+Managerial Economics & Business Strategy
Chapter 1
The Fundamentals of Managerial
Economics
McGraw-Hill/Irwin
Michael R. Baye, Managerial Economics and
Business Strategy
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
+
1-2
Managerial Economics

Manager


Economics


A person who directs resources to achieve a stated goal.
The science of making decisions in the presence of scare
resources.
Managerial Economics

The study of how to direct scarce resources in the way that most
efficiently achieves a managerial goal.
+
1-3
Economic vs. Accounting Profits


Accounting Profits

Total revenue (sales) minus dollar cost of producing goods or services.

Reported on the firm’s income statement.
Economic Profits

Total revenue minus total opportunity cost.
+ Opportunity Cost


Accounting Costs

The explicit costs of the resources needed to produce produce goods or
services.

Reported on the firm’s income statement.
Opportunity Cost


The cost of the explicit and implicit resources that are foregone when a
decision is made.
Economic Profits

Total revenue minus total opportunity cost.
1-4
+
1-5
Profits as a Signal

Profits signal to resource holders where resources are most
highly valued by society.

Resources will flow into industries that are most highly valued by
society.
Marginal (Incremental) Analysis


1-6
Control Variable Examples:

Output

Price

Product Quality

Advertising

R&D
Basic Managerial Question: How much of the control variable
should be used to maximize net benefits?
+
1-7
Net Benefits

Net Benefits = Total Benefits - Total Costs

Profits = Revenue - Costs
1-8
Marginal Benefit (MB)

Change in total benefits arising from a change in the control
variable, Q:
B
MB 
Q
 Slope (calculus derivative) of the total benefit curve.
1-9
Marginal Cost (MC)

Change in total costs arising from a change in the control
variable, Q:
C
MC 
Q

Slope (calculus derivative) of the total cost curve
+ Marginal Principle

To maximize net benefits, the managerial control variable
should be increased up to the point where MB = MC.

MB > MC means the last unit of the control variable increased
benefits more than it increased costs.

MB < MC means the last unit of the control variable increased
costs more than it increased benefits.
1-10
+ The Geometry of Optimization: Total
Benefit and Cost
Total Benefits
& Total Costs
Costs
Slope =MB
Benefits
B
Slope = MC
C
Q*
Q
1-11
+ The Geometry of Optimization: Net
Benefits
Net Benefits
Maximum net benefits
Slope = MNB
Q*
Q
1-12
+Managerial Economics & Business Strategy
Chapter 2
Market Forces: Demand and
Supply
McGraw-Hill/Irwin
Michael R. Baye, Managerial Economics and
Business Strategy
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
2-14
Overview
I. Market Demand
Curve



The Demand Function
Determinants of Demand
Consumer Surplus
II. Market Supply
Curve



The Supply Function
Supply Shifters
Producer Surplus
III. Market Equilibrium
IV. Price Restrictions
V. Comparative Statics
+
2-15
Market Demand Curve

Shows the amount of a good that will be purchased at
alternative prices, holding other factors constant.

Law of Demand

The demand curve is downward sloping.
Price
D
Quantity
2-16
Determinants of Demand
 Income
 Normal good
 Inferior good
 Prices of Related Goods
 Prices of substitutes
 Prices of complements
 Advertising
and
consumer tastes
 Population
 Consumer
expectations
+
2-17
The Demand Function
A
general equation representing the demand
curve
Qxd = f(Px ,PY , M, H,)



Qxd = quantity demand of good X.
Px = price of good X.
PY = price of a related good Y.




Substitute good.
Complement good.
M = income.
 Normal good.
 Inferior good.
H = any other variable affecting demand.
+
2-18
Inverse Demand Function
Price
as a function of quantity
demanded.
Example:

Demand Function


Qxd = 10 – 2Px
Inverse Demand Function:

2Px = 10 – Qxd

Px = 5 – 0.5Qxd
Change in Quantity Demanded
Price
A to B: Increase in quantity demanded
10
A
B
6
D0
4
7
Quantity
2-19
2-20
Change in Demand
Price
D0 to D1: Increase in Demand
6
D1
D0
7
13
Quantity
2-21
Consumer Surplus:

The value consumers get
from a good but do not have
to pay for.

Consumer surplus will prove
particularly useful in
marketing and other
disciplines emphasizing
strategies like value pricing
and price discrimination.
2-22
I got a great deal!
 That
company offers a lot
of bang for the buck!
 Dell
provides good value.
 Total
value greatly
exceeds total amount
paid.
 Consumer
large.
surplus is
2-23
I got a lousy deal!
 That
car dealer drives a
hard bargain!
I
almost decided not to
buy it!
 They
tried to squeeze the
very last cent from me!
 Total
amount paid is close
to total value.
 Consumer
surplus is low.
+ Consumer Surplus:
The Discrete Case
2-24
Price
Consumer Surplus:
The value received but not
paid for. Consumer surplus =
(8-2) + (6-2) + (4-2) = $12.
10
8
6
4
2
D
1
2
3
4
5
Quantity
Consumer
Surplus:
+
The Continuous Case
2-25
Price $
10
Consumer
Surplus =
$24 - $8 =
$16
Value
of 4 units = $24
8
6
Expenditure on 4 units = $2
x 4 = $8
4
2
D
1
2
3
4
5
Quantity
2-26
+ Market Supply Curve

The supply curve shows the amount of a good that will be
produced at alternative prices.

Law of Supply

The supply curve is upward sloping.
Price
S0
Quantity
2-27
Supply Shifters

Input prices

Technology or
government regulations

Number of firms


Entry
Exit

Substitutes in production

Taxes



Excise tax
Ad valorem tax
Producer expectations
+
2-28
The Supply Function

An equation representing the supply curve:
QxS = f(Px ,PR ,W, H,)

QxS = quantity supplied of good X.

Px = price of good X.

PR = price of a production substitute.

W = price of inputs (e.g., wages).

H = other variable affecting supply.
+
2-29
Inverse Supply Function
Price
as a function of quantity
supplied.
Example:

Supply Function


Qxs = 10 + 2Px
Inverse Supply Function:

2Px = 10 + Qxs

Px = 5 + 0.5Qxs
+
2-30
Change in Quantity Supplied
Price
A to B: Increase in quantity supplied
S0
B
20
A
10
5
10
Quantity
2-31
+ Change in Supply
S0 to S1: Increase in supply
Price
S0
S1
8
6
5
7
Quantity
2-32
+ Producer Surplus
 The
amount producers receive in excess of the
amount necessary to induce them to produce the
good.
Price
S0
P*
Q*
Quantity
2-33
Market Equilibrium
 The
Price (P) that
Balances supply and
demand


QxS = Qxd
No shortage or surplus
 Steady-state
2-34
If price is too low…
Price
S
7
6
5
D
Shortage
12 - 6 = 6
6
12
Quantity
2-35
If price is too high…
Surplus
14 - 6 = 8
Price
S
9
8
7
D
6
8
14
Quantity
+ Price Restrictions

Price Ceilings
 The


maximum legal price that can be charged.
Examples:

Gasoline prices in the 1970s.

Housing in New York City.

Proposed restrictions on ATM fees.
Price Floors
 The

minimum legal price that can be charged.
Examples:

Minimum wage.

Agricultural price supports.
2-36
2-37
Impact of a Price Ceiling
Price
S
PF
P*
P Ceiling
D
Shortage
Qs
Q*
Qd
Quantity
+
2-38
Impact of a Price Floor
Price
Surplus
S
PF
P*
D
Qd
Q*
QS
Quantity
+
2-39
Comparative Static Analysis

How do the equilibrium price and quantity change when a
determinant of supply and/or demand change?
+
2-40
Applications of Demand and Supply
Analysis

Event: The WSJ reports that the prices of PC components are
expected to fall by 5-8 percent over the next six months.

Scenario 1: You manage a small firm that manufactures PCs.

Scenario 2: You manage a small software company.
+ Use Comparative Static Analysis to
see the Big Picture!

Comparative static analysis shows how the equilibrium price
and quantity will change when a determinant of supply or
demand changes.
2-41
+
2-42
Scenario 1: Implications for a Small
PC Maker

Step 1: Look for the “Big Picture.”

Step 2: Organize an action plan (worry about details).
Big Picture: Impact of decline in
component prices on PC market
Price
of
PCs
2-43
S
S*
P0
P*
D
Q0
Q*
Quantity of PC’s
+ Big Picture Analysis: PC Market

Equilibrium price of PCs will fall, and equilibrium quantity of
computers sold will increase.

