Transcript Q 1 - Wiley

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Microeconomics
David Besanko &
Ronald R. Braeutigam
3rd Edition
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Analyzing Economic Problems
Demand and Supply Analysis
Consumer Preferences and the Concept of Utility
Consumer Choice
The Theory of Demand
Inputs and Production Functions
Costs and Cost Minimization
Cost Curves
Perfectly Competitive Markets
Competitive Markets: Applications
Monopoly and Monopsony
Capturing Surplus
Market Structure and Competition
Game Theory and Strategic Behavior
Risk and Information
General Equilibrium Theory
Externalities and Public Goods
3
Chapter Directory
Chapter One
Analyzing
Economic
Problems
4
Chapter One
Chapter One Overview
1. Defining Microeconomics
2. Who Should Study Microeconomics?
3. Microeconomic Modeling
• Elements of Models
• Solving the Models
4. The Types of Microeconomic Analysis
5
Chapter One
Microeconomics Defined
Microeconomics is the study of the economic
behavior of individual economic decisionmakers such as consumers, workers, firms or
managers. This study involves both the
behavior of these economic agents on their
own and the way their behavior interacts to
form larger units, such as markets.
6
Chapter One
Who Should Study Microeconomics?
Example: The Railroad Industry in the US
 74.9% of all freight, 1929
 39.8% of all freight, 1970
1970’s:
• Poor profits, bankruptcies, and an inability to invest
1980’s:
• Loosened regulation and union rules improved profitability
7
Chapter One
Who Should Study Microeconomics?
Analysis of these issues requires Microeconomic tools and the key
players below need to know something about Microeconomics.
 Policy Makers
 Managers
 Union Leaders
 Lenders
 Business Owners
8
Chapter One
Microeconomics and Global Warming
Analysis of the impact of Global Warming on:
 World Economic Stability
 National Economic Policies
 Consumer Spending
 Economic Partnerships
 Trade Agreements
9
Chapter One
Key Societal Questions
Societies must answer these questions
that relate to microeconomics:
1. What goods and services will be produced and in what quantities
2. Who will produces these services and how will they produce them
3. Who will receive these goods and services and how will they get them
10
Chapter One
Microeconomic Modeling
Choice vs. Alternatives
Models are like maps – using visual methods, they
simply the process and facilitate understanding of
complex concepts. Microeconomic models need to:
 Resemble Reality
 Be Understandable
 Be an Appropriate Scale
11
Chapter One
Microeconomic Modeling
Choice vs. Alternatives
Price
Per
Pound
Supply (P,W)
Example: World-wide market
for unprocessed coffee beans,
December, 1997
Quantity in Pounds
12
Chapter One
Microeconomic Modeling
Choice vs. Alternatives
Price Per Pound
Supply (P,W)
Example: World-wide market
for unprocessed coffee beans,
December, 1997
Demand (P,I)
Quantity in Pounds
13
Chapter One
Opportunity Cost
Dependent on How One Specifies Alternatives
Defined:
The Opportunity Cost of a resource is the value
of that resource in its best alternative use.
• $100 in facilities yields $800 Revenue
• $100 in R&D yields $1000 revenue
• Opportunity cost of investing in facilities = $1000
• Opportunity cost if investing in R&D = $800
14
Chapter One
The Objective Function
Dependent on How the Objective Function is Specified
Defined:
The Objective Function specifies what the
agent cares about.
• Does manager care
more about raising profits
or increasing “power”?
15
Chapter One
The Constraints
Defined:
Constrains are whatever limits is placed on the
resources available to the agent.
 Time
 Budget
 Other Resources
 Technical Capabilities
 The Marketplace
 Rules, Regulations, and Laws
16
Chapter One
The Constraint Optimization
Behavior can be modeled as optimizing the objective
function, subject to various constraints.
Manager’s Investment Choice
• Facilities ( F ):
• R&D ( R ):
N = budget / $30
N = budget / $100
Cost Per Unit of Time
• Max N
• (F,R)
• Subject to: expenditure < $100
• Where: N is the number of workers
• Facilities workers cost $30
• R&D workers cost $100
17
Chapter One
The Constraint Optimization
Consumer purchases
Food (F), Clothing ( C ), Income (I)
Price of food (pf), price of clothing (pc)
Satisfaction from purchases: S = (FC)1/2
Max S(F,C) - subject to: pfF + pcC < I
Note: "as if modeling"
18
Chapter One
The Constraint Optimization
Example – Consumer Purchases
F
PFF + PCC = I
0
C
Chapter One
19
The Constraint Optimization
Example – Consumer Purchases
F
PFF + PCC = I
(FC)1/2 = S0
0
C
Chapter One
20
The Constraint Optimization
Example – Consumer Purchases
F
PFF + PCC = I
(FC)1/2 = S1
(FC)1/2 = S0
0
C
Chapter One
21
The Constraint Optimization
Example – Consumer Purchases
F
PFF + PCC = I
S2 > S1 > S0
(FC)1/2 = S2
(FC)1/2 = S1
(FC)1/2 = S0
0
C
Chapter One
22
Exogenous & Endogenous Variables
Defined:
Variables that have values taken as given in the analysis are
exogenous variables. Variables that have values determined as
a result of the model’s workings are endogenous variables.
“How would a manager hire the most possible workers on a budget of $100?”
vs.
“How would a manager minimize the cost of hiring three workers?”
OR
“How much food and clothing should the consumer purchase in order to maximize
satisfaction on a budget of I?”
vs.
“What is the minimum level of expenditure that the consumer must receive in order to
reach a subsistence level of satisfaction?”
23
Chapter One
Equilibrium
Defined:
Equilibrium is defined as the point where demand just
equals supply in this market (i.e., the point where the
demand and supply curves cross).
Equilibrium analysis is an analysis of
a system in a state that will continue
indefinitely as long as the exogenous
factors remain unchanged.
24
Chapter One
Equilibrium
Example – Sale of Coffee Beans
25
Chapter One
Equilibrium
Example – Sale of Coffee Beans
•
Demand (P,I)
26
Chapter One
Equilibrium
Example – Sale of Coffee Beans
P*
•
Demand (P,I)
Q*
27
Chapter One
Comparative Statics Analysis
Defined:
A Comparative Statics Analysis
compares the equilibrium state of a
system before a change in the
exogenous
variables
to
the
equilibrium state after the change.
28
Chapter One
Equilibrium
29
Chapter One
Equilibrium
•
Demand (P,I)
30
Chapter One
Equilibrium
•
•
New Supply (P,W)
Demand (P,I)
31
Chapter One
Equilibrium
P
*
P**
•
•
New Supply (P,W)
Demand (P,I)
Q* Q**
Chapter One
32
Consumer Choice Revisited
33
Chapter One
Consumer Choice Revisited
(FC)1/2 = S0
•
34
Chapter One
Consumer Choice Revisited
(FC)1/2 = S0
•
PFF + PCC = I1
35
Chapter One
Consumer Choice Revisited
(FC)1/2 = S0
•
•
(FC)1/2 = S1
PFF + PCC = I1
36
Chapter One
Consumer Choice Revisited
S0 > S1
I0 > I 1
(FC)1/2 = S0
F*
F**
•
•
(FC)1/2 = S1
PFF + PCC = I1
C** C*
37
Chapter One
Marginal Impact
Defined:
The Marginal Impact of a change
in the exogenous variable is the
incremental impact of the last unit
of the exogenous variable on the
endogenous variable.
38
Chapter One
Marginal Impact
Advertising Example
Budget = $1M to allocate between TV ( T ) and radio ( R )
Problem: Max B(T,R) (T,R)
Subject to: pTT + pRR < $1m
where: B is "barrels“ and pT, pR are the prices of TV and
radio advertising, respectively.
39
Chapter One
Marginal Impact
Advertising Example
40
Chapter One
Microeconomic Analysis
Some Types
Positive Analysis:
• Can explain what has happened due to an
economic policy or it can predict what
might happen due to an economic policy.
Normative Analysis:
• Is an analysis of what should be done
41
Chapter One
Microeconomic Analysis
Some Examples
Example: “Should we increase income
equality rather than focus on economic
efficiency?”
Example: “Should we impose a
progressive income tax or a sales tax to
increase income equality?”
Example: “Will a progressive income
tax reduce aggregate hours worked?”
42
Chapter One
Chapter Two
Demand and
Supply Analysis
43
Chapter Two
Chapter Two Overview
1. Motivation – U.S. dot coms
2. Competitive Markets Defined
3. The Market Demand Curve
4. The Market Supply Curve
5. Equilibrium
6. Characterizing Demand and Supply – Elasticity
7. Back of the Envelope Techniques
44
Chapter Two
Motivations
Example: 1995 U.S. Corn Market
Historical price:
$2.00 per bushel
Prices rose to $2.70 per bushel
• Long term contracts based on this price
Prices rise to $5.00 per bushel
• Litigation to annul contracts
Why?
