Analysis, Regression.• Enter data for dependent variables lnP in

Input Y.• Enter data for independent data lnQ and

lnPop in Input X.• Hit Enter.

4


SUMMARY OUTPUT

Regression StatisticsMultiple R 0.92R Square 0.85Adjusted R Square 0.81Standard Error 0.32Observations 10.00

ANOVAdf SS MS F Significance F

Regression 2.00 4.02 2.01 19.95 0.00Residual 7.00 0.71 0.10Total 9.00 4.73

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept 2.23 0.43 5.24 0.00 1.23 3.24 1.23 3.24ln Pop 1.25 0.20 6.11 0.00 0.77 1.73 0.77 1.73ln Q -1.20 0.20 -6.10 0.00 -1.66 -0.73 -1.66 -0.73

Regression Results


Insert values for Pop and QForecasting Auction Prices:

lnP = 2.23 + 1.25*lnPop - 1.2*lnQ

Pop lnPop Q lnQ32.00 3.47 6.00 1.79

lnP = 2.23 + 1.25 * 3.47 -1.2 *1.79 = 4.41P = elnP= e4.41 = 82.44

Link


Table 3-8 DataData• Open Excel• Run the regression• Check your results

Quantity Price180 475590 400430 450250 550275 575720 375660 375490 450700 400210 500


Table 3-8 Regression ResultsRegression Statistics

Multiple R 0.87R Square 0.75Adjusted R Square 0.72Standard Error 112.22Observations 10.00

Analysis of Variancedf SS MS F Significance F


Coefficients Standard Error t Statastic P-value Lower 95% Upper 95%Intercept 1631.47 243.97 6.69 0.0002 1068.87 2194.07Price -2.60 0.53 -4.89 0.0012 -3.82 -1.37


Table 3-9 Data• Data• Regression

Quantity Price Advertising Distance28.00 250.00 11.00 12.0069.00 400.00 24.00 6.0043.00 450.00 15.00 5.0032.00 550.00 31.00 7.0042.00 575.00 34.00 4.0072.00 375.00 22.00 2.0066.00 375.00 12.00 5.0049.00 450.00 24.00 7.0070.00 400.00 22.00 4.0060.00 375.00 10.00 5.00


Table 3-9 ResultsRegression Statistics

Multiple R 0.89R Square 0.79Adjusted R Square 0.69Standard Error 9.18Observations 10.00

Analysis of Variancedf SS MS F Significance F


Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 135.15 20.65 6.54 0.0006 84.61 185.68Price -0.14 0.06 -2.41 0.0527 -0.29 0.00Advertising 0.54 0.64 0.85 0.4296 -1.02 2.09Distance -5.78 1.26 -4.61 0.0037 -8.86 -2.71

5


Project 1• Groups of up to four members• Read directions carefully• Excel guide in EXCELREG.doc• Use assigned data to analyze regressions• Write 2-3 page business report that

addresses the questions in the assignment • Provide calculations and regression results

in appendix and regressions on disk


Instructions• Send me an email with the names in your

group• I will set up a group on Bb with an assigned

data set• Your group can then communicate and

exchange documents through the group page.


1

Lecture 4 Production and Costs

Before a firm can determine the quantity to produce that maximizes its profits, it needs to know the cost of producing any particular quantity. Production technology and costs are closely connected. Understanding the nature of the production function helps to understand the nature of costs. Production depends on the technology available and the inputs used. A production function gives the maximum output that can be generated with the technology and amounts of inputs. Inputs can be either fixed or variable. Fixed inputs are those which, for the current planning horizon, cannot be increased and cannot be put to any other use. Variable inputs can be increased or decreased. Planning horizons can vary in length. The short-run is any length of time over which some input is fixed. In the long run all inputs are variable. There are two concepts of productivity that are crucial to understanding the relationship between production and costs. These are marginal productivity, which is a short-run concept, and economies of scale, which is a long-run concept. Marginal productivity is the measure of the additional output generated from increasing one input while holding all others fixed. Marginal product may be initially increasing, but is eventually decreasing, due to the existence of other fixed inputs. The marginal product and the price of the output determine the firm’s demand for the input in the short-run. In the long run, all inputs are variable and may be substitutable. If the rate of substitution between inputs is the same, no matter what combinations are used, then these inputs are perfect substitutes. If inputs cannot be substituted at all, then they are perfect complements. If the substitutability of inputs varies, then this substitutability is equal to the ratio of the marginal products. This substitutability is called the marginal rate of substitution. The goal of the firm’s production problem is to produce whatever quantity the firm thinks is optimal at the least cost. An isoquant is all combinations of inputs that generate a given level of output. An isocost line is all combinations of inputs that generate the same expenditure. The optimal combination of inputs is the one that is on the isoquant for the desired quantity and on the lowest isocost line. At this point, the two curves are tangent and the ability of the firm to substitute between inputs is equal to the rate at which they can be traded at their market prices. A cost function is the cost of these optimal input combinations for any quantity of output the firm wants to produce. The costs of fixed inputs are fixed costs and the costs of variable inputs are variable costs. The shape of total costs in the short-run depends on the shape of the production function. If there is initially increasing marginal productivity but eventual decreasing marginal productivity, then the total cost curve is increasing at a decreasing rate initially and then increasing at a decreasing rate. This implies that marginal cost, the slope of total cost, is U-shaped.

There are several important relationships among the different types of costs. If marginal cost is below average cost (either total or variable), then average cost is falling. If marginal cost is above average cost then average cost is rising. Marginal cost equals average cost at the minimum of average cost.

In the long run, we are concerned with whether or not production exhibits economies of scale. Production can be scaled up only if all inputs are variable.


2

Increasing returns to scale result in declining average costs. If average costs are constant, then the firm has constant returns to scale. Decreasing returns to scale occur if average costs are rising. This cost structures will be very important in determining the structure of industry.

Up to now we have considered a single product firm. However, many firms produce multiple products. There are two reasons for this. One is indivisible inputs that are not used to capacity by one input. This results in economies of scope. It is cheaper to produce two products with the same indivisible input than for two firms to duplicate this input and produce the two products separately.

Another reason for multi-product production is that producing a second input may lower the marginal costs of producing one product. This occurs when the second product generates byproduct that is an input for the first product. The cost of this byproduct is essentially zero. This is called cost complementarity.

1


Chapter 4Individual Behavior

Theory of consumer choice explains how consumption depends on prices,

income and preferences.


De gustibus non disputandum est

• Preferences are taken as given, except for four assumptions of rationality:

1. Completeness: A � B or B � A or A ~ B.

2. Nonsatiability: more � less

3. Transitivity: If A � B and B � C, then A � C.


Diminishing marginal rate of substitution (MRS)

• You are less willing to trade for something you have more of.

• The first unit goes to highest valued use.• The next unit goes to next highest valued

use.• The first unit is of greater value than the

second.


Indifference Curves• All bundles that are considered equivalent• Completeness implies ICs fill the plane.• More � less implies negative slope.

C � B � A

X

Y

A•B•

C•


• AB •

C •

Y

X

• Transitivity implies they do not cross.• A ~ C and B ~ C so A ~ B.• But A � B, more of X and Y.


4. Diminishing MRS implies that the slope of an IC is decreasing (in absolute value).

� AMRSA

MRSB

B�

∆X=1 ∆X=1 X

Y

The MRS at a point is the slope of the indifference curve. Willingness to trade Y for X

2


Constraints

With given income M and prices PX and PY, the consumer cannot spend more than income.