Use this to organize an action plan

contracts/suppliers?

inventories?

human resources?

marketing?

do I need quantitative estimates?
2-44
+ Scenario 2: Software Maker

More complicated chain of reasoning to arrive at the “Big
Picture.”

Step 1: Use analysis like that in Scenario 1 to deduce that lower
component prices will lead to


a lower equilibrium price for computers.

a greater number of computers sold.
Step 2: How will these changes affect the “Big Picture” in the
software market?
2-45
Big Picture: Impact of lower PC prices on
the software market
2-46
Price
of Software
S
P1
P0
D*
D
Q0 Q1
Quantity of
Software
+
2-47
Big Picture Analysis: Software
Market

Software prices are likely to rise, and more software will be
sold.

Use this to organize an action plan.
+Managerial Economics & Business Strategy
Chapter 3
Quantitative Demand Analysis
McGraw-Hill/Irwin
Michael R. Baye, Managerial Economics and
Business Strategy
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
+ Overview
I. The Elasticity Concept

Own Price Elasticity

Elasticity and Total Revenue

Cross-Price Elasticity

Income Elasticity
II. Linear Demand Functions
3-49
+
3-50
The Elasticity Concept

How responsive is variable “G” to a change in variable
“S”
EG , S
% G

% S
If EG,S > 0, then S and G are directly related.
If EG,S < 0, then S and G are inversely related.
If EG,S = 0, then S and G are unrelated.
+
3-51
The Elasticity Concept Using
Calculus

An alternative way to measure the elasticity of a function G =
f(S) is
EG , S
dG S

dS G
If EG,S > 0, then S and G are directly related.
If EG,S < 0, then S and G are inversely related.
If EG,S = 0, then S and G are unrelated.
+
3-52
Own Price Elasticity of Demand
EQ X , PX

% Q X

% PX
d
Negative according to the “law of demand.”
Elastic:
EQ X , PX  1
Inelastic: EQ X , PX  1
Unitary:
EQ X , PX  1
+
3-53
Perfectly Elastic &
Inelastic Demand
Price
Price
D
D
Quantity
Perfectly Elastic ( EQX ,PX  )
Quantity
Perfectly Inelastic ( EQX , PX  0)
3-54
+
Own-Price Elasticity
and Total Revenue

Elastic


Inelastic


Increase (a decrease) in price leads to a decrease (an increase) in
total revenue.
Increase (a decrease) in price leads to an increase (a decrease) in
total revenue.
Unitary

Total revenue is maximized at the point where demand is unitary
elastic.
+
3-55
Elasticity, Total Revenue and Linear
Demand
P
100
TR
0
10
20
30
40
50 Q
0
Q
+
3-56
Elasticity, Total Revenue and Linear
Demand
P
100
TR
80
800
0
10
20
30
40
50
Q
0
10
20
30
40
50 Q
+
3-57
Elasticity, Total Revenue and Linear
Demand
P
100
TR
80
1200
60
800
0
10
20
30
40
50
Q
0
10
20
30
40
50 Q
+
3-58
Elasticity, Total Revenue and Linear
Demand
P
100
TR
80
1200
60
40
800
0
10
20
30
40
50
Q
0
10
20
30
40
50 Q
+
3-59
Elasticity, Total Revenue and Linear
Demand
P
100
TR
80
1200
60
40
800
20
0
10
20
30
40
50
Q
0
10
20
30
40
50 Q
+
3-60
Elasticity, Total Revenue and Linear
Demand
P
100
TR
Elastic
80
1200
60
40
800
20
0
10
20
30
40
50
Q
0
10
20
Elastic
30
40
50 Q
+
3-61
Elasticity, Total Revenue and Linear
Demand
P
100
TR
Elastic
80
1200
60
Inelastic
40
800
20
0
10
20
30
40
50
Q
0
10
Elastic
20
30
40
Inelastic
50 Q
+
3-62
Elasticity, Total Revenue and Linear
Demand
P
100
TR
Unit elastic
Elastic
Unit elastic
80
1200
60
Inelastic
40
800
20
0
10
20
30
40
50
Q
0
10
Elastic
20
30
40
Inelastic
50 Q
+
3-63
Demand, Marginal Revenue (MR)
and Elasticity
 For
a linear
inverse demand
function, MR(Q) =
a + 2bQ, where b
< 0.
P
100
Elastic
Unit elastic
80
60
Inelastic
40
20
0
10
20
40
MR
50
Q
 When
 MR > 0, demand is
elastic;
 MR = 0, demand is unit
elastic;
 MR < 0, demand is
inelastic.
Factors
Affecting
+
Own Price Elasticity

Available Substitutes



3-64
The more substitutes available for the good, the more elastic the
demand.
Time

Demand tends to be more inelastic in the short term than in the long
term.

Time allows consumers to seek out available substitutes.
Expenditure Share

Goods that comprise a small share of consumer’s budgets tend to
be more inelastic than goods for which consumers spend a large
portion of their incomes.
+
3-65
Cross Price Elasticity of Demand
EQX , PY
%QX

%PY
d
If EQX,PY > 0, then X and Y are substitutes.
If EQX,PY < 0, then X and Y are complements.
+
3-66
Income Elasticity
EQX , M
%QX

%M
d
If EQX,M > 0, then X is a normal good.
If EQX,M < 0, then X is a inferior good.
+
3-67
Uses of Elasticities

Pricing.

Managing cash flows.

Impact of changes in competitors’ prices.

Impact of economic booms and recessions.

Impact of advertising campaigns.

And lots more!
+
3-68
Example 1: Pricing and Cash Flows

According to an FTC Report by Michael Ward, AT&T’s own
price elasticity of demand for long distance services is -8.64.

AT&T needs to boost revenues in order to meet it’s marketing
goals.

To accomplish this goal, should AT&T raise or lower it’s
price?
+
3-69
Answer: Lower price!

Since demand is elastic, a reduction in price will increase
quantity demanded by a greater percentage than the price
decline, resulting in more revenues for AT&T.
+ Example 2: Quantifying the Change

If AT&T lowered price by 3 percent, what would happen to the
volume of long distance telephone calls routed through AT&T?
3-70
+ Answer
3-71
• Calls would increase by 25.92 percent!
EQX , PX
%QX
 8.64 
%PX
d
%QX
 8.64 
 3%
d
 3%   8.64   %QX
d
%QX  25.92%
d
+ Example 3: Impact of a change in a
competitor’s price

According to an FTC Report by Michael Ward, AT&T’s cross
price elasticity of demand for long distance services is 9.06.

If competitors reduced their prices by 4 percent, what would
happen to the demand for AT&T services?
3-72
+ Answer
3-73
• AT&T’s demand would fall by 36.24 percent!
EQX , PY
%QX
 9.06 
%PY
%QX
9.06 
 4%
d
 4%  9.06  %QX
d
%QX  36.24%
d
d
+
Interpreting Demand Functions

Mathematical representations of demand curves.

Example:
QX  10  2 PX  3PY  2M
d

Law of demand holds (coefficient of PX is negative).

X and Y are substitutes (coefficient of PY is positive).

X is an inferior good (coefficient of M is negative).
3-74
+Managerial Economics & Business Strategy
Chapter 4
The Theory of Individual Behavior
McGraw-Hill/Irwin
Michael R. Baye, Managerial Economics and
Business Strategy
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
+ Overview
I. Consumer Behavior


Indifference Curve Analysis
Consumer Preference Ordering
II. Constraints



The Budget Constraint
Changes in Income
Changes in Prices
III. Consumer Equilibrium
IV. Indifference Curve Analysis & Demand
Curves


Individual Demand
Market Demand
4-76
+ Consumer Behavior

Consumer Opportunities


Consumer Preferences


The possible goods and services consumer can afford to consume.
The goods and services consumers actually consume.
Given the choice between 2 bundles of goods a consumer
either

Prefers bundle A to bundle B: A  B.

Prefers bundle B to bundle A: A  B.