• Weather
• Asian economic boom
45
Chapter Two
Motivations
Example: 1995 U.S. Corn Market
Historical price:
$2.00 per bushel
Prices return to $2.00 per bushel
Why?
• Increased acreage
• Asian economic cool-down
46
Chapter Two
Competitive Markets
Defined:
Competitive Markets are those
with sellers and buyers that are
small and numerous enough that
they take the market price as
given when they decide how
much to buy and sell.
47
Chapter Two
The Market Demand Function
Defined:
The Market Demand Function tells us
how the quantity of a good demanded
by the sum of all consumers in the
market depends on various factors.
48
Chapter Two
Demand Curves
Defined:
The Demand Curve plots the aggregate
quantity of a good that consumers are
willing to buy at different prices, holding
constant other demand drivers such as prices
of other goods, consumer income, quality.
49
Chapter Two
The Demand for Cars
50
Chapter Two
The Demand for Cars
We always graph P on vertical axis and Q on horizontal axis, but
we write demand as Q as a function of P… If P is written as
function of Q, it is called the inverse demand.
Markets defined by commodity, geography, time.
51
Chapter Two
The Law of Demand
Defined:
The Law of Demand states that the
quantity of a good demanded decreases
when the price of this good increases.
The Demand Curve shifts when factors other than own price change such as:
 If the change increases the willingness of consumers
to acquire the good, the demand curve shifts right
 If the change decreases the willingness of consumers
to acquire the good, the demand curve shifts left
52
Chapter Two
Demand Curve Rule
Defined:
A move along the demand curve for a
good can only be triggered by a change in
the price of that good. Any change in
another factor that affects the consumers’
willingness to pay for the good results in a
shift in the demand curve for the good.
53
Chapter Two
Market Supply vs. Demand
Tells us how the quantity of a good
supplied by the sum of all producers in
the market depends on various factors
Plots the aggregate quantity of a good that
will be offered for sale at different prices.
54
Chapter Two
Supply Curve for Wheat
55
Chapter Two
The Law of Supply
Defined:
The Law of Supply states that the
quantity of a good offered increases when
the price of this good increases.
The Supply Curve shifts when factors other than own price change such as:
 If the change increases the willingness of producers to
offer the good at the same price, the supply curve shifts right
 If the change decreases the willingness of producers to
offer the good at the same price, the supply curve shifts left
56
Chapter Two
Supply Curve Rule
Defined:
A move along the supply curve for a good
can only be triggered by a change in the
price of that good. Any change in another
factor that affects the producers’
willingness to offer for the good results in
a shift in the supply curve for the good.
57
Chapter Two
Example: Canadian Wheat
Supply Curve Rule Example
QS = p + .05r
QS = quantity of wheat (billions of bushels)
p = price of wheat (dollars per bushel)
r = average rainfall in western Canada,
May – August (inches per month)
58
Chapter Two
Example: Canadian Wheat
Supply Curve Rule Example
a. Quantity of wheat supplied at price of $2 and
rainfall of 3 inches per month = 2.15
b. Supply curve when rainfall is 3 inches per month:
QS = p + 0.15
c. Law of supply holds
d. As rainfall increases, supply curve shifts right
(e.g., r = 4 => Q = p + 0.2)
59
Chapter Two
Example: Canadian Wheat
60
Chapter Two
Example: Canadian Wheat
.15
61
Chapter Two
Market Equilibrium
Defined:
A Market Equilibrium is a price such
that, at this price, the quantities
demanded and supplied are the same.
Demand and supply curves intersect at equilibrium
62
Chapter Two
Market Equilibrium for Cranberries
Qd = 500 – 4p
QS = -100 + 2p
p = price of cranberries (dollars per barrel)
Q = demand or supply in millions of barrels per year
The equilibrium price of cranberries is calculated by equating demand to supply:
Qd = QS … or…
500 – 4p = -100 + 2p …solving
p* = $100
Plug equilibrium price into either demand or supply to get equilibrium quantity:
63
Chapter Two
Market Equilibrium for Cranberries
Q* = 100
64
Chapter Two
Excess Supply
Defined:
If sellers cannot sell as much as
they would like at the current
price, there is Excess Supply.
If there is no excess supply or excess demand,
there is no pressure for prices to change and
thus there is equilibrium.
When a change in an exogenous variable
causes the demand curve or the supply curve
to shift, the equilibrium shifts as well.
65
Chapter Two
Excess Supply
66
Chapter Two
Price Elasticity
Defined:
The Price Elasticity of Demand is the percentage
change in quantity demanded brought about by a
one-percent change in the price of the good.
Q,P= (Q/Q) = (Q/p)(p/Q)
(p/p)
67
Chapter Two
Price Elasticity
• Slope is the ratio of absolute changes in quantity
and price. (= Q/P).
• Elasticity is the ratio of relative (or percentage)
changes in quantity and price.
68
Chapter Two
Grocery Products Elasticity
69
Chapter Two
Price Elasticity
• When a one percent change in price leads to a greater than one-percent change in quantity
demanded, the demand curve is elastic. (Q,P < -1)
• When a one-percent change in price leads to a less than one-percent change in quantity
demanded, the demand curve is inelastic. (0 > Q,P > -1)
• When a one-percent change in price leads to an exactly one-percent change in quantity
demanded, the demand curve is unit elastic. (Q,P = -1)
70
Chapter Two
Elasticity – Linear Demand Curve
Qd = a – bp
Where:
• a and b are positive constants
• p is price
• b is the slope
• a/b is the choke price
Elasticity is:
71
Chapter Two
Elasticity – Linear Demand Curve
P
a/b
Q,P = -
Elastic region
a/2b
•
Q,P
= -1
Inelastic region
Q,P = 0
0
a
a/2
Q
72
Chapter Two
Elasticity – Linear Demand Curve
73
Chapter Two
Constant Elasticity vs. Linear Demand Curve
Price
•
P
Observed price and quantity
Constant elasticity demand curve
Linear demand curve
0
Q
Quantity
74
Chapter Two
Price Elasticity and Cars
Berry, Levinsohn and Pakes, "Automobile Price in Market Equilibrium," Econometrica 63 (July 1995), 841-890
75
Chapter Two
Price Elasticity and Cars
Berry, Levinsohn and Pakes, "Automobile Price in Market Equilibrium," Econometrica 63 (July 1995), 841-890
76
Chapter Two
Durable Goods
Defined:
The Durable Good is a good that
provides valuable services over a
long time (usually many years).
Demand for non-durables is less elastic in the
short run when consumers can only partially
adapt their behavior. Demand for durables is
more elastic in the short run because
consumers can delay purchase.
77
Chapter Two
Durable Goods
78
Chapter Two
Other Elasticities
79
Chapter Two
Elasticities & the Cola Wars
Source: Gasmi, Laffont and Vuong, "Econometric Analysis of Collusive Behavior in a Soft Drink
Market," Journal of Economics and Management Strategy 1 (Summer, 1992) 278-311.
80
Chapter Two
Estimating Demand & Supply
81
Chapter Two
Estimating Demand & Supply
82
Chapter Two
Estimating Demand & Supply
83
Chapter Two
Estimating Demand & Supply
From Past Shifts
84
Chapter Two
Identifying Demand
By a Shift in Supply
85
Chapter Two
Identifying Demand
By a Shift in Supply
This technique only works if one or the other of the curves
stays constant. Identifying demand when both curves shift
86
Chapter Two
Chapter Three
Consumer
Preferences and the
Concept of Utility
87
Chapter Three
Chapter Three Overview
1. Motivation
2. Consumer Preferences and the Concept of Utility
3. Indifference Curves
4. The Marginal Rate of Substitution
5. The Utility Function
• Marginal Utility and Diminishing Marginal Utility
6. Some Special Functional Forms
• Marginal Utility and the Marginal Rate of Substitution
88
Chapter Three
Motivation
• Equilibrium/comparative statics studies may predict
the direction of change but:
• Over what price range?
• How much?
• Elasticity good descriptive measure of demand and
supply but it not predictive
• Back of the envelope techniques miss nonlinearities
89
Chapter Three
Consumer Preferences
Consumer Preferences tell us how the consumer would
rank (that is, compare the desirability of) any two
combinations or allotments of goods, assuming these
allotments were available to the consumer at no cost.
These allotments of goods are referred to as baskets or
bundles. These baskets are assumed to be available for
consumption at a particular time, place and under particular
physical circumstances.