PXX + PYY ≤ M To graph the constraint, solve for Y:

Y = XPP

PM

Y

X

Y

−


Budget Constraint

Y

slope = - PX/PY

X

M/PY

M/PX

Y = XPP

PM

Y

X

Y

−


Changes in income M

Y

M’/PY

M/PY

M/PX M’/PX X

if M’ > M


Increase in PY

M/PY

M/PY’ slope = −PX/PY

slope = −PX/PY’

Y

M/PX X


Consumer Equilibrium

Most preferred bundle that satisfies budget constraint.

Y

A •Y* • C

• B

X* X


Equilibrium prices Reflect Preferences

At A, MRS > PX/PY.Willing to trade more Yfor X than prices require.

At B, MRS < PX/PY.Prefer to trade X for Y.

At C, MRS = PX/PY.No incentive to trade.

Y

A •Y* • C

• B

X* X

slope = MRS

slope = -PX/PY

3


Excel Workbook• Use this workbook to practice calculating

the slope and axis of the budget line.

Consumer Budget

PXX + PYY ≤ M

PX PY M5 2 50PX/PY M/PX M/PY

2.5 10 25Y = 25 -2.5

Consumer Budget

0

5

10

15

20

25

30

0 10 20 30 X

Y

Y

XPP

PM

YY

X

Y

−=


Deriving Consumer Demand• Y is a composite good

• Holding PY constant, at price PX, X(PX) is chosen.

• If PX increases to PX’, then X(PX’) is chosen.

Y

X(PX’) X(PX) X


Consumer DemandThese two points generate two points onconsumer’s demand for X.At each point on D, PX/PY = MRS ormarginal value of X.

PX’

PX

X(PX’) X(PX)

D


Law of Demand?

• If X is a normal good, then demand is

negatively sloped.

• If X is an inferior good, demand is

negatively sloped as long as PXX is not too

great a proportion of M.


Overtime or Wage Increase?Income

leisure24

A •

LA

• BC •

LBLC


1

Lecture 5 Organization of the Firm

Firms exist because they can generate goods more cheaply than if each person produced for their own needs. The last chapter described three reasons for this: economies of scale, economies of scope and cost complementarity. But to porduce the product, firms must acquire resources. Many resources are bought outright, while others, such as labor, are hired temporarily. Labor presents some special consideration, because the providers of labor services still retain some freedom to choose they actions. The problem for the firm is to determine the best way to hire and motivate labor services. Typically, labor services are hired in one of three ways: spot exchange, contracts and internally. Each of these practices has advantages and disadvantages and each is best in different situations. Spot exchange occurs in markets where a payment is made at the time of service at an easily determined and enforeable price and quality of service. Contracts allow the buyer and seller to make specific arrangements for cusomized delivery of services and payments. Internal labor services occur when a person is hired at a wage or salary and the employee’s task are only vaguely set out at the time of hiring. Which of these types of purchase techniques is used depends on the existence of transaction costs. Transaction costs are caused by the costs of time spent searching for the service, negotiating the terms of trade and enforcing the agreement. Search costs arise when the service required is not readilly available on spot markets. Negotiation costs include the time spent explaining the desired characteristics of the service and negotiating terms which motivate the supply of those services. Enforcement costs arise when there are specific investments by one or more parties. Specific invests are expenditures which cannot be recouped by trading with any other partner. When these exist, each party to the transaction has an incentive to renegotiate the terms after the specific investments have been made. Specific investments can be in specialized equipment, choice of location, of acquisition of human capital. Because of the possibility of this “hold-up” problem, parties are reluctant to engage in specific investments. Spot exchanges have the benefit of economizing on time. If the desired service is widely produced and easily obtainable at given prices, spot exchange requires little time or attention. If the quality of the service is easily observed, then there is no need for contracting. If there are no specific investments, then there is no opportunity for hold-up. However, the need for customized services, then contracting is useful for specifying the desired services. This imposes contracting costs but provides the buyer with the desired service. If there are no specific investments, then neither trade need worry about enforcement. Specific investments require stronger contracts to assure that each party lives up to the agreement.

If the service required is complex or vague enough, then it cannot be specified in a contract. In this case, the seller agrees to a wage or salary, depending on time served, and accepts direction of the buyer. The buyer (employer) can now specify exactly what service is desired at different times but bears the cost of spending time giving directions to the seller (employee). Thus, internalizing the trade within the firm requires more attention from the buyer but customizes the service.

The internal transaction does not eleiminate the problem of motivating the activities of the seller. If the actions desired by the employer cannot be perfectly


2

monitored and are costly to the employee, then, if given a fixed wage or salary, the employee has an incentive to shirk. If the employer makes the compensation dependent on some measure of the employees performance, then this is called an incentive contract. However, if the employee cannot control the measure of performance, then the employee is subject to risk. The optimal incentive is usually a combination of a base salary, to minimize risk, and a performance component, such as a bonus, which motivate high performance.

This is an example of the more general principal-agent problem. The principal hires the agent to perform tasks which benefit the principal. However, these task are costly to the agent and are not perfectly monitored by the principal. The relationship between stockholders and managers of a company is another example of the principal-agent problem. Incentives are used by stockholders to motivate managers’ effort to maximize the value of the stock. However, if managers are rewarded according to current stock prices, they will concentrate on short-run profits, perhaps to the detrimant of the future value of the firm. Stock options have the advantage of providing managers with incentives to maximize the long-term value of the firm.

However, managers cannot pefectly control the stock value of the firm, as this will be dependent on many outside influences. To minimize the risk that managers face, they are also paid a base salary aling with bonuses and stock options. If managers perform well and the value of the stock increase dramatically, then managers can receive extremely high incomes.

This same approsch is used to motivate employees of the firm other than top management. Employees often participate in profit-sharing programs. An extreme version is compensation by piece rate. This method ties an employees income to the number of units the employee produces. Commissions are a form of piece rate. if the employee can closely control the number of units produced, then this method generates little risk for the employee while providing powerful incentives.

1


Chapter 5

Production and Costs

Productivity determines the relationship between inputs and

outputs and the various measures of costs.


Production function• Output is produced from inputs, given a

particular technology• 2 inputs: labor L and capital K Q = F(K,L)• Efficient production: generates any output

level at the least cost.• Short-run: some input is fixed.• Long-run: all inputs are variable.


Some Definitions

• Total product (TP) is the most that can be produced with given inputs.

• Average product of labor (APL) is TP/L.

• Marginal product of labor (MPL) is ∆TP/∆L.


Total and Marginal Product• TP is increasing with additional L if the

MPL > 0. • Diminishing marginal returns occur when

MPL > 0 but decreasing.Q TP

L

MPL ↑

MPL ↓

L0


Marginal Productivity• This is a short-run concept: only one input

changes.• As long as marginal product is positive

output is increasing.• If marginal product is decreasing, then

output increases at a decreasing rate.• In general, firms will produce where there

are diminishing marginal returns.


Excel Workbook• Compare TP with AP and MP click here

Total, Marginal and Average Product TP = aQ + bQ2 - cQ3

a b c50 25 1L TP MP AP0 0 0 01 74 74 742 192 118 963 348 156 1164 536 188 1345 750 214 1506 984 234 1647 1232 248 1768 1488 256 1869 1746 258 194

10 2000 254 20011 2244 244 20412 2472 228 20613 2678 206 206

Total Product

0500

100015002000250030003500

0 5 10 15 20L

Q

TP

Marginal and Average Product

2


Value of Marginal Product

• The value of marginal product of labor VMPL is the additional revenue generated by the additional input.

• If P is the price of the product, then VMPL = P⋅MPL

• If w is paid for L and w < VMPL, then the firm should buy more L.

• If w > VMPL, then firm should buy less of L.


Optimal Employment

• Firm’s optimal purchase of L is where w = VMPL and VMPL is decreasing.