Is indifferent between the two: A  B.
4-77
Indifference Curve Analysis
Indifference Curve
 A curve that defines the
combinations of 2 or more
goods that give a consumer the
same level of satisfaction.
4-78
Good Y
III.
II.
I.
Marginal Rate of Substitution
 The rate at which a consumer is
willing to substitute one good
for another and maintain the
same satisfaction level.
Good X
+
4-79
Consumer Preference Ordering
Properties

Completeness

More is Better

Diminishing Marginal Rate of Substitution

Transitivity
4-80
Complete Preferences

Completeness Property
 Consumer is capable of
expressing preferences (or
indifference) between all
possible bundles. (“I don’t
know” is NOT an option!)
 If the only bundles available
to a consumer are A, B, and C,
then the consumer

is indifferent between A and C
(they are on the same
indifference curve).

will prefer B to A.

will prefer B to C.
Good Y
III.
II.
I.
A
B
C
Good X
4-81
More Is Better!
 More

Is Better Property
Bundles that have at least as much
of every good and more of some
good are preferred to other
bundles.
 Bundle B is preferred to A since B
contains at least as much of good
Y and strictly more of good X.
 Bundle B is also preferred to C
since B contains at least as much
of good X and strictly more of
good Y.
 More generally, all bundles on
ICIII are preferred to bundles on
ICII or ICI. And all bundles on ICII
are preferred to ICI.
Good Y
III.
II.
I.
100
A
B
C
33.33
1
3
Good X
4-82
Diminishing Marginal Rate of
Substitution
 Marginal Rate of Substitution





The amount of good Y the consumer is
willing to give up to maintain the same
satisfaction level decreases as more of
good X is acquired.
The rate at which a consumer is willing to
substitute one good for another and
maintain the same satisfaction level.
To go from consumption bundle A
to B the consumer must give up 50
units of Y to get one additional unit
of X.
To go from consumption bundle B to
C the consumer must give up 16.67
units of Y to get one additional unit
of X.
To go from consumption bundle C
to D the consumer must give up
only 8.33 units of Y to get one
additional unit of X.
Good Y
III.
II.
I.
A
100
B
50
C
33.33
25
1
2
3
D
4
Good X
4-83
Consistent Bundle Orderings

Transitivity Property
 For the three bundles A, B, and
C, the transitivity property
implies that if C  B and B  A,
then C  A.

Good Y
Transitive preferences along
with the more-is-better property 100
imply that
75
 indifference curves will not
50
intersect.
 the consumer will not get
caught in a perpetual cycle of
indecision.
III.
II.
I.
A
C
B
1
2
5
7 Good X
4-84
The Budget Constraint

Opportunity Set

The set of consumption bundles that are
affordable.
 PxX

Y
+ PyY  M.
Budget Line
M/PY
Budget Line

Y = M/PY – (PX/PY)X
The bundles of goods that exhaust
a consumers income.
 PxX
+ PyY = M.
 Market

The Opportunity Set
Rate of Substitution
The slope of the budget line
 -Px
/ Py
M/PX
X
4-85
Changes in the Budget Line
Y
 Changes in Income
 Increases lead to a parallel,
outward shift in the budget
line (M1 > M0).
 Decreases lead to a parallel,
downward shift (M2 < M0).
 Changes in Price
 A decreases in the price of
good X rotates the budget
line counter-clockwise (PX0 >
PX1).
 An increases rotates the
budget line clockwise (not
shown).
M1/PY
M0/PY
M2/PY
Y
M0/PY
M2/PX
M0/PX
M1/PX
X
New Budget Line for
a price decrease.
M0/PX0
M0/PX1
X
4-86
Consumer Equilibrium
 The
equilibrium
consumption bundle
is the affordable
bundle that yields
the highest level of
satisfaction.


Consumer equilibrium
occurs at a point where
MRS = PX / PY.
Equivalently, the slope of
the indifference curve
equals the budget line.
Y
M/PY
Consumer
Equilibrium
III.
II.
I.
M/PX
X
+
4-87
Price Changes and Consumer
Equilibrium

Substitute Goods


An increase (decrease) in the price of good X leads to an increase
(decrease) in the consumption of good Y.
 Examples:
 Coke and Pepsi.
 Verizon Wireless or AT&T.
Complementary Goods

An increase (decrease) in the price of good X leads to a decrease
(increase) in the consumption of good Y.
 Examples:
 DVD and DVD players.
 Computer CPUs and monitors.
+
4-88
Complementary Goods
When the price of
Pretzels (Y)
good X falls and the
consumption of Y
rises, then X and Y M/PY
1
are complementary
goods. (PX1 > PX2)
B
Y2
II
A
Y1
I
0
X1 M/PX1
X2
M/PX2
Beer (X)
+
Income Changes and Consumer
Equilibrium

Normal Goods


Good X is a normal good if an increase (decrease) in income leads
to an increase (decrease) in its consumption.
Inferior Goods

Good X is an inferior good if an increase (decrease) in income
leads to a decrease (increase) in its consumption.
4-89
+
4-90
Normal Goods
An increase in
income increases
the consumption of
normal goods.
Y
M1/Y
(M0 < M1).
B
Y1
M0/Y
II
A
Y0
I
0
X0 M0/X
X1
M1/X
X
+
4-91
Decomposing the Income and
Substitution Effects
Initially, bundle A is consumed.
A decrease in the price of good
X expands the consumer’s
opportunity set.
Y
C
The substitution effect (SE)
causes the consumer to move
from bundle A to B.
A
II
A higher “real income” allows
the consumer to achieve a
higher indifference curve.
The movement from bundle B to
C represents the income effect
(IE). The new equilibrium is
achieved at point C.
B
I
0
IE
SE
X
+
4-92
A Classic Marketing Application
Other
goods
(Y)
A buy-one,
get-one free
pizza deal.
A
C
E
D
II
I
0
0.5
1
2
B
F
Pizza
(X)
4-93
Individual Demand Curve
Y
 An
individual’s
demand curve is
derived from each
new equilibrium
point found on the
indifference curve
as the price of good
X is varied.
II
I
X
$
P0
D
P1
X0
X1
X
4-94
Market Demand
 The
market demand curve is the horizontal
summation of individual demand curves.
 It
indicates the total quantity all consumers
would purchase at each price point.
$
Individual Demand
Curves
$
Market Demand Curve
50
40
D1
1 2
D2
Q
1 2 3
DM
Q
+
4-95
Conclusion
 Indifference
curve properties reveal
information about consumers’ preferences
between bundles of goods.




Completeness.
More is better.
Diminishing marginal rate of substitution.
Transitivity.
 Indifference
curves along with price changes
determine individuals’ demand curves.
 Market
demand is the horizontal summation of
individuals’ demands.
+Managerial Economics & Business Strategy
Chapter 5
The Production Process and Costs
McGraw-Hill/Irwin
Michael R. Baye, Managerial Economics and
Business Strategy
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
+
5-97
Overview
I. Production Analysis

Total Product, Marginal Product, Average Product

Isoquants

Isocosts

Cost Minimization
II. Cost Analysis

Total Cost, Variable Cost, Fixed Costs

Cubic Cost Function

Cost Relations
+
5-98
Production Analysis
 Production

Q = F(K,L)





Function
Q is quantity of output produced.
K is capital input.
L is labor input.
F is a functional form relating the inputs to output.
The maximum amount of output that can be produced with K units
of capital and L units of labor.
 Short-Run
 Fixed
vs. Long-Run Decisions
vs. Variable Inputs
5-99
Production Function Algebraic
Forms
 Linear
production function: inputs are perfect
substitutes.
Q  F K , L  aK  bL
 Leontief
production function: inputs are used in
fixed proportions.
Q  F K , L  min bK , cL
 Cobb-Douglas
production function: inputs have a
degree of substitutability.
Q  F K , L   K L
a b
+
Productivity Measures:
Total Product
 Total
Product (TP): maximum output produced
with given amounts of inputs.
 Example:
Cobb-Douglas Production Function:
Q = F(K,L) = K.5 L.5


K is fixed at 16 units.
Short run Cobb-Douglass production function:
Q = (16).5 L.5 = 4 L.5

Total Product when 100 units of labor are used?
Q = 4 (100).5 = 4(10) = 40 units
5100
+
Productivity Measures: Average
Product of an Input
 Average
Product of an Input: measure of
output produced per unit of input.

Average Product of Labor: APL = Q/L.
 Measures the output of an “average” worker.
 Example: Q = F(K,L) = K.5 L.5


If the inputs are K = 16 and L = 16, then the average product
of labor is APL = [(16) 0.5(16)0.5]/16 = 1.
Average Product of Capital: APK = Q/K.
 Measures the output of an “average” unit of capital.
 Example: Q = F(K,L) = K.5 L.5

If the inputs are K = 16 and L = 16, then the average product
of capital is APK = [(16)0.5(16)0.5]/16 = 1.
5101
+ Productivity Measures: Marginal
Product of an Input
 Marginal
Product on an Input: change in total
output attributable to the last unit of an input.