90
Chapter Three
Consumer Preferences
Preferences are complete if the consumer can rank any
two baskets of goods (A preferred to B; B preferred to
A; or indifferent between A and B)
Preferences are transitive if a consumer who prefers
basket A to basket B, and basket B to basket C also
prefers basket A to basket C
A  B; B  C = > A  C
91
Chapter Three
Consumer Preferences
Preferences are monotonic if a
basket with more of at least one
good and no less of any good is
preferred to the original basket.
92
Chapter Three
Intransitivity and Age
Age
4
5
6
7
8
9
10
11
12
13
Adults
Number of Subjects Intransitive (%)
39
33
23
35
40
52
45
65
81
81
99
83
82
82
78
68
57
52
37
23
41
13
Source: See Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth Edition. Prentice Hall:
Upper Saddle River, New Jersey. 1998.
93
Chapter Three
Indifference Curves
An Indifference Curve or Indifference Set: is the set
of all baskets for which the consumer is indifferent
An Indifference Map : Illustrates a set of indifference
curves for a consumer
Averages preferred to extremes =>
indifference curves are bowed toward
the origin (convex to the origin).
94
Chapter Three
Indifference Curves
1). Monotonicity => indifference curves have negative
slope – and indifference curves are not “thick”
2). Transitivity => indifference curves do not cross
3). Completeness => each basket lies on only one
indifference curve
95
Chapter Three
Indifference Curves
Number of
Children
Number of
Boys
Number of
Families
2
2
1
0
3
2
1
0
4
3
2
1
0
35,674
64,585
31,607
10,431
26,497
24,897
8,948
2,619
8,260
11,489
7,527
2,241
3
4
Families that
had another Child
56
51
56
47
44
45
48
40
40
38
40
41
Source: See Hirshleifer,
Jack and D. Hirshleifer,
Price
Theory
and
Applications.
Sixth
Edition.
Prentice Hall:
Upper Saddle River, New
Jersey. 1998.
96
Chapter Three
Indifference Curves
boys
Preference direction (locally)
2
1
•
0
1
Indifference curves
2
girls
97
Chapter Three
Indifference Curves
98
Chapter Three
Indifference Curves
99
Chapter Three
Indifference Curves
Suppose that B preferred to A.
but..by definition of IC,
B indifferent to C
A indifferent to C => B indifferent
to C by transitivity.
And thus a contradiction.
100
Chapter Three
Indifference Curves
101
Chapter Three
Indifference Curves
Non-monotonic
preferences with
a bliss point.
102
Chapter Three
Indifference Curves
Are these: Compete, Transitive, Monotonic
– are averages preferred to extremes?
103
Chapter Three
Marginal Rate of Substitution
The marginal rate of substitution: is the maximum rate at which the
consumer would be willing to substitute a little more of good x for a little less
of good y;
It is the increase in good x that the consumer would require in exchange for a
small decrease in good y in order to leave the consumer just indifferent
between consuming the old basket or the new basket;
It is the rate of exchange between goods x and y that does not affect the
consumer’s welfare;
It is the negative of the slope of the indifference curve:
MRSx,y = -y/x
(for a constant level of preference)
104
Chapter Three
Indifference Curves
If the more of good x you have, the
more you are willing to give up to
get a little of good y or the
indifference curves get flatter as we
move out along the horizontal axis
and steeper as we move up along
the vertical axis
105
Chapter Three
Indifference Curves
Example: For the
following indifference
curves, the marginal
rate of substitution
between x and y is: 1,
.5, 2, 5 diminishing?
106
Chapter Three
Indifference Curves
Example: For the
following indifference
curves, the marginal
rate of substitution
between x and y is:
 0?
Infinite?
undefined ?
Diminishing?
all of the above?
107
Chapter Three
The Utility Function
The utility function assigns a number to each
basket so that more preferred baskets get a
higher number than less preferred baskets.
Utility is an ordinal concept: the precise
magnitude of the number that the function
assigns has no significance.
108
Chapter Three
The Utility Function
Students take an exam. After the exam, the students are ranked
according to their performance. An ordinal ranking lists the
students in order of their performance (i.e., Harry did best, Joe
did second best, Betty did third best, and so on). A cardinal
ranking gives the mark of the exam, based on an absolute
marking standard (i.e., Harry got 80, Joe got 75, Betty got 74
and so on). Alternatively, if the exam were graded on a curve,
the marks would be an ordinal ranking.
109
Chapter Three
The Utility Function
Difference in magnitudes of utility have no interpretation per se utility not
comparable across individuals any transformation of a utility function that
preserves the original ranking of bundles is an equally good representation of
preferences. e.g. U = xy vs. U = xy + 2 represent the same preferences.
Example: U = xy
Check that underlying preferences are complete, transitive, monotonic and
averages are preferred to extremes.
110
Chapter Three
The Utility Function
Example: Utility
and the single
indifference curve.
111
Chapter Three
Marginal Utility
The marginal utility of a good, x, is the additional
utility that the consumer gets from consuming a little
more of x when the consumption of all the other goods
in the consumer’s basket remain constant.
• U/x (y held constant) = MUx
• U/y (x held constant) = MUy
The marginal utility of x is the slope of the utility
function with respect to x. The principle of diminishing
marginal utility states that the marginal utility falls as
the consumer consumes more of a good.
112
Chapter Three
Marginal Utility
Relative Income and Life Satisfaction
Within Nations
Relative Income
Percent > "Satisfied"
Lowest quartile
70
Second quartile
78
Third quartile
82
Highest quartile
85
Source: Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth
Edition. Prentice Hall: Upper Saddle River, New Jersey. 1998.
113
Chapter Three
Marginal Utility
Relative Income and Life Satisfaction
Across Nations
Source: Hirshleifer, Jack and D. Hirshleifer, Price Theory and Applications. Sixth
Edition. Prentice Hall: Upper Saddle River, New Jersey. 1998.
Chapter Three
114
Marginal Utility
MUx(x) + MUy(y) = 0 …along an IC…
MUx/MUy = -y/x = MRSx,y
Positive marginal utility implies the indifference curve
has a negative slope (implies monotonicity)
Diminishing marginal utility implies the indifference
curves are convex to the origin (implies averages
preferred to extremes)
115
Chapter Three
Marginal Utility
Example: U = Ax2+By2; MUx=2Ax; MUy=2By
(where: A and B positive)
MRSx,y = MUx/MUy = 2Ax/2By
= Ax/By
Marginal utilities are positive (for positive x and y)
Marginal utility of x increases in x;
marginal utility of y increases in y
116
Chapter Three
Marginal Utility
Implications of this substitution:
• Indifference curves are negatively-sloped, bowed out
from the origin, preference direction is up and right
• Indifference curves intersect the axes
117
Chapter Three
Indifference Curves
y
Example: Graphing Indifference Curves
Preference direction
IC1
IC2
0
x
Chapter Three
118
Indifference Curves
Example: U= (xy).5;MUx=y.5/2x.5; MUy=x.5/2y.5
A. Is more better for both goods? Yes, since
marginal utilities are positive for both.
B. Are the marginal utility for x and y
diminishing? Yes. (For example, as x increases,
for y constant, MUx falls.)
C. What is the marginal rate of substitution of x for y?
MRSx,y = MUx/MUy = y/x
119
Chapter Three
Indifference Curves
Do the indifference
intersect the axes?
curves
A value of x = 0 or y = 0 is
inconsistent with any positive
level of utility.
120
Chapter Three
Indifference Curves
y
Example: Graphing Indifference Curves
Preference direction
IC2
IC1
x
Chapter Three
121
Special Functional Forms
Cobb-Douglas: U = Axy
where:  +  = 1; A, , positive constants
MUX = Ax-1y
Axy-1

MUY =
MRSx,y = (y)/(x)
“Standard” case
122
Chapter Three
Special Functional Forms
y
Example: Cobb-Douglas (speed vs. maneuverability)
Preference Direction
IC2
IC1
x
Chapter Three
123
Special Functional Forms
Perfect Substitutes: U = Ax + By
Where: A, B positive constants
MUx = A
MUy = B
MRSx,y = A/B so that 1 unit of x is equal to
B/A units of y everywhere
(constant MRS).
124
Chapter Three
Special Functional Forms
y
Example: Perfect Substitutes
• (Tylenol, Extra-Strength Tylenol)
Slope = -A/B
IC1
IC2
0
IC3
x
Chapter Three
125
Special Functional Forms
Perfect Complements: U = Amin(x,y)
where: A is a positive constant.
MUx = 0 or A
MUy = 0 or A
MRSx,y is 0 or infinite or undefined (corner)
126
Chapter Three
Special Functional Forms
y
Example: Perfect Complements
• (nuts and bolts)
IC2
IC1
0
x
Chapter Three
127
Special Functional Forms
U = v(x) + Ay
Where: A is a positive constant.