• This implies diminishing MPL.

w

VMPL

$

L*


Short-Run vs. Long-run

• In the SR some inputs are fixed.

• In the LR all inputs are variable.

• In the LR the firm is able to substitute some of one input for some of another and keep output the same (on same isoquant).

• This is called the marginal rate of technical substitution (MRTS).


Perfect Substitutes Q = 4K + L• If L is decreased by 1, Q decreases by 1. • If K is increased by 1, Q increases by 4.• Rate of substitution is ∆K/∆L = − 1/4.

K

5.55

2 22 L

Q = 22


Perfect Complements

Q = min {K/4, L}

• If K/4 > L, then can only produce L.• Must have 1 unit of L for every 4 of K• No substitution: fixed proportions


No Substitution Q = min {K/4, L}

• If K = 4 and L = 1, can produce Q(4,1) = 1.• K > 4 when L = 1 does not increase Q.

K

4

1 L

Q = 1

3


Variable Substitution

Q = K0.5 L0.5

• The ability to substitute is

MRTSKL = MPL/MPK

• MPL = 0.5K0.5L0.5-1 = K0.5/2L0.5

• MPL depends on level of K and L.


K

10

Q = 10

10 L

Q = K0.5 L0.5

Graph of Isoquant


Costs• Economic costs are the opportunity cost of

production.• With efficient production each level of Q is

produced at lowest costs.• To minimize the cost of producing any Q,

find lowest expenditure C = rK + wL

on K and L which produces Q.


Iso-Cost Line• All bundles of K and L that cost the same.• Solve iso-cost equation for K to graph it:

Lrw

rC

K −=

slope = - w /r

K

C/r

C/w L


Optimal Inputs for Q

• Use K and L on isoquant for Q and on lowest isocost.

K

C/r

K*

L* C/w L

Q

C’/w

C’/r


“Bang-per-buck”

• At cost minimizing K* and L*, slopes are equal

MRTSKL = MPL/MPK = w/r

or “bang-per-buck” is the same.

rMP

wMP KL =

4


Cost Definitions

• TC(Q) = FC + VC(Q)

• MC(Q) = dTC(Q)/dQ = dVC(Q)/dQ

• AVC(Q) = VC(Q)/Q

• AFC(Q) = FC/Q

• ATC(Q) = TC(Q)/Q = AFC(Q) + AVC(Q)


An Example• If TC(Q) = 200 + 2Q2

• FC = 200

• VC(Q) = 2Q2

• MC(Q) = 4Q

• AVC(Q) = 2Q2/Q = 2Q

• AFC(Q) = 200/Q

• ATC(Q) = 200/Q + 2Q


Graph of Example

$ MCAVC

ATC

Q

MC(Q) = 4QAVC(Q) = 2QAFC(Q) = 200/QATC(Q) = 200/Q + 2Q


Productivity and Costs• The shape of the TP curve determines the

shape of VC and TC.• If L is variable input, K is fixed input:• VC = w⋅L• FC = r⋅K• TC = VC + FC• MC is slope of TC


Q TP

L

w⋅L

Q

TC

VC

FC

• Multiply L by the wage and flip the graph.• Vertical axis measures costs.• ↑ slope of TP implies ↓ slope of VC.


Graph of MC• Initial ↑ MPL implies initial ↓ MC• Eventual ↓ MPL implies eventual ↑ MC• MC is U-shaped

Q

MC$

↑ MPL ↓ MPL

5


MC and AVC• If MC < AVC, then AVC is falling.• If MC > AVC, then AVC is rising.• If MC = AVC, AVC is minimized.

Q

AVCATC

MC

min AVC

min ATC

$


Example

• TC(Q) = 100 + 10Q − 18Q2 + 2Q3

• MC(Q) = 10 − 36Q + 6Q2

• dMC/dQ = − 36 + 12 Q

• MC is declining for Q < 3

• and increasing for Q > 3.


Excel Worksheet• Compare TC, AC and MC click hereProductivity and Costs TC(Q) = w*L(Q)

w

10

Q TC AC MC L

0 0 0

74 10 0.135 0.135 1

192 20 0.104 0.085 2

348 30 0.086 0.064 3

536 40 0.075 0.053 4

750 50 0.067 0.047 5

984 60 0.061 0.043 6

1232 70 0.057 0.040 7

Total Costs

0

50

100

150

200

0 2000 4000Q

$

TC


ATC and AFC• AFC = FC/Q is declining.• ATC = AVC + AFC

AFC

Q

AFC

AVC

ATCMC

AFC


LR Costs

• In the long-run FC = 0.

• Economies of scale is a long-run concept:

increasing if LAC is falling

decreasing if LAC is rising

constant if LAC is constant


One technology may exhibit all three properties

$

↑ rts ↓ rtsconstantrts

Q

LAC

6


Next Week• Organization of the Firm.• Project 1 is due next week.• Midterm Exam in 2 weeks


Multi-Product Production

• Economies of scope: lower costs to produce two products together.

C(Q1,0) + C(0,Q2) > C(Q1,Q2)

• Due to shared resources (indivisible inputs).

• Hub-and-spoke airline operations.


• Cost complementarity: production of a second product lowers MC of the first.

MC1(Q1,0) > MC1(Q1,Q2)

• One product uses byproduct of production of the other product.

• Lumber mills generate sawdust and shavings as byproduct of sawing and shaving lumber.

• MC of byproduct is zero.


1

Lecture 6: Nature of Industry There are two measures of the degree of concentration in an industry. The concentration ration gives the percentage of sales in some number of firms (four-firm concentration: sales of top four firms) and measures the degree of market dominance by a small number of firms.

The Herfindahl-Hirschman Index is the sum of the squared market shares of all firms in the relevant market, which therefore reflects unequal shares and all the of the firms (more firms, lower index). There is evidence that increased concentration leads to increased prices and profits. Concentration is not necessarily bad for consumers. Concentration may be due to the greater efficiency of a few firms which come to dominate the industry. A large number of smaller may be less efficient, and so charge even higher prices. The main limitation of the use these measures is that one must be able to define the relevant market.

The rest of this chapter is concerned with why industry structure matters. This is primarily a concern about whether firms have market power to exploit and whether the threat of potential entrants will spur better industry performance. Structure is easier to observe than performance, so we are at a disadvantage. This is why there is so much argument among economists and lawyers about the break-up of firms and the deregulation of industry.

We will see that competition promotes the most "social welfare". But sometimes, the lack of a monopoly means the lack of a market altogether. The threat of entry can keep firms from charging high prices, even if they have no current competition. the threat of entry can also promote more technological innovation. But it can also prevent firms from undertaking large investments unless they can protect the market for their product.

Describing the structure of a market may not be too hard, but we have to remember that what we are most concerned with is the incentives for firm behavior. Be sure to read the paper on the California electricity market under "External Links" on the course site.

1


Chapter 6

Organization of the Firm


Organizing Transactions• Labor services can be hired in many ways.• Labor input must be motivated to perform

to achieve firm’s objectives.• Three types of transactions

Spot exchangeContractInternal organization


Transaction Costs• Most effective organization depends on TC• Three sources of transaction costs

SearchingNegotiatingSpecialized investments


Spot Exchange• One time trade and immediate exchange of

serviceknown service quality (commodity)verifiable delivery at payment

• Service must be easily “found”• No search costs.• Service provider bears no transaction-

specific costs.• May be repeated over time.


Spot Exchange, cont’d.

• Getting required quality of service does not

require direction of seller’s effort by the

buyer.

• Prices are sufficient information.

• Price system economizes on time and

attention.