Marginal Product of Labor: MPL = Q/L
 Measures the output produced by the last worker.
 Slope of the short-run production function (with respect to
labor).

Marginal Product of Capital: MPK = Q/K
 Measures the output produced by the last unit of capital.
 When capital is allowed to vary in the short run, MPK is the
slope of the production function (with respect to capital).
5102
Increasing, Diminishing and
Negative Marginal Returns
Q
Increasin DiminishingNegative
g
Marginal Marginal
Marginal
Returns Returns
Returns
Q=F(K,L)
MP
AP
L
5103
+
Guiding the Production Process

Producing on the production function


Aligning incentives to induce maximum worker effort.
Employing the right level of inputs

When labor or capital vary in the short run, to maximize profit a
manager will hire
 labor until the value of marginal product of labor equals the
wage: VMPL = w, where VMPL = P x MPL.
 capital until the value of marginal product of capital equals the
rental rate: VMPK = r, where VMPK = P x MPK .
5104
5105
Isoquant

Illustrates the long-run combinations of inputs (K, L) that yield
the producer the same level of output.

The shape of an isoquant reflects the ease with which a
producer can substitute among inputs while maintaining the
same level of output.
5106
Marginal Rate of Technical
Substitution (MRTS)

The rate at which two inputs are substituted while maintaining
the same output level.
MRTS KL
MPL

MPK
5107
Linear Isoquants
 Capital
and labor
are perfect
substitutes



Q = aK + bL
MRTSKL = b/a
Linear isoquants imply that
inputs are substituted at a
constant rate, independent
of the input levels
employed.
K
Increasing
Output
Q1
Q2
Q3
L
5108
Leontief Isoquants

Capital and labor are perfect
K
complements.

Capital and labor are used in
fixed-proportions.

Q = min {bK, cL}

Since capital and labor are
consumed in fixed
proportions there is no input
substitution along isoquants
(hence, no MRTSKL).
Q3
Q2
Q1
Increasing
Output
L
5109
Cobb-Douglas Isoquants


Inputs are not perfectly
substitutable.
Diminishing marginal rate
of technical substitution.

K
Q3
Q2
Q1
Increasing
Output
As less of one input is used in
the production process,
increasingly more of the other
input must be employed to
produce the same output level.

Q = KaLb

MRTSKL = MPL/MPK
L
5110
Isocost

The combinations of inputs that
K
produce a given level of output
at the same cost:
C1/r
wL + rK = C

C0/r
Rearranging,
New Isocost Line
associated with
higher costs (C0
< C1).
C
C
0
C0/w
C11/w
K= (1/r)C - (w/r)L
K

For given input prices, isocosts
farther from the origin are
C/r
associated with higher costs.

Changes in input prices
change the slope of the isocost
line.
L
New Isocost
Line for a
decrease in the
wage (price of
labor: w0 >
w1).
C/w1
C/w0
L
5-111
+
Cost Minimization


Marginal product per dollar spent should be equal for all
inputs:
But, this is just
MPL MPK
MPL w



w
r
MPK r
MRTS KL 
w
r
+
5112
Cost Minimization
K
Slope of Isocost
=
Slope of Isoquant
Point of
Cost
Minimizatio
n
Q
L
5113
+
Optimal Input Substitution

A firm initially produces Q0
by employing the
combination of inputs
represented by point A at a
cost of C0.

Suppose w0 falls to w1.



The isocost curve rotates
counterclockwise; which
represents the same cost level
prior to the wage change.
To produce the same level of
output, Q0, the firm will
produce on a lower isocost line
(C1) at a point B.
The slope of the new isocost
line represents the lower wage
relative to the rental rate of
capital.
K
K0
K1
A
B
Q0
0 L0 L1 C0/w0
C1/w1
C0/w1L
5114
Cost Analysis
 Types


of Costs
Short-Run
 Fixed costs (FC)
 Sunk costs
 Short-run variable costs
(VC)
 Short-run total costs
(TC)
Long-Run
 All costs are variable
 No fixed costs
Total and Variable Costs
C(Q): Minimum total cost $
of producing alternative
levels of output:
C(Q) = VC +
FC
VC(
Q)
C(Q) = VC(Q) + FC
VC(Q): Costs that vary
with output.
FC: Costs that do not vary
with output.
5115
F
C
0
Q
5116
Fixed and Sunk Costs
FC: Costs that do not change $
as output changes.
Sunk Cost: A cost that is
forever lost after it has been
paid.
Decision makers should
ignore sunk costs to
maximize profit or minimize
losses
C(Q) = VC +
FC
VC(
Q)
F
C
Q
5117
Some Definitions
Average Total Cost
ATC = AVC + AFC
ATC = C(Q)/Q
$
MC
ATC
AVC
Average Variable Cost
AVC = VC(Q)/Q
MR
Average Fixed Cost
AFC = FC/Q
Marginal Cost
MC = C/Q
AF
C
Q
5118
Fixed Cost
Q0(ATC-AVC)
$
= Q0 AFC
= Q0(FC/ Q0)
MC
ATC
AVC
= FC
ATC
AFC
Fixed Cost
AVC
Q0
Q
5119
Variable Cost
$
Q0AVC
= Q0[VC(Q0)/ Q0]
= VC(Q0)
MC
ATC
AVC
AVC
Variable Cost
Minimum of AVC
Q0
Q
5120
Total Cost
Q0ATC
$
= Q0[C(Q0)/ Q0]
= C(Q0)
MC
ATC
AVC
ATC
Minimum of ATC
Total Cost
Q0
Q
+
Cubic Cost Function

C(Q) = f + a Q + b Q2 + cQ3

Marginal Cost?

Memorize:
MC(Q) = a + 2bQ + 3cQ2

Calculus:
dC/dQ = a + 2bQ + 3cQ2
5121
+ An Example


Total Cost: C(Q) = 10 + Q + Q2
Variable cost function:
VC(Q) = Q + Q2

Variable cost of producing 2 units:
VC(2) = 2 + (2)2 = 6

Fixed costs:
FC = 10

Marginal cost function:
MC(Q) = 1 + 2Q

Marginal cost of producing 2 units:
MC(2) = 1 + 2(2) = 5
5122
5123
Long-Run Average Costs
$
LRAC
Economies
of Scale
Diseconomies
of Scale
Q*
Q
+
Economies of Scope

C(Q1, 0) + C(0, Q2) > C(Q1, Q2).


It is cheaper to produce the two outputs jointly instead of
separately.
Example:

It is cheaper for Time-Warner to produce Internet connections
and Instant Messaging services jointly than separately.
5124
+
5125
Cost Complementarity

The marginal cost of producing good 1 declines as more of
good two is produced:
MC Q1,Q2) /Q
1

Example:

Cow hides and steaks.
2
< 0.
+ Conclusion
 To
maximize profits (minimize costs)
managers must use inputs such that the value
of marginal of each input reflects price the
firm must pay to employ the input.
 The
optimal mix of inputs is achieved when
the MRTSKL = (w/r).
 Cost
functions are the foundation for helping
to determine profit-maximizing behavior in
future chapters.
5126
+Managerial Economics & Business Strategy
Chapter 8
Managing in Competitive,
Monopolistic, and Monopolistically
Competitive Markets
McGraw-Hill/Irwin
Michael R. Baye, Managerial Economics and
Business Strategy
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
+ Overview
I. Perfect Competition

Characteristics and profit outlook.

Effect of new entrants.
II. Monopolies

Sources of monopoly power.

Maximizing monopoly profits.

Pros and cons.
III. Monopolistic Competition

Profit maximization.

Long run equilibrium.
8128
8129
Perfect Competition Environment

Many buyers and sellers.

Homogeneous (identical) product.

Perfect information on both sides of market.

No transaction costs.

Free entry and exit.
8130
Key Implications

Firms are “price takers” (P = MR).

In the short-run, firms may earn profits or losses.

Entry and exit forces long-run profits to zero.
+
Unrealistic? Why Learn?
8131
 Many
small businesses are “price-takers,” and
decision rules for such firms are similar to those of
perfectly competitive firms.
 It
is a useful benchmark.
 Explains
why governments oppose monopolies.
 Illuminates
the “danger” to managers of
competitive environments.