MUx = v’(x) = V(x)/x, where  small MUy = A
"The only thing that determines your personal trade-off
between x and y is how much x you already have."
*can be used to "add up" utilities across individuals*
128
Chapter Three
Special Functional Forms
y
Example: Quasi-linear Preferences
• (consumption of beverages)
IC2
IC’s have same
slopes on any
vertical line
IC1
•
•
0
x
Chapter Three
129
Chapter Four
Consumer
Choice
130
Chapter Four
Chapter Four Overview
1. Motivation
2. The Budget Constraint
3. Consumer Choice
4. Duality
5. Some Applications
6. Revealed Preference
131
Chapter Four
Motivation
Consumer Expenditures, US, 2001
Yearly After Tax Income: $42,362
Yearly Total Expenditures: $40,900
Allocation of Spending
Food
$5,904
Housing
$12,248
Transportation
$8,672
Health care
$2,239
Entertainment
$1,958
132
Chapter Four
The Budget Constraint
Assume only two goods available: X and Y
• Price of x: Px ; Price of y: Py
• Income: I
Total expenditure on basket (X,Y): PxX + PyY
The Basket is Affordable if total expenditure
does not exceed total Income:
PXX + PYY ≤ I
133
Chapter Four
Key Definitions
Budget Set:
• The set of baskets that are affordable
Budget Constraint:
• The set of baskets that the consumer may purchase
given the limits of the available income.
Budget Line:
• The set of baskets that one can purchase when
spending all available income.
PxX + PyY = I
Y = I/Py – (Px/Py)X
134
Chapter Four
A Budget Constraint Example
Two goods available: X and Y
I = $10
Px = $1
Py = $2
Budget Line 1:
1X + 2Y = 10
Or
Y = 5 – X/2
135
Chapter Four
A Budget Constraint Example
Y
If the price of X rises, the budget line gets
steeper and the horizontal intercept shifts in
If the price of X falls, the budget line gets
flatter and the horizontal intercept shifts out
Budget line = BL1
I/PY= 5 A
•
-PX/PY = -1/2
B
•C
•
I/PX = 10
Chapter Four
X
136
A Budget Constraint Example
Y
I = $12
PX = $1
PY = $2
Shift of a budget line
If the price of X rises, the budget line gets
steeper and the horizontal intercept shifts in
6 Y = 6 - X/2 …. BL2
5
If the price of X falls, the budget line gets
flatter and the horizontal intercept shifts out
BL2
BL1
10
12
X
137
Chapter Four
A Budget Constraint Example
Y
Rotation of a budget line
If the price of X rises, the budget
line gets steeper and the
horizontal intercept shifts in
I = $10
PX = $1
BL1 PY = $3
6
5
If the price of X falls, the budget
line gets flatter and the horizontal
intercept shifts out
Y = 3.33 - X/3 …. BL2
3.33
BL2
10
Chapter Four
X
138
Consumer Choice
Assume:
 Only non-negative quantities
 "Rational” choice: The consumer chooses the
basket that maximizes his satisfaction given the
constraint that his budget imposes.
Consumer’s Problem:
Max U(X,Y) (X,Y)
Subject to: PxX + PyY < I
139
Chapter Four
Interior Optimum
Interior Optimum: The optimal consumption basket is
at a point where the indifference curve is just tangent to
the budget line.
A tangent: to a function is a straight line that has the
same slope as the function…therefore….
MRSx,y = Px/Py
“The rate at which the consumer would be willing to
exchange X for Y is the same as the rate at which they
are exchanged in the marketplace.”
140
Chapter Four
Interior Consumer Optimum
Y
•
B
Preference Direction
•
•C
Optimal Choice (interior solution)
IC
BL
X
0
Chapter Four
141
Interior Consumer Optimum
• U (X,Y) = XY and MUX =Y while MUY = X
• I = $1,000
• PX = $50 and PY = $200
• Basket A contains (X=4, Y=4)
• Basket B contains (X=10, Y=2.5)
• Question:
• Is either basket the optimal choice for the consumer?
Basket A:
MRSx,y = MUx/MUy = Y/X = 4/4 = 1
Slope of budget line = -Px/Py = -1/4
Basket B:
MRSx,y = MUx/MUy = Y/X = 1/4
142
Chapter Four
Interior Consumer Optimum
Y
50X + 200Y = E
25 = XY (constraint)
Y/X = 1/4 (tangency condition)
2.5
•
0
10
U = 25
Chapter Four
X
143
Equal Slope Condition
“At the optimal basket, each good gives
equal bang for the buck”
Now, we have two equations to solve for two unknowns
(quantities of X and Y in the optimal basket):
1. MUx/Px = MUY/PY
2. PxX + PyY = I
144
Chapter Four
Contained Optimization
What are the equations that the optimal
consumption basket must fulfill if we
want to represent the consumer’s
choice among three goods?
• MUX / PX = MUY / PY is an example of “marginal reasoning” to maximize
• PX X + PY Y = “I” reflects the constraint
145
Chapter Four
Corner Solution
A corner solution occurs when the optimal
bundle contains none of one of the goods.
The tangency condition may not hold at a
corner solution.
How do you know whether the optimal
bundle is interior or at a corner?
 Graph the indifference curves
 Check to see whether tangency condition ever
holds at positive quantities of X and Y
146
Chapter Four
Corner Solution
Example: Let U(X,Y) = X + Y. I = $1000, Px = $50 and
PY = $200. What is the optimal consumption basket?
Budget line: Y = $5 - X/4
147
Chapter Four
Corner Consumer Optimum
What would be the optimal consumption bundle
if PX = PY = $50? What if PX = $200, PY = $50?
148
Chapter Four
Corner Consumer Optimum
Example: Let U(X,Y) = min(X,Y). Let I = $1000, Px = $50
and PY = $200. What is the optimal consumption basket?
Budget line: Y = $5 - X/4
149
Chapter Four
Duality
The mirror image of the original (primal) constrained
optimization problem is called the dual problem.
Min PxX + PyY
(X,Y) subject to: U(X,Y) = U*
where: U* is a target level of utility.
If U* is the level of utility that solves the
primal problem, then an interior
optimum, if it exists, of the dual problem
also solves the primal problem.
150
Chapter Four
Optimal Choice
Y
Example: Expenditure Minimization
•
Optimal Choice (interior solution)
U = U*
Decreases in
expenditure level
PXX + PYY = E*
0
X
151
Chapter Four
Optimal Choice
Y
Example: A consumer purchases X and Y and has utility U(X,Y)
= XY, with marginal utilities MUx = Y and MUY = X. Let PX =
$50 and PY = $200. What is the basket that minimizes the
expenditure necessary to attain a utility level of U = 25?
50X + 200Y = E
25 = XY (constraint)
Y/X = 1/4 (tangency condition)
2.5
0
X
10
152
Chapter Four
Optimal Choice
Y
Example: Expenditure Minimization
50X + 200Y = E
25 = XY (constraint)
Y/X = 1/4 (tangency condition)
2.5
•
0
10
U = 25
X
153
Chapter Four
Optimal Choice
Composite Good, Units
I+V
Example: Housing Vouchers and Income Subsidies
•
I
Which is a better way to increase the amount of
housing chosen by the consumer?
B
A
hA hF
I/Ph
(I+V)/Ph
Housing (units)
154
Chapter Four
Optimal Choice
I+S
I+V
Composite Good, Units
Preference Direction
C
•
I
B
•
A
hA hF
I/Ph
(I+V)/Ph (I+S)/Ph Housing (units)
155
Chapter Four
Optimal Choice
I+S
I+V
Composite Good, Units
Preference Direction
I
•
B
• •D
A
hA hF
C
hB I/Ph
(I+V)/Ph (I+S)/Ph Housing (units)
156
Chapter Four
Optimal Choice
I2 +
I1(1+r)
I2
C2, spending next year ($)
•A
Example: Borrowing and Lending
•B
C2B
Preference Direction
IC2
IC1
I1
C1B
I1+I2/(1+r)
Chapter Four
C1, spending
this year ($)157
Optimal Choice
300
Composite
Good
Preference
Direction
200
Example:
Discount Clubs
IC1
•
• Should the
A
consumer join the
IC2
club or not?
•
B
CDs (number)
0
10
15
Chapter Four
20
158
Revealed Preference
Suppose that preferences are not
known. Can we infer them from
purchasing behavior?
If A purchased, it must be preferred
to all other affordable bundles
159
Chapter Four
Revealed Preference
Suppose that preferences are “standard” – then:
All baskets to the Northeast of A must be
preferred to A.