Using Spot Transactions• Manager of Pizza-Shack pays drivers to

deliver pizzas.• Pays fee per delivery.• Are drivers easily found when needed?• If paid ahead, can driver just take the pizza? • If paid after, can manager stiff the driver?• What if the driver has to buy a uniform and

decals for the car?

2


Contracts

• Contract is required if service provider incurs transaction specific costs (uniform).

• Service provider retains control over how it meets requirements of contract (not closely monitored).

• Contract must specify quality and motivations (timeliness, distance).

• Enforcement is required (penalty for nonperformance, legal enforcement).

• Contracts require attention to write.


Using a Contract• Manager writes contract specifying terms

(delivery, payments, penalties).• Penalties for nonperformance must be

enforced by courts (small claims court).• Costly to write a contract for each delivery.• Who pays for uniform and decals?


Transaction Costs

• Required fixed costs in addition to price incurred to purchase an input or service.

• Search, negotiate, investments.

• Must revenues to seller (price x quantity) cover production costs (VC) and transaction costs (FC)?


Specific investments• Provider buys specialized equipment,

location, human capital.• Bargaining problems arise because there is

a single buyer and seller.• Once specific investments are made, they

are sunk costs.• This leads to opportunism: renegotiation of

terms: “hold-up problem”.• Seller may under-invest in specific assets.


Specific investments prevent spot exchange

• Seller cannot recoup cost of investment.• Buyer will not make investment for seller.• If these specific investments are high

enough internalization is best• Then the buyer makes the investment.


Internalize• Purchaser acquires “control” over how

service is provided.• Services required are not explicitly

specified in contract.• Service provider accepts direction of efforts

from buyer.• Service is fitted to needs of buyer.• Provider requires direction (attention) from

buyer.

3


Hiring the Driver• Manager pays for and controls driver’s time

(monthly salary).• Time and distance for each delivery are not

specified (driver is on standby).• Driver makes whatever deliveries required

by the manager.• Manager still must spend time giving the

driver instructions.


The Principal-agent Problem

• Employee motivation and compensation

• Example: stockholders and management

• Performance of stock depends on manager’s

effort and other factors.

• Manager’s effort is costly to manager.

• Owner cannot perfectly monitor manager.


Piece Rates

• An extreme version of incentives is piece rate: the manager is paid by the number of units produced.

• If the manager can control production measure, then risk is minimal.

• Must be able to measure output individually.


Flat Salary• Manager’s pay does not depend on

performance.• In extreme case, manager has no incentive

to work at all.• However, if long-term performance can be

observed, manager may be fired if performance is low.

• If pay is higher than opportunity cost, manager wants to keep job.


Using Stock Performance

• With fixed salary, independent of stock performance, manager may shirk.

• Incentive contract, based solely on stock performance, puts manager’s income at risk.

• Compensation based on stock price along with base salary reduces risk and rewards high effort.

• But manager may focus an short-term performance only.


Long-term Compensation

• Stock options reward effort which generates improved future performance.

• Stock options for other employees provide incentives if employees feel their behavior strongly affects stock price.

• Managers cannot sell stocks in large quantities without disclosure.

• How did Enron managers get around this?

4


Market Incentives• Reputation as good manager increases value

on employment market.• Bad performance may eliminate future

employment.• Some managers become entrenched because

of influence with board members.• Firms with poor management are subject to

takeovers which replace management.• Why didn’t these controls work for Enron?


• Project 1 due today.• Midterm exam is next week.• Test yourself with the Study Guide.• Sample exam with answers is on Bb.• You may bring one 8(1/2) x 11sheet of

paper with notes but no magnifying glass.• Write out your notes yourself.• You may want a calculator.• The exam will be for 2 hours.


1

Lecture 7: Perfect Competition, Monopoly, and Monopolistic Competition This chapter covers the three main industry models: perfect competition, monopoly, and monopolistic competition. Oligopoly models are described in the next chapter (next week).

The fundamental assumptions of perfect competition are: a) Both buyers and sellers (the firms in the market) are price takers. b) All firms produce the same product at the same costs. c) There is perfect information about product and price. d) There are no transaction costs. e) There is free entry into the market. "Price taking" means taking the price as given and believing that you cannot change it through your actions. In the context of a firm in a PC market this means that they take the market price as given and believe that no matter their output the price will remain fixed. This is like facing a perfectly horizontal demand curve at the given price. Marginal revenue is therefore simply the given price. "Free entry" simply means that there are no barriers to entry and any firm can enter the market and begin producing the given product if they choose to.

In the short run, the number of firms in the industry is fixed (no entry or exit occurs) and the firms face their short run cost curves. An individual firm follows two rules in determining its short run action: a) If P < AVC (short run) they shut down (Q = 0). b) If they produce they do so at the Q which satisfies MC(Q) = P. It follows that a firm's short run supply curve is its short run marginal cost curve in the region where short run marginal cost exceeds short run average variable cost. Firms would rather shut down than sell at a price below average variable cost.

The overall market short run supply curve is therefore the horizontal sum of all the individual firm's short run supply curves. By summing the quantities supplied by each firm at the given price, you derive the quantity supplied by the market at that price. Doing this for every price results in the market supply as a function of price. The short run competitive equilibrium is at the intersection of the market supply and market demand curves. This determines the price that the firms take as given in choosing their quantities and the amount of output the industry as a whole produces. The amount an individual firm produces is where the equilibrium price crosses the individual firm's supply curve.

In the long run firms enter the market if there are positive profits and exit the market if there are negative profits. Therefore, the long run equilibrium price is equal to average cost, making profits zero. Since this must also maximize profits, price equals marginal cost as well. Therefore, the long-run equilibrium price is equal to the minimum of average costs, where average cost equals marginal cost.

A monopoly is an industry that is served by a single firm. Because it is the only firm in the market, the demand curve facing a monopolist is the market demand curve. Any firm is said to have market power when they face a downward sloping firm demand curve. Entry into a market governed by a monopoly is assumed to be completely blocked. In other words there are barriers to entry. These barriers allow a monopolist who makes profits to persist. There are many different types of barriers to entry that can be broadly classified as legal (government protected monopoly, copyrights, patents, etc.),


2

technological (the potential entrant can't access key resources, is at a cost disadvantage (scale economies), lacks specific knowledge, etc.) and strategic (these are barriers that could fall into the other two categories, but are barriers that the monopolist has erected, like establishing a brand name (product differentiation), brand proliferation, limit pricing, etc.).

The fundamental assumptions governing an economic model of monopoly are: a) Sellers are price makers (i.e. they dictate the market price through their action). b) Entry into the industry is completely blocked. c) Buyers are price takers. The monopoly quantity will be where marginal cost equals marginal revenue. Since the marginal revenue is less than the price, this implies that the monopolist’s price will be greater than marginal cost. This implies that there are buyers who are willing to pay prices higher than the marginal cost but are unable to purchase the product. This implies a dead weight loss from monopoly due to reduced trade. Less output is produced and sold by a monopolist than the amount that would maximize the gains from trade. A monopolist with multiple plants for producing its product faces a similar but more complicated problem than a competitive firm with multiple plants. In both cases, the total cost of producing the output is minimized if the production is distributed between the plants so that the marginal cost of an additional unit of output is the same at both plants. The competitive firm only has to choose output where the marginal cost in each plant is equal to marginal revenue, which is the price of the product. The monopolist will also choose output at each plant where marginal cost is equal to marginal revenue, but for the monopolist, marginal revenue depends on the total amount produced. A monopolistic competitive market is one in which a) there are many buyers and sellers (like perfect competition) b) free entry and exit in the long-run (like perfect competition) c) but each firm produces differentiated product(s). This last assumption implies that firms face negatively sloping firm demands for their products. Therefore, they price like monopolists, since they have market power. However, free entry and exit implies that positive profits cannot be sustained in the long-run. If a firm is making positive profits, other firms are free to enter this market. This results in a decreased demand for the firm’s product, reducing profits as well. Entry continues until profits fall to zero.