Importance of product differentiation.

Sustainable advantage.
Managing a Perfectly Competitive
Firm
(or Price-Taking Business)
8132
8133
Setting Price
$
$
S
Pe
Df
D
QM
Market
Firm
Qf
8134
Profit-Maximizing Output Decision

MR = MC.

Since, MR = P,

Set P = MC to maximize profits.
Graphically: Representative
Firm’s Output Decision
Profit = (Pe - ATC)  Qf*
MC
$
ATC
AVC
Pe = Df = MR
Pe
ATC
Qf*
Qf
8135
A
Numerical
Example
+


Given

P=$10

C(Q) = 5 + Q2
Optimal Price?



P=$10
Optimal Output?

MR = P = $10 and MC = 2Q

10 = 2Q

Q = 5 units
Maximum Profits?

PQ - C(Q) = (10)(5) - (5 + 25) = $20
8136
8137
+ Should this Firm Sustain Short Run
Losses or Shut Down?
Profit = (Pe - ATC)  Qf* < 0
ATC
MC
$
AVC
ATC
Pe
Loss
Pe = Df = MR
Qf*
Qf
+ Shutdown Decision Rule

A profit-maximizing firm should continue to operate (sustain
short-run losses) if its operating loss is less than its fixed costs.


Operating results in a smaller loss than ceasing operations.
Decision rule:

A firm should shutdown when P < min AVC.

Continue operating as long as P ≥ min AVC.
8138
+ Firm’s Short-Run Supply Curve:
MC Above Min AVC
ATC
MC
$
AVC
P min AVC
Qf*
Qf
8139
+ Short-Run Market Supply Curve
8140
 The
market supply curve is the summation of
each individual firm’s supply at each price.
P
Firm 1
Market
Firm 2
P
P
S1
S2
SM
15
5
10
18
Q
20
25
Q
30
43Q
+
Long Run Adjustments?

If firms are price takers but there are barriers to entry, profits
will persist.

If the industry is perfectly competitive, firms are not only
price takers but there is free entry.

Other “greedy capitalists” enter the market.
8141
+
8142
Effect of Entry on Price?
$
$
S
Entry
S*
Pe
Pe*
Df
Df*
D
QM
Market
Firm
Qf
Effect of Entry on the Firm’s
Output and Profits?
MC
$
AC
Pe
Df
Pe*
Df*
QL Qf*
Q
8143
+
8144
Summary of Logic

Short run profits leads to entry.

Entry increases market supply, drives down the market price,
increases the market quantity.

Demand for individual firm’s product shifts down.

Firm reduces output to maximize profit.

Long run profits are zero.
+
Features of Long Run Competitive
Equilibrium

P = MC


Socially efficient output.
P = minimum AC

Efficient plant size.

Zero profits

Firms are earning just enough to offset their opportunity cost.
8145
8146
Monopoly Environment

Single firm serves the “relevant market.”

Most monopolies are “local” monopolies.

The demand for the firm’s product is the market demand
curve.

Firm has control over price.

But the price charged affects the quantity demanded of the
monopolist’s product.
+
8147
“Natural” Sources of
Monopoly Power

Economies of scale

Economies of scope

Cost complementarities
8148
“Created” Sources of
Monopoly Power

Patents and other legal barriers (like licenses)

Tying contracts

Exclusive contracts

Collusion
Contract...
I.
II.
III.
8149
Managing a Monopoly

Market power permits you to price
above MC

Is the sky the limit?

No. How much you sell depends on
the price you set!
8150
A Monopolist’s Marginal Revenue
P
100
TR
Unit elastic
Elastic
Unit elastic
1200
60
Inelastic
40
800
20
0
10
20
30
40
50 Q
0
10
20
30
40
MR
Elastic
Inelastic
50 Q
Monopoly Profit Maximization
Produce where MR = MC.
Charge the price on the demand curve that corresponds to that quantity.
MC
$
ATC
Profit
PM
ATC
D
QM
MR
Q
8151
+
Alternative Profit Computation
  Total Revenue - Total Cost
  P  Q  Total Cost
 P  Q  Total Cost
Q

Q

Total Cost
 P
Q
Q

Q
 P  ATC
  P  ATC Q
8152
8153
Useful Formulae
 What’s
the MR if a firm faces a linear
demand curve for its product?
P  a  bQ
MR  a  2bQ, where b  0.
1 E 

 Alternatively, MR  P
 E 


A
Numerical
Example
+



Given estimates of

P = 10 - Q

C(Q) = 6 + 2Q
Optimal output?

MR = 10 - 2Q

MC = 2

10 - 2Q = 2

Q = 4 units
Optimal price?


P = 10 - (4) = $6
Maximum profits?

PQ - C(Q) = (6)(4) - (6 + 8) = $10
8154
8155
Long Run Adjustments?

None, unless the source of
monopoly power is
eliminated.
8156
Why Government Dislikes
Monopoly?
P

> MC
Too little output, at too high a price.
 Deadweight
monopoly.
loss of
8157
+ Deadweight Loss of Monopoly
$
MC
Deadweight Loss
of Monopoly
ATC
PM
D
MC
QM
MR
Q
+
Arguments for Monopoly

The beneficial effects of economies of scale, economies of
scope, and cost complementarities on price and output may
outweigh the negative effects of market power.

Encourages innovation.
8158
8159
Monopolistic Competition:
Environment and Implications

Numerous buyers and sellers

Differentiated products

Implication: Since products are differentiated, each firm faces a
downward sloping demand curve.


Consumers view differentiated products as close substitutes: there
exists some willingness to substitute.
Free entry and exit

Implication: Firms will earn zero profits in the long run.
Managing a Monopolistically
Competitive Firm
 Like
a monopoly, monopolistically
competitive firms


have market power that permits pricing above marginal cost.
level of sales depends on the price it sets.
 But …
 The presence of other brands in the market makes the
demand for your brand more elastic than if you were a
monopolist.
 Free entry and exit impacts profitability.
 Therefore, monopolistically
competitive
firms have limited market power.
8160
8161
Marginal Revenue Like a Monopolist
P
100
TR
Unit elastic
Elastic
Unit elastic
1200
60
Inelastic
40
800
20
0
10
20
30
40
50 Q
0
10
20
30
40
MR
Elastic
Inelastic
50 Q
+
Monopolistic Competition:
Profit Maximization

Maximize profits like a monopolist

Produce output where MR = MC.

Charge the price on the demand curve that corresponds to that
quantity.
8162
Short-Run Monopolistic
Competition
MC
$
ATC
Profit
PM
ATC
D
QM
MR
Quantity of Brand X
8163
+
Long Run Adjustments?

If the industry is truly monopolistically competitive, there is
free entry.

In this case other “greedy capitalists” enter, and their new
brands steal market share.

This reduces the demand for your product until profits are
ultimately zero.
8164
+ Long-Run Monopolistic Competition
Long Run Equilibrium
(P = AC, so zero profits)
$
MC
AC
P*
P1
Entry
MR
Q1 Q*
MR1
D
D1
Quantity of Brand
X
8165
8166
Monopolistic Competition
The Good (To Consumers)

Product Variety
The Bad (To Society)


P > MC
Excess capacity

Unexploited economies of scale
The Ugly (To Managers)

P = ATC > minimum of
average costs.
 Zero Profits (in the long run)!
+ Maximizing Profits: A Synthesizing
Example

C(Q) = 125 + 4Q2

Determine the profit-maximizing output and price, and discuss its
implications, if
8167

You are a price taker and other firms charge $40 per unit;

You are a monopolist and the inverse demand for your product is P = 100
- Q;

You are a monopolistically competitive firm and the inverse demand for
your brand is P = 100 – Q.
+
Marginal Cost

C(Q) = 125 + 4Q2,

So MC = 8Q.

This is independent of market structure.
8168
Price
Taker
+

MR = P = $40.

Set MR = MC.


40 = 8Q.

Q = 5 units.
Cost of producing 5 units.


C(Q) = 125 + 4Q2 = 125 + 100 = $225.
Revenues:

PQ = (40)(5) = $200.

Maximum profits of -$25.

Implications: Expect exit in the long-run.
8169
Monopoly/Monopolistic
Competition
+

MR = 100 - 2Q (since P = 100 - Q).

Set MR = MC, or 100 - 2Q = 8Q.