This gives us a narrower range over which
indifference curve must lie
This type of analysis is called revealed
preference analysis.
160
Chapter Four
Revealed Preference
Can we test whether a consumer is maximizing utility by
using revealed preference analysis? Suppose that
preferences do not change over the period of observation.
1. Let basket A be purchased in period 1. Let basket B
be affordable at period 1 prices.
2. A  B
3. Let basket B be purchased in period 2.
161
Chapter Four
Revealed Preference
4. Let basket A be purchased in period 1. Let
basket B be affordable at period 1 prices.
AB
5. Let basket B be purchased in period 2.
6. In fact, if both are affordable and B is bought,
the consumer cannot be behaving according to
utility maximization.
162
Chapter Four
Revealed Preference
Alternatively: If: PxXA+PyYA > PxXB+PyYB … and A
chosen, then it must NOT be the case that:
P’xXB+P’yYB > P’xXA+P’yYA … and B chosen
(“Weak Axiom of Revealed Preference”)
163
Chapter Four
Revealed Preference
Example: Consumer Choice that Fails to Maximize Utility
Two goods, X and Y:
I = $24
(PX,PY) = (4,2)
(P’x,P’Y) = (3,3)
(XA,YA) = (5,2)
A chosen when BL is BL1
(XB,YB) = (2,6) B chosen when BL is BL2
164
Chapter Four
Revealed Preference
12 Composite
Good
BL1
C
8
•
•
BL1 Y = 12 - 2X
BL2 Y = 8 - X
B
•
A
D
•
BL2
X
6
8
Chapter Four
165
Revealed Preference
IF PxXA + PyYA > PxXB + PyYB
4(5)+2(2) > 4(2)+2(6)
(i.e., if A is chosen when budget is BL1
but B is affordable)
Then it must NOT
be the case that:
P’xXB + P’yYB > P’xXA + P’yYA
3(2)+3(6) > 3(5)+3(2)?
(i.e. at the new prices for BL2, B is
chosen when A is affordable)
So utility maximization condition fails
166
Chapter Four
Chapter Five
The Theory
Of Demand
167
Chapter Five
Chapter Five Overview
1. Individual Demand Curves
2. Income and Substitution Effects &
the Slope of Demand
• Applications:
 The Work-Leisure Trade-off
 Consumer Surplus
3. Constructing Aggregate Demand
168
Chapter Five
Individual Demand Curves
The Price Consumption Curve of Good X:
Is the set of optimal baskets for
every possible price of good x,
holding all other prices and
income constant.
169
Chapter Five
Price Consumption Curves
Y (units)
The price consumption curve for good x
can be written as the quantity consumed
of good x for any price of x. This is the
individual’s demand curve for good x.
PY = $4
I = $40
10
•
0
XA=2
Price Consumption Curve
•
PX = 4
XB=10
•
PX = 1
PX = 2
XC=16
Chapter Five
20
X (units)
170
Individual Demand Curve
PX
Individual
Demand Curve
For X
PX = 4
•
PX = 2
PX = 1
XA
•
XB
•
XC
Chapter Five
U increasing
X
171
Individual Demand Curve
 The consumer is maximizing utility at
every point along the demand curve
 The marginal rate of substitution falls
along the demand curve as the price of x
falls (if there was an interior solution).
 As the price of x falls, utility increases
along the demand curve.
172
Chapter Five
Price Consumption Curve
Y (units)
Example: Suppose U = x + y.
Income, I, is spent only on x and y.
Prices are px and py.
Y*=I/PY
When px < py, the price consumption
curve is I/px= x. When px > py, the
price consumption curve is I/py = y*.
Between, it is x + y = I
PX>PY
X (units)
0
173
Chapter Five
Price Consumption Curve
Y (units)
Y*=I/PY
PX<PY
PX=PY
PX>PY
X (units)
0
174
Chapter Five
Price Consumption Curve
Y (units)
IC1
IC2
IC3
Y*=I/PY
PX<PY
PX=PY
PX>PY
X (units)
0
175
Chapter Five
Demand Curve for “X”
PX
PY
I/PX
The corresponding
demand for x is:
py
py
0
I/PY -Y
X = I/px when px <
I – y when px =
when px > py
X
176
Chapter Five
Demand Curve for “X”
Algebraically, we can solve for the individual’s
demand using the following equations:
1. pxx + pyy = I
2. MUx/px = MUy/py – at a tangency.
(If this never holds, a corner point may be
substituted where x = 0 or y = 0)
177
Chapter Five
Demand Curve with an Interior Solution
Suppose that U(x,y) = xy. MUx = y and
MUy = x. The prices of x and y are px
and py, respectively and income = I.
We Have:
1. pxx + pyy = I
2. x/py = y/px
Substituting the second condition into the budget
constraint, we then have:
3. pxx + py(px/py)x = I or…x = I/2px
178
Chapter Five
Demand Curve with a Corner Point
Suppose U = xy + 10x. MUx=y + 10 and MUy = x.
All the other notation is as in the last example.
Recall that indifference curves such as these are
convex and intersect the x axis.
We Have:
1. pxx + pyy = I
2. (y+10)/x = px/py
Substituting the second equation into the
budget line, we have the demand curve for y:
3. y = (I-10py)/(2py)
4. If I > 10py, demand for y is positive.
179
Chapter Five
Demand Curve with a Corner Point
What if I < 10py? We have a corner point
because:
At y = 0, it is the case that:
MUx/px = (y+10)/pX = 10/pX
MUy/py = x/py = (I/px)/py
y=0 will be the optimal choice only if:
MUx/px > MUy/py …or…
10/px >(I/px)/py …or…
I – 10py < 0
180
Chapter Five
Change in Income & Demand
The income consumption curve of
good x is the set of optimal baskets
for every possible level of income.
We can graph the points on the
income consumption curve as
points on a shifting demand curve.
181
Chapter Five
Income Consumption Curve
182
Chapter Five
Engel Curves
The income consumption curve for
good x also can be written as the
quantity consumed of good x for any
income level. This is the individual’s
Engel Curve for good x. When the
income
consumption
curve
is
positively sloped, the slope of the
Engel Curve is positive.
183
Chapter Five
Engel Curves
I ($)
“X is a normal good”
40
0
X (units)
10
184
Chapter Five
Engel Curves
I ($)
“X is a normal good”
68
40
0
10
X (units)
18
185
Chapter Five
Engel Curves
I ($)
“X is a normal good”
92
68
40
0
10
18
X (units)
24
186
Chapter Five
Engel Curves
I ($)
Engel Curve
“X is a normal good”
92
68
40
0
10
18
X (units)
24
187
Chapter Five
Definitions of Goods
• If the income consumption curve shows that the
consumer purchases more of good x as her income rises,
good x is a normal good.
• Equivalently, if the slope of the Engel curve is
positive, the good is a normal good.
• If the income consumption curve shows that the
consumer purchases less of good x as her income rises,
good x is an inferior good.
• Equivalently, if the slope of the Engel curve is
negative, the good is an inferior good.
188
Chapter Five
Definitions of Goods
Example: Backward Bending
Engel Curve – a good can be
normal over some ranges and
inferior over others
189
Chapter Five
Price & Demand – What’s the Connection?
Definition: As the price of x falls, all else
constant, purchasing power rises. This is
called the income effect of a change in price.
The income effect may be positive (normal
good) or negative (inferior good).
190
Chapter Five
The Substitution Effect
• As the price of x falls, all else constant, good x
becomes cheaper relative to good y. This change
in relative prices alone causes the consumer to
adjust his/ her consumption basket. This effect is
called the substitution effect.
• The substitution effect always is negative.
• Usually, a move along a demand curve will be
composed of both effects.
The Substitution Effect Can be Depicted Graphically
191
Chapter Five
The Substitution Effect
192
Chapter Five
The Substitution Effect
193
Chapter Five
Giffen Goods
If a good is so inferior that the net effect of a price
decrease of good x, all else constant, is a decrease in
consumption of good x, good x is a Giffen good.
For Giffen goods, demand does not slope down.
When might an income effect be large enough to
offset the substitution effect? The good would have to
represent a very large proportion of the budget.
194
Chapter Five
Giffen Goods – Income and Substitution Effects
195
Chapter Five
Giffen Goods – Income and Substitution Effects
Example: Suppose U(x,y) = 2x1/2 + y. MUx
= 1/x1/2 MUy = 1. Py = $1 and I = $10.
Suppose that px = $0.50. What is the (initial)
optimal consumption basket?
Tangency Condition: MUx/MUy = px/py 
px = 1/x1/2
196
Chapter Five
Giffen Goods – Income and Substitution Effects
Solving for x as a function of its price,
x = 1/(px2)
Substituting, xA = 4 at the initial price.