The firm will still be pricing above marginal cost and have average costs above the minimum in the long-run equilibrium. This implies that this market results in a dead weight loss similar to monopoly. The only way to remove this dead weight loss is for all the firms to produce the same product and behave as perfect competitors. This eliminates the dead weight loss but also the variety of products. The value of this variety is difficult to measure.

1


Chapter 7

The Nature of Industry


Market Structure

• Optimal firm decisions depend on the firm’s market environment.

number of firms

their relative sizes

costs

demand conditions

ease of entry and exit


Number and Size of Firms

• Some industries are dominated by a few

large firms.

• Concentration ratios measure how much

output is produced by the largest firms.

• Concentration ratios are a rough measure of

the size distribution of firms in an industry.


Concentration Ratios• S1,…,S4 are the sales of the four largest

firms.• ST is total sales of all firms.

T

43214 S

SSSSC

+++=


Using Market Shares

• Equivalently, with w1,…,w4 the shares of the four largest firms,

C4 = w1+w2+w3+w4.

• For highly concentrated industries, C4 is close to 1.


Herfindahl-Hirshman Index

• The Herfindahl-Hirshman index uses squared market shares wi of all firms and eliminates decimal places.

• Larger weights on larger firms.

�= =N

1i2iw00010HHI �

2


Shortcomings

• Both indices depend on definition of the market.

• Products with large positive cross-price elasticities are in the same market.

• Exclude foreign firms.• Ignores difference between national and

local markets.• Both indices are trying to measure market

power.


Using Price Elasticities• A firm’s elasticity of demand is greater than

the market elasticity if there are substitutes.• market elasticity ET< EF firm

elasticity• The Rothschild index: 0 < ET/EF < 1• If Rothschild index is close to one, the firm

has monopoly power.• In some markets price is easily observed

while in others it is difficult.


Using Price Mark-up

• Lerner index measures price markup over marginal cost.

• Firms in a competitive market will have L close to zero.

• A better measure, but requires more information.

PMCP

L−=


Ease of Entry

• Measures of concentration and market elasticity are for a fixed number of firms.

• Ease of entry of new firms in the long run depends on barriers to entry:capital requirements,

licenses,

patents,

market size.


Consolidation• In the long run, firms may merge as well.

• Vertical integration unites a firm with a supplier or customer.

• This can reduce transaction costs.

• Horizontal mergers are between firms producing a similar product.

• This can reduce costs due to economies of scale or increase market power.


Other Consolidations

• Conglomerate mergers combine different

products.

• This can spread risk and improve cash

flows.

• Hostile takeovers remove inefficient

management.

3


Market Performance

• Firm performance is measured by profits and by contributions to social welfare.

• The Dansby-Willig performance index measures how much consumer and producer surplus would increase if a market expanded to the socially efficient output.


Industry Analysis

• Industry analysis models firm conduct and

performance for different market structures.

• Structure-Conduct-Performance Paradigm

assumes that concentration causes

monopoly pricing which causes high profits

and poor social performance.


• Feedback view recognizes that high profits

affect structure by encouraging new firms to

enter the market, affecting conduct and

future performance.

• In addition, low prices and good social

performance can occur with few firms.


Two extreme cases

• 1. Perfect competitionmany firmssimilar productssimilar technologies and costseasy entry

• 2. Monopolyone firmno entry


Many Intermediate Cases

• 1. Monopolistic competitionmany firms

product differentiation

easy entry

• 2. Oligopoly: few firms, similar products, no entry. Includes Sweezy, Cournot, Bertrand, Dominant Firm, and others.


Project 2• Groups can have up 4 members.• Choose an industry that you are interested

in.• Be sure to carefully review each member's

contribution to the report.• Project is due on class before Final Exam.


1

Lecture 8: Basic Oligopoly Models

Oligopoly refers to market structures in which there are more than one firm but there are few enough that each has a material effect on the market price. Unlike perfect competition and monopoly, there is no single theory of oligopoly. Oligopoly can refer to any situation that occurs between the two theoretical extremes of perfect competition and monopoly. However, we can list the basic assumptions:

a) Sellers are price makers b) Sellers behave strategically c) There are barriers to entry in most models d) Buyers are price takers

The Sweezy Model (Kinked Demand) explains stable prices even as costs

fluctuate. There is a kink in the firm demand curve at the current price because the firm believes that if it lowers its price, the other firms will match this price reduction. If the firm raises its price, it assumes the other firms will not match the price increase. This implies that the demand curve is more elastic above the current price than below it. The result is a discontinuity in the MR curve, with MC passing through the gap. Small shifts in MC do not result in any price changes.

In the Cournot Model (Quantity Competition) all firms produce the same standardized product. The total quantity produced and demand determine the price. Each firm chooses its quantity taking the other firms' quantities as given. In duopoly, each firm takes the other firm's quantity as given and uses a reaction function to choose quantity to maximize profits. A Cournot duopoly produces a total market quantity which is 2/3 of the competitive quantity, which is more than the monopoly quantity of 1/2 the competitive quantity. If there are more firms in the market the quantity produced increases and approaches the competitive quantity as the number of firms increases.

Collusion (Cartel) is a formal or informal effort to prevent quantity competition from lowering the market price below the monopoly price. Both firms are better off if they maintain the monopoly price.

In the Stackelberg Model (Price Leadership) the optimal production decision of a one firm must take into account how the follower firm will react. The leader determines its residual demand by subtracting the followers' supply from the market demand. Using this residual demand, the price leader chooses the quantity to maximize its profits. The follower’s supply the rest of the market taking the leader’s quantity as given. In the Bertrand Model (Price Competition) firms choose prices and the firm with the lower price gets the entire market. This leads to a price war, which drives the price down to marginal cost. The price, market quantity and profits are the same as in a perfectly competitive market. In Contestable Markets, there is free entry and exit, so the number of firms is not given, as in the other oligopoly models. If current firms make positive profits, then additional firms enter the market and the price falls. This continues until price falls to average costs. If there are negative profits, then some current firms exit the market. This continues until price rises to equal average costs. The market is in long-run equilibrium when there is no incentive for firms to enter or exit the market. Therefore, the condition


2

for long-run equilibrium is zero profits. The quantity, price and profits are the same as the competitive long-run equilibrium, even though there may be few firms.

1


Chapter 8

Competition, Monopoly and Monopolistic Competition


Perfect Competition

• 1. many buyers and sellers (all price takers)

• 2. Firms produce the same product

• 3. perfect information

• 4. no transaction costs

• 5. free entry and exit of firms

• Examples: agriculture, stock and commodity markets.


Implications

• Market price is the market equilibriumprice. Firms are price takers.

• Firm can sell all it wants at the market price. Each firm is small.

• Firm demand is horizontal line at market price. P= MR.

• Each additional unit of output can be sold at this price.


Market Determines Price

• Market equilibrium Pe is where supply equals demand

• Firm demand is horizontal line: price-taker.

QFQM

Market

D

DFPe

PSPFirm


MR = P

• Marginal revenue is equal to the market price

because the price does not depend on the firm’s

production level.

• TR(Q) = P⋅Q

• MR(Q) = dTR(Q)/dQ = P


Maximizing Profits

• Profits: total revenue minus total costs

π(Q) = P⋅Q – TC(Q)

• Setting dπ(Q)/dQ = 0 gives

P − MC(Q) = 0

• or P = MC(Q).