Optimal output: Q = 10.

Optimal price: P = 100 - (10) = $90.

Maximal profits:


PQ - C(Q) = (90)(10) -(125 + 4(100)) = $375.
Implications

Monopolist will not face entry (unless patent or other entry barriers are
eliminated).

Monopolistically competitive firm should expect other firms to clone, so
profits will decline over time.
8170
Conclusion
+
8171
 Firms
operating in a perfectly competitive
market take the market price as given.



Produce output where P = MC.
Firms may earn profits or losses in the short run.
… but, in the long run, entry or exit forces profits to zero.
A
monopoly firm, in contrast, can earn persistent
profits provided that source of monopoly power
is not eliminated.
A
monopolistically competitive firm can earn
profits in the short run, but entry by competing
brands will erode these profits over time.
+Managerial Economics & Business Strategy
Chapter 9
Basic Oligopoly Models
McGraw-Hill/Irwin
Michael R. Baye, Managerial Economics and
Business Strategy
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
+ Overview
I. Conditions for Oligopoly?
II. Role of Strategic Interdependence
III. Profit Maximization in Four Oligopoly Settings

Sweezy (Kinked-Demand) Model

Cournot Model

Stackelberg Model

Bertrand Model
9173
+
9174
Oligopoly Environment
 Relatively few firms, usually
 Duopoly - two firms
 Triopoly - three firms
less than 10.
 The
products firms offer can be either
differentiated or homogeneous.
 Firms’
decisions impact one another.
 Many
different strategic variables are
modeled:

No single oligopoly model.
9175
Role of Strategic Interaction

Your actions affect the profits
of your rivals.

Your rivals’ actions affect
your profits.

How will rivals respond to
your actions?
9176
+
An Example

You and another firm sell differentiated products.

How does the quantity demanded for your product change
when you change your price?
9177
+
P
D2 (Rival matches your price change)
PH
P0
PL
D1 (Rival holds its
price constant)
QH1 QH2 Q0 QL2
QL1
Q
9178
+
P
D2 (Rival matches your price change)
Demand if Rivals Match Price
Reductions but not Price Increases
P0
D1
D
Q0
(Rival holds its
price constant)
Q
+
9179
Key Insight
 The
effect of a price reduction on the quantity
demanded of your product depends upon whether
your rivals respond by cutting their prices too!
 The
effect of a price increase on the quantity
demanded of your product depends upon whether
your rivals respond by raising their prices too!
 Strategic
interdependence: You aren’t in complete
control of your own destiny!
+
Sweezy (Kinked-Demand) Model
Environment
 Few
firms in the market serving many
consumers.
 Firms
produce differentiated products.
 Barriers
to entry.
 Each
firm believes rivals will match (or follow)
price reductions, but won’t match (or follow)
price increases.
 Key

feature of Sweezy Model
Price-Rigidity.
9180
+ Sweezy Demand and Marginal
Revenue
P
D2 (Rival matches your price change)
DS: Sweezy Demand
P0
D1
(Rival holds its
price constant)
MR1
MR2
MRS: Sweezy MR
Q0
Q
9181
+ Sweezy Profit-Maximizing Decision
P
D2 (Rival matches your price change)
MC1
MC2
MC3
P0
D1 (Rival holds price
constant)
MRS
Q0
DS: Sweezy Demand
Q
9182
9183
+
Sweezy Oligopoly Summary

Firms believe rivals match price cuts, but not price increases.

Firms operating in a Sweezy oligopoly maximize profit by
producing where
MRS = MC.


The kinked-shaped marginal revenue curve implies that there exists a
range over which changes in MC will not impact the profit-maximizing
level of output.
Therefore, the firm may have no incentive to change price provided that
marginal cost remains in a given range.
+ Cournot Model Environment
A
few firms produce goods that are either
perfect substitutes (homogeneous) or
imperfect substitutes (differentiated).
 Firms’
control variable is output in contrast
to price.
 Each
firm believes their rivals will hold
output constant if it changes its own output
(The output of rivals is viewed as given or
“fixed”).
 Barriers
to entry exist.
9184
9185
Inverse Demand in a Cournot
Duopoly
 Market
demand in a homogeneous-product
Cournot duopoly is
P  a  bQ1  Q2 
 Thus, each
firm’s marginal revenue depends
on the output produced by the other firm.
More formally,
MR  a  bQ  2bQ
1
2
1
MR2  a  bQ1  2bQ2
+ Best-Response Function
 Since
a firm’s marginal revenue in a
homogeneous Cournot oligopoly depends on both
its output and its rivals, each firm needs a way to
“respond” to rival’s output decisions.
 Firm
1’s best-response (or reaction) function is a
schedule summarizing the amount of Q1 firm 1
should produce in order to maximize its profits for
each quantity of Q2 produced by firm 2.
 Since
the products are substitutes, an increase in
firm 2’s output leads to a decrease in the profitmaximizing amount of firm 1’s product.
9186
9187
Best-Response Function for a
Cournot Duopoly
 To
find a firm’s best-response function, equate
its marginal revenue to marginal cost and solve
for its output as a function of its rival’s output.
 Firm
MC)
 Firm
MC)
1’s best-response function is (c1 is firm 1’s
Q1  r1 Q2  
a  c1 1
 Q2
2b
2
2’s best-response function is (c2 is firm 2’s
a  c2 1
Q2  r2 Q1  
 Q1
2b
2
+ Graph of Firm 1’s Best-Response
Function
9188
Q2
(a-c1)/b
Q1 = r1(Q2) = (a-c1)/2b - 0.5Q2
Q2
r1 (Firm 1’s Reaction Function)
Q1
Q1M
Q1
+ Cournot Equilibrium
 Situation
where each firm produces the
output that maximizes its profits, given the
the output of rival firms.
 No
firm can gain by unilaterally changing
its own output to improve its profit.

A point where the two firm’s best-response functions intersect.
9189
9190
+ Graph of Cournot Equilibrium
Q2
(a-c1)/b
r1
Cournot Equilibrium
M
Q2
Q2*
r2
Q1*
Q1M
(a-c2)/b
Q1
+
Summary of Cournot Equilibrium

The output Q1* maximizes firm 1’s profits, given that firm 2
produces Q2*.

The output Q2* maximizes firm 2’s profits, given that firm 1
produces Q1*.

Neither firm has an incentive to change its output, given the
output of the rival.

Beliefs are consistent:

In equilibrium, each firm “thinks” rivals will stick to their current
output – and they do!
9191
+
Stackelberg Model Environment
 Few
firms serving many consumers.
 Firms
produce differentiated or
homogeneous products.
 Barriers
 Firm

to entry.
one is the leader.
The leader commits to an output before all other firms.
 Remaining

firms are followers.
They choose their outputs so as to maximize profits, given the
leader’s output.
9192
9193
The Algebra of the Stackelberg
Model
 Since
the follower reacts to the leader’s
output, the follower’s output is determined by
its reaction function
a  c2
Q2  r2 Q1  
 0.5Q1
2b
 The
Stackelberg leader uses this reaction
function to determine its profit maximizing
output level, which simplifies
a  c2  2c1 to
Q1 
2b
+ Stackelberg Summary

Stackelberg model illustrates how commitment can enhance
profits in strategic environments.

Leader produces more than the Cournot equilibrium output.


Larger market share, higher profits.

First-mover advantage.
Follower produces less than the Cournot equilibrium output.

Smaller market share, lower profits.
9194
+
9195
Bertrand Model Environment
 Few
firms that sell to many consumers.
 Firms
produce identical products at constant
marginal cost.
 Each
firm independently sets its price in order
to maximize profits (price is each firms’
control variable).
 Barriers
to entry exist.
 Consumers enjoy
 Perfect information.
 Zero transaction costs.
+ Bertrand Equilibrium
 Firms
set P1 = P2 = MC! Why?
 Suppose
MC < P1 < P2.
 Firm
1 earns (P1 - MC) on each unit sold, while
firm 2 earns nothing.
 Firm
2 has an incentive to slightly undercut
firm 1’s price to capture the entire market.
 Firm
1 then has an incentive to undercut firm
2’s price. This undercutting continues...
 Equilibrium:
Each firm charges P1 = P2 = MC.
9196
+ Conclusion
 Different
oligopoly scenarios give rise to
different optimal strategies and different
outcomes.
 Your
optimal price and output depends on
…

Beliefs about the reactions of rivals.