Budget Constraint: pxx + pyy = 10 
yA = 8 at the initial price.
(UA = 2xA1/2 +yA=2(41/2)+8=12)
197
Chapter Five
Giffen Goods – Income and Substitution Effects
Suppose that px = $0.20. What is the
(final) optimal consumption basket?
Using the demand derived in (a), xC =
25 and yC =5
(UC=2xC1/2+yC=2(251/2)+5=15)
198
Chapter Five
Giffen Goods – Income and Substitution Effects
What are the substitution and income effects that
result from the decline in px?
Decomposition Basket:
Constraint: U = 2x1/2 + y = 12
Tangency: MUx/MUy = px/py  1/x1/2 = .2
So that xB = 25 and yB = 2
Substitution Effect: xB-xA = 25 - 4 = 21
Income Effect: xC-xB = 25 - 25 = 0
199
Chapter Five
Quasi-Linear Utility
For this type of utility, the income effect due to a
price change for good x is zero. In other words,
all the income effect is concentrated in y.
Let U(x,y) = v(x) + Ay (where A is a constant).
Then MUx = v’(x) and MUy = A.
At an interior optimum, MUx/MUy = px/py =>
MUx/A = px/py
200
Chapter Five
Quasi-Linear Utility
As income changes, MUx must remain the
same at the new consumption bundle.
But if x changes, MUx will change, in
general. Therefore, x must stay the same.
In other words, (x/I) = 0.
Similarly, the income effect due to a price
change must also be zero
201
Chapter Five
Income & Substitution Effects
“ Pay rises may have worsened the nursing shortage
in Massachusetts by enabling nurses to work fewer
hours, the American Hospital Association says.”
“Labor” includes all work hours when the consumer is earning income.
(L hours per day at wage rate w per hour. Let w = $5)
“Leisure” includes all nonwork activities (so hours of leisure, l = 24 – L)
U= U(y,l)
The consumer likes the "good", leisure.
202
Chapter Five
Income & Substitution Effects
The composite good, y, has price py = $1
Daily income = wL
The budget line gives all the combinations of y
and l that the consumer can afford.
If l = 24, y = 0
If l = 0, y = 120
Slope of budget line is -$5
As the wage rate rises, y is less expensive in terms of
hours of work needed to purchase a unit of y. The
budget line rotates. The optimal choice shifts. Why?
203
Chapter Five
Income & Substitution Effects
• The substitution effect leads to less leisure and
more labor as w increases.
• As w increases, the consumer feels as though he
has more income because less work is needed to buy
a unit of y. This creates an income effect.
• If leisure is a normal good, the income effect on
leisure is positive
• Therefore, the income effect on labor is negative
204
Chapter Five
Income & Substitution Effects
This information can be used to construct the consumer’s labor
supply function, L(w).
 If the income effect of a wage increase outweighs the
substitution effect, the labor supply curve bends backwards.
This information can be used to construct the consumer’s labor
supply function, L(w).
 If the income effect of a wage increase outweighs the
substitution effect, the labor supply curve bends backwards.
205
Chapter Five
Income & Substitution Effects
Wage ($/hour)
Example: Leisure Trade-Off
Supply of Labor
25
•
20
15
10
5
•
•
•
•
Work (hours/day)
9 10 11
206
Chapter Five
Income & Substitution Effects
Daily Income in units of composite good, Y
207
Chapter Five
Consumer Surplus
• The individual’s demand curve can
be seen as the individual’s willingness
to pay curve.
• On the other hand, the individual
must only actually pay the market
price for (all) the units consumed.
208
Chapter Five
Consumer Surplus
PX
G = .5(10-3)(28) = 98
H+I= 28 +2 = 30
CS2 = .5(10-2)(32) = 128
CSP = (10-P)(40-4P)
10
X = 40 - 4PX
• Demand
G
3
2
H
I
28
Chapter Five
32
40
X
209
Consumer Surplus
Definition: The net economic benefit to the
consumer due to a purchase (i.e. the
willingness to pay of the consumer net of
the actual expenditure on the good) is
called consumer surplus.
The area under an ordinary demand curve
and above the market price provides a
measure of consumer surplus
210
Chapter Five
Aggregate Demand
The market, or aggregate, demand function is the
horizontal sum of the individual (or segment) demands.
In other words, market demand is obtained by adding
the quantities demanded by the individuals (or
segments) at each price and plotting this total quantity
for all possible prices.
211
Chapter Five
Aggregate Demand
P
10
P
Q = 10 - p
P
Q = 20 - 5p
4
Segment 1
Q
Segment 2
Q
Aggregate demand
Q
212
Chapter Five
Network Externalities
If one consumer's demand for a good changes with the
number of other consumers who buy the good, there
are network externalities.
If one person's demand decreases with the number of
other consumers, then the externality is positive.
If one person's demand decreases with the number of
other consumers, then the externality is negative.
Examples:
• Telephone (physical network)
• Software (virtual network)
213
Chapter Five
Network Externalities
D60
PX
Bandwagon Effect:
• (increased quantity demanded
D30
when more consumers purchase)
20
10
•
A
•
B
Pure
Price
Effect
30 38
•
C
Market Demand
Bandwagon Effect
60
Chapter Five
X (units)
214
Network Externalities
PX
Market Demand
1200
900
Snob Effect:
• (decreased quantity demanded
when more consumers purchase)
•
A
•
•
C
B
D1000
D1300
Snob Effect
X (units)
Pure Price Effect
1000 1300
1800
Chapter Five
215
Chapter Six
Inputs and
Production
Functions
216
Chapter Six
Chapter Six Overview
1. Motivation
2. The Production Function
 Marginal and Average Products
 Isoquants
 The Marginal Rate of Technical Substitution
3. Technical Progress
4. Returns to Scale
5. Some Special Functional Forms
217
Chapter Six
Production of Semiconductor Chips
 “Fabs” cost $1 to $2 billion to
construct and obsolete in 3 to 5 years
 Must get fab design “right”
 Choice: Robots or Humans?
 Up-front investment in robotics vs.
better chip yields and lower labor costs?
 Capital-intensive or labor-intensive
production process?
218
Chapter Six
Key Concepts
Productive resources, such as labor and capital
equipment, that firms use to manufacture goods and
services are called inputs or factors of production.
The amount of goods and services produces by the firm
is the firm’s output.
Production transforms a set of inputs into a set of outputs
Technology determines the quantity of output that is
feasible to attain for a given set of inputs.
219
Chapter Six
Key Concepts
The production function tells us the maximum
possible output that can be attained by the firm
for any given quantity of inputs.
Example: Q = f(L,K,M)
Example: Q = f(P,F,L,A)
Example: Chips = f1(L,K,M) = f2(L,K,M)
A technically efficient is attaining the
maximum possible output from its inputs
(using whatever technology is appropriate)
220
Chapter Six
The Production Function & Technical Efficiency
Q
Production Function
Q = f(L)
D
C
•
•A
•
•B
Production Set
L
221
Chapter Six
The Production Function & Technical Efficiency
Definition: The feasible but
inefficient points below the
production function make up
the firm’s production set.

Are firms technically efficient?
• Shirking, “perquisites”
• Strategic reasons for technical inefficiency
• Imperfect information on “best practices”
• “63% efficient”
222
Chapter Six
The Production Function & Technical Efficiency
• The variables in the production function are flows
(the amount of the input used per unit of time), not
stocks (the absolute quantity of the input).
• Example: stock of capital is the total factory
installation; flow of capital is the machine hours used
per unit of time in production (including
depreciation).
• Capital refers to physical capital (definition: goods
that are themselves produced goods) and not
financial capital (definition: the money required to
start or maintain production).
223
Chapter Six
The Production Function & Technical Efficiency
Q = (1/192)[K2-(1/36)K3][L2 – (1/36)L3]
Q = K1/2L1/2
224
Chapter Six
The Production Function & Technical Efficiency
Production Function Q = K1/2L1/2 in Table Form
K: 0
10
20
30
40
50
L:
0
0
0
0
0
0
0
10
0
10
14
17
20
22
20
0
14
20
24
28
32
30
0
17
24
30
35
39
40
0
20
28
35
40
45
50
0
22
32
39
45
50
225
Chapter Six
The Production & Utility Functions
Production Function Utility Function
Output from inputs Preference level
from purchases
Derived from
technologies
Derived from
preferences
Cardinal(Defn: given Ordinal
amount of inputs
yields a unique and
specific amount of
output)
Marginal Product
Marginal Utility
226
Chapter Six
The Production & Utility Functions
Production Function
Utility Function
Isoquant(Defn: all
Indifference Curve
possible
combinations of
inputs that just
suffice to produce a
given amount of
output)
Marginal Rate of
Marginal Rate of
Technical
Substitution
Substitution
227
Chapter Six
The Marginal Product
Definition: The marginal product of an input is the
change in output that results from a small change in an
input holding the levels of all other inputs constant.