2


Firm SupplyThe firm supplies the quantity Q* at which the

MC(Q*) = P.

MC

AVC

Q

$P

Q*


Firm Profits

• If P > ATC(QF), then

π = [P − ATC(QF)]QF > 0

• If P = ATC(QF), then π = 0.

• This occurs at the min ATC.

• If P= min ATC, then π = 0.

• min ATC is where ATC = MC.


• Firm may produce at a loss in the short run.• Pe < ATC so π < 0: profits are negative.• But Pe > AVC. Revenues cover variables

costs.

MCATC

$

AVCPe

QF Q


Losses in the short-run• Firm’s choice is to produce QF or Q = 0

• Better to produce QF > 0 if

π(QF) = P⋅QF − VC(QF) − FC > π(0) = − FC

P⋅QF − VC(QF) > 0

QF[P − AVC(QF)] > 0

P > AVC(QF)

• If P < min AVC, then it is better to shut down in the short run.


Firm Supply

• The firm’s short-run supply curve is the MC curve above min AVC.

• min AVC can be found by setting AVC = MC. MC

AVC

Q

$


Market Supply

• Market supply is the horizontal sum of all firm supplies in the industry.

minAVC

SMSFP

Q

3


Algebraic Example

If TC(Q) = 100 + 10Q2 then MC(Q) = 20Q

and firm supply is

P = 20Q = MC and QF = P/20.

If there are 100 firms then market quantity is

QM = 100QF = 100P/20 = 5P

and market supply is

P = QM/5.


Entry and Exit• In the long-run, firms choose to enter or exit

the market.• If π > 0 at P0, additional firms will enter.• Market supply shifts out and the

equilibrium price falls to P1 where π = 0.S0

S1

P0

P

P1

D

Q


• If π < 0 at P0, additional firms will exit.• Market supply shifts back and the

equilibrium price rises to P1 where π = 0.

P

D

Q

P0

P1

S0S1


Long-run Equilibrium• A long-run equilibrium is P = min LAC.• No firms want to enter or exit.

$LAC

min LAC

Q


Long-run Efficiency

• Profits are maximize (P = LMC) and profits are zero (P = LAC).

• Economic profits take into account the opportunity cost of the owner(s) of the firm.

• The long-run equilibrium Pe can be found by setting LAC = LMC


An Example

If LRC = 100Q + 100Q2 − 5Q3

Set LAC = LMC and solve for Q:

100 + 100Q − 5Q2 =100 + 200Q −15Q2

100Q − 5Q2 = 200Q − 15Q2

15Q − 5Q = 10Q = 200 − 100 = 100

Q = 10 and LAC(10) = 600 = Pe in the LR.

4


Practice CalculationsExcel Sheet: Make small changes in a,b,c or f tocheck your calculations of minATC and minAVC

Total, Marginal and Average Costs TC = f + aQ + bQ^2 - cQ^a b c f

500 40 2 1000Q TC MC ATC AVC

1 1462 426 1462 4622 1856 364 928 4283 2194 314 731.3 3984 2488 276 622 3725 2750 250 550 3506 2992 236 498.7 3327 3226 234 460.9 3188 3464 244 433 3089 3718 266 413.1 302

10 4000 300 400 30011 4322 346 392.9 30212 4696 404 391.3 30813 5134 474 394.9 31814 5648 556 403.4 33215 6250 650 416.7 350

Total Costs

0

5000

10000

15000

0 5 10

Q

Marginal and Average Costs

300

400

500

600

700

800

Q


Gains from Trade• Because MC = MB, gains from trade are

maximized in a perfectly competitive market.

S = MC

D = MB

CS

PS

Q

P


Monopoly• A monopoly can arise from economies of

scale, scope or cost complementarities that give one firm a cost advantage.

• A monopoly may be licensed or own a patent.

• A monopoly faces the market demand.

• If a monopoly firm wants to sell more of its product, it must lower it’s price.


MR < PThe change in revenue from selling one more

unit of output is TR(Q0+1) − TR(Q0) = P1⋅(Q0+1) − P0⋅Q0

= B − A = P1 − A < P1

B

AP0

P1

D

Q0 Q0+1 Q


Linear Demand

If demand is P = 100 − 2 Q then

TR(Q) = P⋅Q = (100 − 2 Q)⋅Q = 100 Q − 2Q2.

MR(Q) = dTR(Q)/dQ = 100 − 4 Q.


• MR has the same vertical intercept and twice the slope as a linear demand

• At Q = 25, MR = 0, TR is max’d, EP = -1

Q50MR25

D

slope = -2slope = -4

P100

5


Profit maximization

Set MR(Q) = MC(Q).

If TC(Q) = 10 + 2Q, then

MC(Q) = 2

Set MR(Q) = 100 − 4 Q = 2 = MC

Solve for the optimal Q = 24.5.

Optimal P = 100 − 2(24.5) = 5.1


There is no supply curve for a monopolist.

MC

P100

5.1

2D

24.5MR

Q


Implications of Monopoly• If P > AC, π > 0. No entry of other firms

due to barriers to entry.

P MC

P(QM)AC(QM)

AC

MR DQM Q


InefficiencyA: lost gains from trade due to QM < QPC

P MC

A

MR D

QM QPC Q


Multiple Plants

• Same product produced by two plants,

1 and 2.

π(Q1,Q2) = R(Q1 + Q2) − TC1(Q1) − TC2(Q2)

• Optimal production implies

MC1(Q1) = MC2(Q2)


Demand for product: P = 70 − 0.5Q, whereQ = Q1+Q2. Then

MR(Q) = 70 − (Q1+Q2)

MC1(Q1) = 3Q1 MC2(Q2) = Q2

MC1(Q1) = 3Q1 = 70 − Q1 − Q2 = MR(Q1+Q2)

and

MC2(Q2) = Q2 = 70 − Q1 − Q2 = MR(Q1+Q2)

6


Two equations with two unknowns, Q1 and Q2.Solve the second one for Q1 as a function of Q2

Q1 = 70 − 2Q2

substitute into the first equation

Q2 = 70 − 4Q1 = 70 − 4(70 − 2Q2)

and solve for Q2 = 30 and

Q1 = 70 − 2Q2 = 10.

Then Q1+Q2 = 40 and P = 70 − 0.5 Q = 50.


MC Equal Across Plants• MC1(10) = 3⋅10 = 30 = MC2(30)• So MC(40) = 30 = MR(Q) = 70 − Q

P MC1 MC2 MC(Q)

30MR D

10 30 40 Q


Monopolistic Competition• 1. many buyers and sellers (like PC)• 2. free entry and exit (like PC)• 3. firms produce differentiated products• Products are close, not perfect, substitutes• Common consumer products:

cereals, personal hygiene, detergents• Each variation designed to fit a niche in

consumer tastes. • Product distinctions require advertising.


• Each firm faces a negatively sloping demand for its product.

• Firms price like monopolists.

• Positive profits lead to entry of firms in the LR.

• Entry reduces firm’s demand.

• Entry and exit imply zero profits in the long run.


Positive profits in the SR

P MC

P(QMC)AC(QMC)

AC

MR D

QMC Q


Zero Profit in LR• Entry in the long run decreases firm’s

demandP MC

P(QMC)=AC(QMC)

AC

DMR' D’

QMC Q

7


Implications• In the long-run equilibrium, profits are zero

but P > MC : inefficient• and AC > min AC : inefficient• Alternative is a homogeneous product

produced by all firms.• This would be a perfectly competitive

market.• Value of variety of products is hard to

measure.