Your choice variable (P or Q) and the nature of the product market
(differentiated or homogeneous products).

Your ability to credibly commit prior to your rivals.
9197
+ Managerial Economics & Business Strategy
Chapter 10
Game Theory: Inside
Oligopoly
McGraw-Hill/Irwin
Michael R. Baye, Managerial Economics and
Business Strategy
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
+
Game Environments
 Players’
planned decisions are called
strategies.
 Payoffs to players are the profits or losses
resulting from strategies.
 Order of play is important:


Simultaneous-move game: each player makes decisions with
knowledge of other players’ decisions.
Sequential-move game: one player observes its rival’s move
prior to selecting a strategy.
 Frequency of rival interaction
 One-shot game: game is played once.
 Repeated game: game is played more than once; either a finite
or infinite number of interactions.
10199
+ Simultaneous-Move, One-Shot
Games: Normal Form Game
A


Normal Form Game consists of:
Set of players i ∈ {1, 2, … n} where n is a finite number.
Each players strategy set or feasible actions consist of a finite
number of strategies.
 Player
1’s strategies are S1 = {a, b, c, …}.
 Player 2’s strategies are S2 = {A, B, C, …}.

Payoffs.
 Player
1’s payoff: π1(a,B) = 11.
 Player 2’s payoff: π2(b,C) = 12.
10200
10-201
+
Real World Examples of Collusion

Garbage Collection Industry

OPEC

NASDAQ

Airlines
+
10-202
Pricing to Prevent Entry: An Application
of Game Theory
 Two
firms: an incumbent and potential entrant.
 Potential entrant’s strategies:


Enter.
Stay Out.
 Incumbent’s strategies:
 {if enter, play hard}.
 {if enter, play soft}.
 {if stay out, play hard}.
 {if stay out, play soft}.
 Move Sequence:
 Entrant moves first. Incumbent observes entrant’s action and
selects an action.
+ The Pricing to Prevent Entry Game in
Extensive Form
-1, 1
Hard
Incumbent
Enter
Soft
5, 5
Entrant
Out
0, 10
10-203
10-204
+ Identify Nash and Subgame Perfect
Equilibria
-1, 1
Hard
Incumbent
Enter
Soft
5, 5
Entrant
Out
0, 10
10-205
+ Two Nash Equilibria
-1, 1
Hard
Incumbent
Enter
Soft
5, 5
Entrant
Out
0, 10
Nash Equilibria Strategies {player 1; player 2}:
{enter; If enter, play soft}
{stay out; If enter, play hard}
+ One Subgame Perfect Equilibrium
-1, 1
Hard
Incumbent
Enter
Soft
5, 5
Entrant
Out
0, 10
Subgame Perfect Equilibrium Strategy:
{enter; If enter, play soft}
10-206
+
10-207
Insights

Establishing a reputation for being unkind to entrants can
enhance long-term profits.

It is costly to do so in the short-term, so much so that it isn’t
optimal to do so in a one-shot game.
+Managerial Economics & Business Strategy
Chapter 11
Pricing Strategies for Firms with Market Power
McGraw-Hill/Irwin
Michael R. Baye, Managerial Economics and
Business Strategy
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.
11209
+ Overview
I. Basic Pricing Strategies


Monopoly & Monopolistic Competition
Cournot Oligopoly
II. Extracting Consumer Surplus


Price Discrimination Two-Part Pricing
Block Pricing
Commodity Bundling
III. Pricing for Special Cost and Demand Structures


Peak-Load Pricing
Cross Subsidies
Transfer Pricing
IV. Pricing in Markets with Intense Price Competition


Price Matching
Brand Loyalty
Randomized Pricing
+ Standard Pricing and Profits for
Firms with Market Power
Price
Profits from standard pricing
= $8
10
8
6
4
MC
2
P = 10 - 2Q
1
2
3
4
5
MR = 10 - 4Q
Quantity
11210
+
11211
An Algebraic Example
P
= 10 - 2Q
 C(Q)
= 2Q
 If
the firm must charge a single price to all
consumers, the profit-maximizing price is
obtained by setting MR = MC.
 10
- 4Q = 2, so Q* = 2.
 P*
= 10 - 2(2) = 6.
 Profits
= (6)(2) - 2(2) = $8.
A
Simple
Markup
Rule
+

Suppose the elasticity of demand for the firm’s product is
EF.

Since MR = P[1 + EF]/ EF.

Setting MR = MC and simplifying yields this simple pricing
formula:
P = [EF/(1+ EF)]  MC.

The optimal price is a simple markup over relevant costs!


More elastic the demand, lower markup.
Less elastic the demand, higher markup.
11212
An
Example
+

Elasticity of demand for Kodak film is -2.

P = [EF/(1+ EF)]  MC

P = [-2/(1 - 2)]  MC

P = 2  MC

Price is twice marginal cost.

Fifty percent of Kodak’s price is margin above manufacturing
costs.
11213
+ Markup Rule for Cournot Oligopoly
 Homogeneous
N
product Cournot oligopoly.
= total number of firms in the industry.
 Market
elasticity of demand EM .
 Elasticity
of individual firm’s demand is given
by EF = N x EM.
 Since
P = [EF/(1+ EF)]  MC,
 Then, P
 The
= [NEM/(1+ NEM)]  MC.
greater the number of firms, the lower the
profit-maximizing markup factor.
11214
An
Example
+
 Homogeneous
firms.
 MC
product Cournot industry, 3
= $10.
 Elasticity
of market demand = - ½.
 Determine
 EF
11215
the profit-maximizing price?
= N EM = 3  (-1/2) = -1.5.
P
= [EF/(1+ EF)]  MC.
P
= [-1.5/(1- 1.5]  $10.
P
= 3  $10 = $30.
+
Extracting Consumer Surplus:
Moving From Single Price Markets
 Most
models examined to this point involve a
“single” equilibrium price.
 In reality, there are many different prices being
charged in the market.
 Price discrimination is the practice of charging
different prices to consumer for the same good
to achieve higher prices.
 The three basic forms of price discrimination
are:



First-degree (or perfect) price discrimination.
Second-degree price discrimination.
Third-degree price discrimiation.
11216
+ First-Degree or Perfect
Price Discrimination
 Practice
of charging each consumer the
maximum amount he or she will pay for each
incremental unit.
 Permits
a firm to extract all surplus from
consumers.
11217
11218
Perfect
Price Discrimination
+
Price
Profits*:
.5(4-0)(10 - 2)
= $16
10
8
6
4
Total Cost* = $8
2
MC
D
1
* Assuming no fixed costs
2
3
4
5
Quantity
+
Caveats:
 In
practice, transactions costs and
information constraints make this difficult to
implement perfectly (but car dealers and
some professionals come close).
 Price
discrimination won’t work if
consumers can resell the good.
11219
11220
Second-Degree
Price Discrimination
 The
practice of posting
a discrete schedule of
declining prices for
different quantities.
 Eliminates
the
information constraint
present in first-degree
price discrimination.
Price
MC
$10
$8
$5
 Example: Electric
utilities
D
2
4
Quantity
+
Third-Degree
Price Discrimination
 The
practice of charging different
groups of consumers different prices
for the same product.
 Group
must have observable
characteristics for third-degree price
discrimination to work.
 Examples
include student discounts,
senior citizen’s discounts, regional &
international pricing.
11221
+
Implementing Third-Degree Price
Discrimination
 Suppose
the total demand for a product is
comprised of two groups with different
elasticities, E1 < E2.
 Notice
that group 1 is more price sensitive than
group 2.
 Profit-maximizing
 P1
prices?
= [E1/(1+ E1)]  MC
 P2 =
[E2/(1+ E2)]  MC
11222
An
Example
+
 Suppose
the elasticity of demand for Kodak
film in the US is EU = -1.5, and the elasticity of
demand in Japan is EJ = -2.5.
 Marginal
 PU
$9
cost of manufacturing film is $3.
= [EU/(1+ EU)]  MC = [-1.5/(1 - 1.5)]  $3 =
= [EJ/(1+ EJ)]  MC = [-2.5/(1 - 2.5)]  $3 =
$5
 PJ
 Kodak’s
optimal third-degree pricing
strategy is to charge a higher price in the US,
where demand is less elastic.
11223
+
11224
Two-Part Pricing
 When
it isn’t feasible to charge different
prices for different units sold, but demand
information is known, two-part pricing may
permit you to extract all surplus from
consumers.
 Two-part
pricing consists of a fixed fee and
a per unit charge.