MPL = Q/L
• (holding constant all other inputs)
MPK = Q/K
• (holding constant all other inputs)
Example:
MPL = (1/2)L-1/2K1/2
MPK = (1/2)K-1/2L1/2
228
Chapter Six
The Average Product & Diminishing Returns
Definition: The average product of an input is
equal to the total output that is to be produced
divided by the quantity of the input that is used
in its production:
APL = Q/L
APK = Q/K
Example:
APL = [K1/2L1/2]/L = K1/2L-1/2
APK = [K1/2L1/2]/K = L1/2K-1/2
Definition: The law of diminishing marginal returns
states that marginal products (eventually) decline as the
quantity used of a single input increases.
229
Chapter Six
Total, Average, and Marginal Magnitudes
Student Height (CM)
Arrival Height Total Average Marginal
1
2
3
4
5
160
180
190
150
150
160
340
530
680
830
160
170
176.67
170
166
"TP"
"AP"
160
180
190
150
150
"MP"
230
Chapter Six
Total, Average, and Marginal Magnitudes
• When a total magnitude is rising,
corresponding marginal magnitude is positive.
the
• When an average magnitude is falling, the
corresponding marginal magnitude must be smaller
than the average magnitude.
231
Chapter Six
Total, Average, and Marginal Magnitudes
TPL maximized where MPL
is zero. TPL falls where MPL
is negative; TPL rises where
MPL is positive.
232
Chapter Six
Isoquants
Definition: An isoquant traces out
all the combinations of inputs (labor
and capital) that allow that firm to
produce the same quantity of output
Example: Q = K1/2L1/2
What is the equation of the isoquant for Q =
20?
20 = K1/2L1/2
=> 400 = KL
=> K = 400/L
And…
233
Chapter Six
Isoquants
…and the isoquant for Q = Q*?
1/2 1/2
Q* = K L
 Q*2 = KL
 K = Q*2/L
234
Chapter Six
Isoquants
K
All combinations of (L,K) along the
isoquant produce 20 units of output.
Q = 20
Slope=K/L
Q = 10
L
0
235
Chapter Six
Marginal Rate of Technical Substitution
Definition: The marginal rate of technical substitution measures the
amount of an input, L, the firm would require in exchange for using a
little less of another input, K, in order to just be able to produce the same
output as before.
MRTSL,K = -K/L (for a constant level of output)
Marginal products and the MRTS are related:
MPL(L) + MPK(K) = 0
=>
MPL/MPK = -K/L = MRTSL,K
Therefore
236
Chapter Six
Marginal Rate of Technical Substitution
• If both marginal products are positive, the
slope of the isoquant is negative.
• If we have diminishing marginal returns,
we also have a diminishing marginal rate of
technical substitution
• For many production functions, marginal
products eventually become negative. Why
don't most graphs of Isoquants include the
upwards-sloping portion?
237
Chapter Six
Isoquants
Isoquants
K
MPK < 0
Example: The Economic and the
Uneconomic Regions of Production
Q = 20
MPL < 0
Q = 10
L
0
238
Chapter Six
Elasticity of Substitution
Definition: The elasticity of substitution, ,
measures how the capital-labor ratio, K/L, changes
relative to the change in the MRTSL,K.
= [(K/L)/MRTSL,K]x[MRTSL,K/(K/L)]
Example: Suppose that:
• MRTSAL,K = 4, KA/LA = 4
• MRTSBL,K = 1, KB/LB = 1
MRTSL,K = MRTSBL,K - MRTSAL,K = -3
 = [(K/L)/MRTSL,K]x[MRTSL,K/(K/L)] = (-3/-3)(4/4) = 1
239
Chapter Six
Elasticity of Substitution
K
"The shape of the isoquant
indicates
the
degree
of
substitutability of the inputs…"
=0
=1
 = 5
=
L
0
240
Chapter Six
Technological Progress
Definition: Technological progress (or invention)
shifts the production function by allowing the firm
to achieve more output from a given combination of
inputs (or the same output with fewer inputs).
Neutral technological progress shifts the isoquant
corresponding to a given level of output inwards,
but leaves the MRTSL,K unchanged along any ray
from the origin
241
Chapter Six
Technological Progress
Labor saving technological progress
results in a fall in the MRTSL,K along any ray
from the origin
Capital saving technological progress
results in a rise in the MRTSL,K along any
ray from the origin.
242
Chapter Six
Neutral Technological Progress
K
Q = 100 ante
Q = 100 post
MRTS remains same
K/L
L
Chapter Six
243
Labor Saving Technological Progress
K
Q = 100 ante
Q = 100 post
MRTS gets smaller
K/L
L
Chapter Six
244
Capital Saving Technological Progress
K
Q = 100 ante
Q = 100 post
MRTS gets larger
K/L
L
Chapter Six
245
Production Function
Q = 500[L+3K]
its production function becomes:
Q = 1000[.5L + 10K]
MPL1= 500 MPL2 = 500
MPK1= 1500 MPK2 = 10,000
So MRTSL,K has decreased (“labor saving
technological progress has occurred”)
246
Chapter Six
Chemicals in the UK
• Evidence of materials-saving and capital using
technological progress;
• In other words, evidence that MPM DECREASED
relative to the MP0;
• MPK INCREASED relative to MP0;
• Further, 30% growth of input
attributable to technological progress.
productivity
247
Chapter Six
Returns to Sale
• How much will output increase when ALL inputs
increase by a particular amount?
• RTS = [%Q]/[% (all inputs)]
• If a 1% increase in all inputs results in a greater than
1% increase in output, then the production function
exhibits increasing returns to scale.
• If a 1% increase in all inputs results in exactly a 1%
increase in output, then the production function
exhibits constant returns to scale.
• If a 1% increase in all inputs results in a less than
1% increase in output, then the production function
exhibits decreasing returns to scale.
248
Chapter Six
Returns to Sale
K
2K
Q = Q1
K
Q = Q0
0
L
L
2L
249
Chapter Six
Returns to Sale
• The marginal product of a single
factor may diminish while the returns
to scale do not
• Returns to scale need not be the
same at different levels of production
• Many production processes obey
the cube-square rule, resulting in
increasing returns to scale.
250
Chapter Six
Returns to Sale
Example: Q1 = AL1K1
Q2 = A(L1)(K1)
= + AL1K1
= +Q1
So returns to scale will depend on the value of +.
+ = 1 … CRS
+ <1 … DRS
+ >1 … IRS
What are the returns to scale of:
Q1 = 500L1+400K1?
251
Chapter Six
Returns to Sale
Example: Electric Power Generation
1950s, estimate Q = ALKF . Find ++>1
• More recently, find this sum equals 1
Example: Returns to scale in oil pipelines
Q = AH.37D1.73
• Increasing returns to scale in horsepower and diameter
252
Chapter Six
Special Production Functions
Linear Production Function:
Q = aL + bK
MRTS constant - constant
returns to scale  = 
Example
253
Chapter Six
Linear Production Function
254
Chapter Six
Fixed Proportions Function
2. Fixed Proportions Production
Function (Leontief Production
Function) Q = min(aL, bK)


L-shaped isoquants
MRTS varies (0, infinity, undefined)
=0
255
Chapter Six
Fixed Proportions Function
O
2
Q = 2 (molecules)
Q = 1 (molecule)
1
0
2
H
4
256
Chapter Six
Cobb-Douglas Production Function
• Q = aLK
• if  +  > 1 then IRTS
• if  +  = 1 then CRTS
• if  +  < 1 then DRTS
• smooth isoquants
• MRTS varies along isoquants
•=1
257
Chapter Six
Cobb-Douglas Production Function
K
Q = Q1
Q = Q0
0
L
258
Chapter Six
Constant Elasticity Production Function
• Q = [aL+bK]1/
Where  = (-1)/
• if  = 0, we get Leontief case
• if  = , we get linear case
• if  = 1, we get the Cobb-Douglas case
259
Chapter Six
Chapter Seven
Costs and Cost
Minimization
260
Chapter Seven
Chapter Seven Overview
1. Introduction: Burke Mills
2. What are Costs?
3. Long Run Cost Minimization
• The constraint minimization problem
• Comparative statics
• Input demands
4. Short Run Cost Minimization
261
Chapter Seven
Opportunity Cost
The relevant concept of cost is
opportunity cost: the value of a
resource in its best alternative use.