1

Lecture 9: Game theory

Chapter 10 introduces the analytical tools of game theory for modeling the strategic interactions of firms in oligopolies. . Game theory refers to the analysis of situations in which the outcome for each individual player depends not only on his own actions but also on the actions of a small number of other players. The critical element is the importance of strategic thinking. In determining your optimal action you need to consider the actions of the other players which are also made upon considering your action, etc.

All the players in our games are going to be maximizing their own well being (in economic games this is generally profit). Each player also believes that each other player acts this way. The specification of a (single play) game entails three elements: a) the identity of the players, b) the set of strategies available to each player c) the pay-off to each player for each possible combination of strategies.

The set of strategies (one for each player) that is the solution is called the Nash equilibrium. In an equilibrium, neither player wants to change his or her decision, given the other player's decision. One way of finding an equilibrium of a game is through the concept of a dominant strategy. A dominant strategy for any player is a strategy for that player that yields the best payoff no matter what the other player does. If any player has a dominant strategy they would clearly play it. A way to find the solution to the game then is to check for dominant strategies. Dominant strategies will be played.

In the pricing game (Prisoners’ Dilemma), the Nash equilibrium is for both firms to charge a low price, even though they would both be better off if they both charged a high price. This characteristic is also represented in the advertising and quality games. In the coordination game (Battle of the Sexes), there are two equilibria in which both players choose the same strategy. This game represents the problem of choosing a common standard. Often an outside party is needed to determine which standard should be provided. The employee monitoring game has no Nash equilibrium. If employees are monitored, then their best response is to work hard. But if employees are working hard, the firm can lower costs by not monitoring. A typical response to this dilemma is to have random monitoring. In the bargaining game, the strategy of asking for nothing is a dominated strategy. Therefore, any request by one party that generates a positive payoff only if the other party asks for nothing can be ruled out.

Repeated games can be of three types, infinitely repeated, finitely repeated with a known final period and finitely repeated with an uncertain final period. The infinitely repeated game allows players to adopt trigger strategies, which result in effective collusion. This resolves the dilemmas of the one-shot games. In the finitely repeated games, a certain final period eliminates the use of trigger strategies. In the last period, the optimal strategy is to cheat, since there is no future play in which to be punished. However, the same is true of each preceding period, given that cheating is best in the next period. An uncertain final period results in equilibrium trigger strategies just as in the infinitely repeated games.

In multi-stage, or sequential, games, players take turns choosing their strategies, based on the previous strategies of other players. Although a game may have multiple Nash equilibria, some are “better” than others. A subgame perfect Nash equilibrium requires that at each node of the equilibrium path, the player chooses the strategy that has


2

the highest payoff. This eliminates Nash equilibria in which one player makes a threat that is not credible. In the sequential entry game, an incumbent firm cannot prevent entry by another firm by threatening to lower its price after entry. This threat is not believable sine the best strategy for the incumbent firm is to maintain the high price after entry. In a sequential bargaining game, a threat to reject a low offer is not believable since it is better to accept a low offer once it is made.

1


Chapter 9

Basic Oligopoly Models


Several Interacting Firms• Oligopoly refers to markets in which firms

interact strategically.• Each firm’s decision depends upon what it

believes other firms will do.• More than one firm, but not many.• Interdependence of decisions makes

manager’s problem complex.• Number of possible beliefs about other

firm’s behavior leads to many models of oligopoly.


Assumptions• All models assume: 1. Few firms who try to predict reactions of

other firms. 2. Barriers to entry even in the long run.• except for contestable markets, which

assumes free entry and exit.


Sweezy Model (Kinked Demand)• Firms choose prices.• Each firm believes a price reduction will be

matched but a price increase will not be matched.

• Demand is more elastic to price increase than to price decrease.


Kink in Demand

price is matched

price not matched

D

Q

P

P*

• At current price P*, demand is more elastic for a price increase than for a price decrease.


Equilibrium P* and Q*At current Q*, there is a gap in MR. At lower Q, MR > MC. At higher Q, MR < MC.Therefore, Q* is optimal.

QMRQ*

D

MC

PP*

2


Predictions• MC may shift and leave the optimal Q* and

P* unchanged.• Model explains reluctance of firms to

change prices, even as MC changes.• Therefore, price can be “sticky”.


Cournot (Quantity Competition)

• Firms choose quantities, market price depends on total quantity supplied.

• Firms assume other firms’ quantities remain the same.

• Each firm has a reaction function that determines the best quantity for any given level of other firms’ quantities.


A Duopoly Example• The equilibrium choices are given by the

quantities that satisfy both reaction functions.

• Firm 1’s problem: choose Q1 to

max π(Q1,Q2) = P(Q1,Q2)⋅Q1 − TC1(Q1)

where

P(Q1,Q2) = 10 − (Q1+Q2)

Set MR1(Q1,Q2) = MC1(Q1)2/26/2008 Managerial Economic Analysis Prof. Sharon Gifford Rutgers University 10

Deriving MR

• Firm 1’s demand can be written P = (10 − Q2) − Q1

• Firm 2's quantity is assumed constant and so is part of the intercept. The slope of demand is −1.

• MR1 = (10 − Q2) − 2Q1

• Same intercept, twice the slope.


Firm 1’s Reaction Function

• If MC1 = 0, then set

MR1 = (10 − Q2) − 2Q1 = 0 = MC

• and solve for Q1 as a function of Q2:

Q1*(Q2) = 5 − (1/2)Q2

• This is firm 1’s reaction function.

• It specifies what Q1 should be for any Q2.


Firm 2’s Reaction Function

• Firm 2’s problem is similar and reaction function is

Q2*(Q1) = 5 − (1/2)Q1

• This is due to symmetry of the example.

• Solve these two equations for the two unknowns, Q1* and Q2*.

3


Solve for Q2*

Q2*(Q1) = 5 − (1/2)Q1

= 5 − (1/2) [5 − (1/2)Q2]

= 2.5 + (1/4)Q2

Q2* = (4/3)(2.5) = 10/3.


Solve for Q1*

Similarly

Q1*(Q2) = 5 − (1/2)Q2 = 5 − (1/2)(10/3)

= 5 − 10/6 = 20/6 = 10/3.


Price and Profits

• P(Q1*,Q2*) = 10 − Q = 10 − 20/3 = 10/3.

• Profits for firm 1 are

π1(Q1*,Q2*) = P⋅Q1* − TC1

= (10/3)(10/3) − 0 = 100/9 = 11.11

• Total profits of both firms are

π1 + π2 = 200/9 = 22.22.


Collusion

MRM = 10 − 2QM = 0 = MC => QM*= 5

• If the firms had colluded on quantity, they would choose to each produce half of the monopoly quantity QM = Q1 + Q2.

or QM = 5 and P = 10 − 5 = 5.

• Total profits are

πM = PM⋅QM − 0 = 5⋅5 = 25

• Each firm gets πi = (1/2) 25 = 12.5 > 11.11.


Excel Worksheet (click)

a b c10 1 0

P = a - bQ1- bQ2MR1 = (a - bQ2) - 2bQ1 = c = MCSolve for Q1 as a function of Q2

Q1 = 5 -0.5 * Q2Q2 = 5 -0.5 * Q1

Solve these equations for Q1 and Q2

Q1 = Q2 = 3.33Calculate price P = 3.33

Calculate firm's profit = 11.11Calculate total profit = 22.22 5

Compare to collusion and competition

Collusive Q, P and profits 5.00 5 25Competitive Q, P and profits 10.00 0 0

Cournot Reaction FunctionsReaction Curves

0

5

10

15

20

0 5 10 15 20Q1

Q2 Q1

Q2


Better Off Colluding• Each firm makes a higher profit if the two

firms collude and act like a monopolist.

• This is one explanation for the desire of firms to horizontally merge.