Example: Athletic club memberships.
11225
How Two-Part Pricing Works
1. Set price at marginal cost.
Price
2. Compute consumer surplus.
10
3. Charge a fixed-fee equal to
consumer surplus.
8
6
Per Unit
Charge
Fixed Fee = Profits* = $16
4
MC
2
D
* Assuming no fixed costs
1
2
3
4
5
Quantity
+ Block Pricing

The practice of packaging multiple units of an identical
product together and selling them as one package.

Examples

Paper.

Six-packs of soda.

Different sized of cans of green beans.
11226
+ An Algebraic Example

Typical consumer’s demand is P = 10 - 2Q

C(Q) = 2Q

Optimal number of units in a package?

Optimal package price?
11227
11228
+
Optimal
Quantity To Package: 4 Units
Price
10
8
6
4
MC = AC
2
D
1
2
3
4
5
Quantity
11229
+ Optimal Price for the Package: $24
Price
Consumer’s valuation of 4
units = .5(8)(4) + (2)(4) = $24
Therefore, set P = $24!
10
8
6
4
MC = AC
2
D
1
2
3
4
5
Quantity
11230
+ Costs and Profits with Block
Pricing
Price
10
Profits* = [.5(8)(4) + (2)(4)] – (2)(4)
= $16
8
6
Costs = (2)(4) = $8
4
2
D
1
* Assuming no fixed costs
2
3
4
5
MC = AC
Quantity
+
Commodity Bundling

The practice of bundling two or more products together and
charging one price for the bundle.

Examples

Vacation packages.

Computers and software.

Film and developing.
11231
+ An Example that Illustrates
Kodak’s Moment
 Total
market size for film and developing is 4
million consumers.
 Four




types of consumers
25% will use only Kodak film (F).
25% will use only Kodak developing (D).
25% will use only Kodak film and use only Kodak developing (FD).
25% have no preference (N).
 Zero
costs (for simplicity).
 Maximum
price each type of consumer will
pay is as follows:
11232
+
Reservation Prices for Kodak Film
and Developing by Type of
Consumer
Type
F
FD
D
N
Film Developing
$8
$3
$8
$4
$4
$6
$3
$2
11233
+ Optimal Film Price?
Type
F
FD
D
N
Film Developing
$8
$3
$8
$4
$4
$6
$3
$2
Optimal Price is $8; only types F and FD buy resulting in profits
of $8 x 2 million = $16 Million.
At a price of $4, only types F, FD, and D will buy
(profits of $12 Million).
At a price of $3, all will types will buy (profits of $12 Million).
11234
+
Optimal
Price for Developing?
Type
F
FD
D
N
11235
Film Developing
$8
$3
$8
$4
$4
$6
$3
$2
At a price of $6, only “D” type buys (profits of $6 Million).
At a price of $4, only “D” and “FD” types buy (profits of $8 Million).
At a price of $2, all types buy (profits of $8 Million).
Optimal Price is $3, to earn profits of $3 x 3 million = $9 Million.
+
Total
Profits by Pricing Each Item
Separately?
Type
F
FD
D
N
Film Developing
$8
$3
$8
$4
$4
$6
$3
$2
Total Profit = Film Profits + Development Profits
= $16 Million + $9 Million = $25 Million
Surprisingly, the firm can earn even greater profits by bundling!
11236
+
Pricing a “Bundle” of Film and
Developing
11237
+
Consumer
Valuations of a Bundle
Type
F
FD
D
N
Film
$8
$8
$4
$3
Developing Value of Bundle
$3
$11
$4
$12
$6
$10
$2
$5
11238
+
What’s the Optimal Price for a
Bundle?
Type
F
FD
D
N
Film
$8
$8
$4
$3
Developing Value of Bundle
$3
$11
$4
$12
$6
$10
$2
$5
Optimal Bundle Price = $10 (for profits of $30 million)
11239
11240
Peak-Load Pricing
 When
demand during
peak times is higher
than the capacity of the
firm, the firm should
engage in peak-load
pricing.

Charge a higher price (PH)
during peak times (DH).

Charge a lower price (PL)
during off-peak times (DL).
Price
MC
PH
DH
PL
MRH
MRL
QL
DL
QH Quantity
+
Cross-Subsidies

Prices charged for one product are subsidized by the sale of
another product.

May be profitable when there are significant demand
complementarities effects.
 Examples
Browser and server software.
 Drinks and meals at restaurants.

11241
+
Double
Marginalization
 Consider a large firm with two divisions:
 the upstream division is the sole provider of a key input.
 the downstream division uses the input produced by the upstream
division to produce the final output.
 Incentives
to maximize divisional profits leads the
upstream manager to produce where MRU = MCU.

Implication: PU > MCU.
 Similarly, when
the downstream division has market
power and has an incentive to maximize divisional
profits, the manager will produce where MRD = MCD.

Implication: PD > MCD.
 Thus, both
divisions mark price up over marginal
cost resulting in in a phenomenon called double
marginalization.

Result: less than optimal overall profits for the firm.
11242
+
11243
Transfer Pricing
 To
overcome double marginalization, the
internal price at which an upstream division
sells inputs to a downstream division should be
set in order to maximize the overall firm profits.
 To
achieve this goal, the upstream division
produces such that its marginal cost, MCu,
equals the net marginal revenue to the
downstream division (NMRd):
NMRd = MRd - MCd = MCu
+ Upstream Division’s Problem
 Demand
 C(Q)
for the final product P = 10 - 2Q.
= 2Q.
 Suppose
the upstream manager sets MR =
MC to maximize profits.
 10
 P*
- 4Q = 2, so Q* = 2.
= 10 - 2(2) = $6, so upstream manager
charges the downstream division $6 per unit.
11244
+
11245
Downstream Division’s Problem
 Demand
for the final product P = 10 - 2Q.
 Downstream
division’s marginal cost is the $6
charged by the upstream division.
 Downstream
profits.
 10
 P*
division sets MR = MC to maximize
- 4Q = 6, so Q* = 1.
= 10 - 2(1) = $8, so downstream division
charges $8 per unit.
+ Analysis
 This
pricing strategy by the upstream division
results in less than optimal profits!
 The
upstream division needs the price to be $6
and the quantity sold to be 2 units in order to
maximize profits. Unfortunately,
 The
downstream division sets price at $8, which is
too high; only 1 unit is sold at that price.

Downstream division profits are $8  1 – 6(1) = $2.
upstream division’s profits are $6  1 - 2(1) =
$4 instead of the monopoly profits of $6  2 - 2(2)
= $8.
 The
 Overall
firm profit is $4 + $2 = $6.
11246
11247
+ Upstream Division’s
“Monopoly Profits”
Price
Profit = $8
10
8
6
4
2
MC = AC
P = 10 - 2Q
1
2
3
4
MR = 10 - 4Q
5
Quantity
11248
+ Upstream’s Profits when
Downstream Marks Price Up to
Price
$8
Downstream
Price
Profit = $4
10
8
6
4
2
MC = AC
P = 10 - 2Q
1
2
3
4
MR = 10 - 4Q
5
Quantity
11249
Solutions for the Overall Firm?
 Provide
upstream manager with an incentive
to set the optimal transfer price of $2
(upstream division’s marginal cost).
 Overall
profit with optimal transfer price:
  $6  2  $2  2  $8
+ Pricing in Markets with Intense Price
Competition
 Price



Matching
Advertising a price and a promise to match any lower price
offered by a competitor.
No firm has an incentive to lower their prices.
Each firm charges the monopoly price and shares the market.
 Induce


brand loyalty
Some consumers will remain “loyal” to a firm; even in the face
of price cuts.
Advertising campaigns and “frequent-user” style programs can
help firms induce loyal among consumers.
 Randomized



11250
Pricing
A strategy of constantly changing prices.
Decreases consumers’ incentive to shop around as they cannot
learn from experience which firm charges the lowest price.
Reduces the ability of rival firms to undercut a firm’s prices.
Conclusion
+
 First
degree price discrimination, block pricing,
and two part pricing permit a firm to extract all
consumer surplus.
 Commodity
bundling, second-degree and third
degree price discrimination permit a firm to
extract some (but not all) consumer surplus.
 Simple
markup rules are the easiest to implement,
but leave consumers with the most surplus and
may result in double-marginalization.
 Different
strategies require different information.
11251