• Anti-trust regulation prohibits collusion because it produces less surplus..

• We will return to this later.

4


Stackelberg (Price Leader)

• One firm (follower) chooses a quantity

taking the other firm’s quantity as given.

• “Price” leader chooses a quantity that

considers the supply of follower.

• The follower behaves like a Cournot firm.

• The leader is more sophisticated.


Residual DemandSfollower

Q

Dmarket

DresidualP2

P1

P

At P1, follower supply equals demand.At P2, no follower supply.At intermediate prices, leader faces residual D.


• Leader’s reaction function takes into account the followers reaction function.

• Using the residual demand, the leader determines it’s MR and sets it equal to MC.

Q

Dmarket

DresidualP2

P1

SfollowerP

MRresidual


Algebraic Example• Market demand: P = 50 − (QL+QF)

Costs: TCL = 5 + 2QL

TCF = 5 + 2QF

• Follower’s reaction function: set

MRF = MCF

MRF = (50 − QL) − 2QF = 2 = MCF

• Solve for QF* = 24 − (1/2)QL


The Leader’s QL*

• Substitute the follower's reaction function into market demand function to get the residual demand:

P = 50 − [24 − (1/2)QL] − QL

= 26 − (1/2) QL

• Set MRL = 26 − QL = 2 = MCL

to get QL* = 24.2/26/2008 Managerial Economic Analysis Prof. Sharon Gifford Rutgers University 24

The Follower’s QF*• Substitute QL* into follower’s reaction

function QF* = 24 − (1/2)24 = 12.• Substitute Q = QL* + QF* = 36 into market

demand P = 50 − 36 = 14.

5


Profits

• πL(QL*) = P⋅QL* − 5 − 2QL*

= 14⋅24 − 5 − 2⋅24 = 283.

• πF(QF*) = P⋅QF* − 5 − 2QF*

= 14⋅12 − 5 − 2⋅12 = 139.


Bertrand (Price Competition)

• Firms choose their own prices, taking the other prices as given.

• Firms sell perfect substitutes.

• Buyers choose the firm with the lowest price.

• Firm with the lowest price captures the market.


Firm 1’s Demand

QD if P1 < P2

Q1 = (1/2)QD if P1 = P2

0 if P1 > P2

Given P2, firm 1 chooses P1 < P2. Given P1, firm 2 chooses P2 < P1. Outcome is P = MC.


P

MCD

Q

Equilibrium • Equilibrium price equals marginal cost.


Comparing the ModelsAn Example

• demand: P = 1,000 − Q1 − Q2

• costs: TCi = 4Qi i = 1,2• Competitive market: Q = Q1 + Q2

Ppc = MC = 4, Qpc = 996, πi = 0• Monopoly: MRM = 1,000 − 2Q = 4 = MC QM = 498, PM = 502 πM = (PM − 4)QM = (502 − 4)498 = 248,004


Competition vs. Monopoly• In general, QM = (1/2) Qp

• Total surplus is also half of competitionP

MC

MR D

QM Qpc Q

6


Cournot: Reaction Functions

Q1* = 498 − (1/2)Q2

Q2* = 498 − (1/2)Q1

Q1* = Q2* = 332 = (1/3)Qpc

Pc = 1,000 − 664 = 336, πi = 110,224.

• In general, if there are N Cournot firms

Qi* = Qpc/(N+1)


• Cournot produces more than Monopoly but less than Competition.

• Surplus is also more than Monopoly but less than Competition.

P

MC

MR D

QM Qpc Q

P

MC

MR D

QM Qpc QQC


Collusion and Bertrand

• Cournot collusion is the same as monopoly:

Qi* = (1/2)QM = 249.

Pc = PM = 502, πi = (1/2)πM = 124,002.

• Bertrand is the same as perfect competition:

PB = PPC = MC, QB = Qpc, πi = 0


Entry in Oligopoly

Contestable Markets: Free entry and exit

If π > 0, entry occurs, P falls until P = AC.

If π < 0, exit occurs, P increases until P =AC.

LR equilibrium implies π = 0.

Same as long-run perfect competition, even if there are few firms.


1

Lecture 10: Pricing Strategies Firms with market power (not price takers) have the ability to affect the price of their product. Up to now we have considered only the case in which the firm charges the same price for each unit of the product that it sells. For this case, we have the markup rule which relates the optimal price to the constant elasticity and constant marginal cost of the product. Under special circumstances, a firm with market power may be able to make higher profits with other pricing stragegies. Price discrimination (PD) describes three pricing strategies that result in different customers paying different prices for the same product. The firm must have some information about customers’ willingness to pay for the product and be able to prevent arbitrage. The differences in the three types of PD are due to the amount of information the seller has about customers’ willingness to pay for the product. If the firm can determine each customer’s willingness to pay for each unit purchased, then the firm can practice first degree PD. In this case, each unit of the product is sold for the most the buyer is willing to pay. The seller captures all the gains from trade and so wants to maximize those gains by selling the competitive quantity. If the firm does not have sufficient information to proctice first degree PD, it can offer quantity discounts. This is known as second degree PD. The profits to the firm ate not as great as with first degree PD. If the firm can only distinguish groups of customers by their willingness to pay then the firm can discriminate among market segments and charge different prices to each group. This is third degree PD. A market segments with a higher elasticity of demand will pay a lower price. If a seller cannot distinguish individual customers’ willingness to pay, it can use another method to extract all the gains from trade. A firm can implement a two-part price if it can prevent those who do not buy a “membership” from being able to purchase the product. By charging a fixed fee equal to a consumer’s consumer surplus from buying the product, the firm is able to capture all the gains from trade, and so wants to maximize them. Therefore, the two-part priceing strategy results in the competitive quantity being sold, but the seller captures all the gains from trade. If unable to charge a “membership” a seller can use block pricing to extract consumer surplus. This requires the customer to buy in minimum blocks. The firm charges the total value of the block to the consumer in an all-or-nothing offer . By choosing the block size so that MC equals the marginal value of the good, the firm again maximizes the gains from trade and captures them all. Firms that sell multiple products for which consumers have different valuations can increase its revenues by bundling the goods and selling them together for a single price rather than selling the products individually. Firms which have varying demand at different times can increase sales by lowering the price when demand is low and raising price when demand is high. This is known as peak-load pricing. In addition, cross-subsidies can increase profits. By selling on product at a loss, the firm can increase the demand of a complemetary product. If the increased revenues are greater than the losses generated then this will increase profits. Cost complementarities can also make this strategy profitable. Multiproduct firms that genarate an input in one division for the production of a product in another division want to set transfer prices so that each division has an incentive to maximize the profits of the firm as a whole. If the upstream division chooses a monopoly price, it will reduce the


2

profits of the firm as a whole. By setting the transfer price equal to the marginal cost of producing the input, then the upstream division becomes a price taker and maximizes its divisional profits and the profits of the firm as a whole. Pricing strategies can also be used in oligopoly situations in which price wars are a concern. To eliminate the incentive of a competitor to undercut a firm’s price, it can promise to match any competitor’s advertised price. Then there is not benefit to the competitor undercutting the firm’s price. This can also be achieved by accepting competitor’s coupons. Firms can prevent customers from being attracted to competitors’ lower prices if they can instill “brand loyalty”. This may be done with advertising which distinguishes the firm’s product or with frequent-purchase discounts, such as frequent flyer miles. Finally, a firm can increase the costs of price competition by using random pricing. This makes it difficult for customer to seach for the seller with the lowest price and for competitiors to undercut the firm’s price.

Date post:	12-Nov-2014
Category:	Documents
Upload:	vridhagiri
View:	507 times
Download:	1 times

Combined

Documents