 The only alternative we consider is
the best alternative
262
Chapter Seven
Opportunity Cost
Example: Investing $50M - $50M to invest with four alternatives:
1.) If invest now in CD-ROM factory, expected revenues are $100M
2.) If wait a year, expected revenues from CD-ROM investment are 75M
3.) If build new technology plant now, 50% chance that revenues are $0,
50% chance yields $150M.
4.) If wait a year, will know whether revenues are $0 or $150M.
263
Chapter Seven
Opportunity Cost
What is the opportunity cost of investing in CDROM plant now?
Hence, (4) is the best alternative and the
opportunity cost is $112.5M
Costs depend on the decision being made
Example: Opportunity Cost of Steel
Purchase steel for $1M. Since then, price has
gone up so that it is worth $1.2M
(3) yields .5($0) + .5($150M) = $75M
(4) yields .5($75M) + .5($150M)=$112.5M
264
Chapter Seven
Opportunity Cost
1) Manufacture 2000 automobiles
2) Resell the steel
What is the opportunity cost of manufacturing the cars? $1.2M
 Costs depend on the perspective we take
• Opportunity costs often are implicit
265
Chapter Seven
Opportunity Cost – DRAM Chips
Both a long term and a spot market for
DRAM chips exist
Opportunity cost equals the current spot
price, not the historical contract price
Backflush if opportunity cost of
holding chips rises
Accounting costs may be lower or
higher than economic costs
266
Chapter Seven
Sunk Costs
Sunk Costs are costs that must be incurred no
matter what the decision. These costs are not
part of opportunity costs.
• It costs $5M to build and has no alternative uses
• $5M is not sunk cost for the decision of whether
or not to build the factory
• $5M is sunk cost for the decision of whether to
operate or shut down the factory
267
Chapter Seven
Long-Run Cost Minimization
Suppose that a firm’s owners wish to
minimize costs
Let the desired output be Q0
Technology: Q = f(L,K)
Owner’s problem: min TC = rK + wL
• K,L
• Subject to Q0 = f(L,K)
TC0 = rK + wL …or…
K = TC0/r – (w/r)L
Is the isocost line
A Graphical Solution
268
Chapter Seven
Isocost Lines
K
Direction
of increase
in total cost
TC2/r
TC1/r
TC0/r
Slope = -w/r
TC0/w TC1/w TC2/w
Chapter Seven
L
269
Isocost Lines
• Cost minimization subject to satisfaction of the
isoquant equation: Q0 = f(L,K)
• Note: analogous to expenditure minimization
for the consumer
Tangency Condition:
• MRTSL,K = -MPL/MPK = -w/r
•Constraint: Q0 = f(K,L)
270
Chapter Seven
Cost Minimization
TC2/r K
Direction of
increase
in total cost
TC1/r
TC0/r
•
Isoquant Q = Q0
TC0/w TC1/w TC2/w
Chapter Seven
L
271
Interior Solution
Q = 50L1/2K1/2
MPL = 25L-1/2K1/2
MPK = 25L1/2K-1/2
w = $5
r = $20
Q0 = 1000
MPL/MPK = K/L => K/L = 5/20…or…L=4K
1000 = 50L1/2K1/2
K = 10; L = 40
272
Chapter Seven
Corner Solution
Q = 10L + 2K
MPL = 10
MPK = 2
w = $5
r = $2
Q0 = 200
MPL/MPK = 10/2 > w/r = 5/2
But… the “bang for the buck” in labor larger than the “bang
for the buck” in capital…
MPL/w = 10/5 > MPK/r = 2/2
K = 0; L = 20
What is the effect on the optimal input combination if w = $9?
273
Chapter Seven
Costs Minimization Corner Solution
K
Direction of increase
in total cost
Isoquant Q = Q0
Isocost Lines
•
L
Cost-minimizing input combination
Chapter Seven
274
Comparative Statics
A change in the relative price of inputs
changes the slope of the isocost line.
All else equal, an increase in w must decrease
the cost minimizing quantity of labor and
increase the cost minimizing quantity of
capital with diminishing MRTSL,K.
All else equal, an increase in r must decrease
the cost minimizing quantity of capital and
increase the cost minimizing quantity of labor.
275
Chapter Seven
Change in Relative Prices of Inputs
K
Cost minimizing input combination w=2, r=1
•
Cost minimizing input combination, w=1
r=1
•
Isoquant Q = Q0
0
L
276
Chapter Seven
Some Key Definitions
An increase in Q0 moves the isoquant Northeast.
• Definition: The cost minimizing input combinations,
as Q0 varies, trace out the expansion path.
• Definition: If the cost minimizing quantities of labor
and capital rise as output rises, labor and capital are
normal inputs.
• Definition: If the cost minimizing quantity of an input
decreases as the firm produces more output, the input is
called an inferior input.
277
Chapter Seven
An Expansion Path
TC2/r K
Expansion path
TC1/r
•
TC0/r
•
Isoquant Q = Q0
•
TC0/w TC1/w TC2/w
Chapter Seven
L
278
An Expansion Path
K
Substitution & Income Effects Path
– Burke Mills
•
•
0
L
Chapter Seven
279
Input Demand Functions
Definition: The cost minimizing
quantities of labor and capital for
various levels of Q, w and r are
the input demand functions.
L = L*(Q,w,r)
K = K*(Q,w,r)
280
Chapter Seven
Input Demand Functions
281
Chapter Seven
Input Demand Functions
Q = 50L1/2K1/2
MPL/MPK = w/r => K/L = w/r … or…
K=(w/r)L
This is the equation for the expansion path…
Q0 = 50L1/2[(w/r)L]1/2 =>
L*(Q,w,r) = (Q0/50)(r/w)1/2
K*(Q,w,r) = (Q0/50)(w/r)1/2
• Labor and capital are both normal inputs
• Labor is a decreasing function of w
• Labor is an increasing function of r
282
Chapter Seven
Duality
“Reverse engineering” – the production functions from the input demands.
Example: Cobb-Douglas Revisited
Start with the input demands and solve for w:
L = (Q0/50)(r/w)1/2 => w = [Q0/(50L)]2r =
Plug w into the demand for K
K = (Q0/50)[{Q0/(50L)}2r/r]1/2
= Q02/2500L =>
283
Chapter Seven
Duality
Solve for Q0 as a function of K and L:
Q0 = 50K1/2L1/2
Why can we do this? Because the tangencies
that generate the input demand trace out the
isoquants…by keeping Q fixed, we keep
“purchasing power” fixed.
284
Chapter Seven
Short Run Cost Minimization
Suppose that one factor (say, K) is fixed.
Definition: The firm’s short run cost
minimization problem
is to choose quantities of the variable inputs
so as to minimize total costs given that the
firm wants to produce an output level Q0 –
and under the constraint that the quantities
of the fixed factors do not change.
285
Chapter Seven
Short Run Cost Minimization
Min wL + mM + rK*
L,M
Subject to: Q = f(L,K*,M)
Note: L,M are the variable inputs and:
• L+mM is the total variable cost
• K* is the fixed input and
• rK* is the total fixed cost
Tangency condition: MPL/w = MPM/m
Constraint: Q0 = f(L,K*,M)
286
Chapter Seven
Short Run Input Demand Functions
The demand functions are the
solutions to the short run cost
minimization problem:
Ls = L(Q,K*,w,m)
Ms= M(Q,K*,w,m)
So demand for materials and labor
depends on plant size (and design)
287
Chapter Seven
Short Run Input Demand Functions
Suppose that K* is the long run
cost minimizing level of capital for
output level Q.
Then when the firm produces Q,
the short run demands for L and M
must yield the long run cost
minimizing levels of L and M
288
Chapter Seven
Key Examples
Q = K1/2L1/4M1/4
MPL = (1/4)K1/2L-3/4M1/4
MPK = (1/4)K1/2L1/4M-3/4
w = 16
m=1
r =2
K = K*
289
Chapter Seven
Tangency Condition
What is the solution to the firm’s short run cost
minimization problem?
Tangency Condition: MPL/MPM = w/m =>
(1/4K*1/2L-3/4M1/4)/(1/4K*1/2L1/4M-3/4) = 16/1
M = 16L
Constraint: Q0 = K*1/2L1/4(M)1/4
Combining these, we can obtain the short run (conditional)
demand functions for labor and materials
Ls(Q,K*) = Q2/(4K*)
Ms(Q,K*) = (4Q2)/K*
290
Chapter Seven
Tangency Condition
What is the solution to the firm’s long run
cost minimization problem given that the
firm wants to produce Q units of output?
MPL/MPM = w/m
(1/4K1/2L-3/4M1/4)/(1/4K1/2L1/4M-3/4)=16/1
M = 16L
MPL/MPK = w/r
(1/4K1/2L-3/4M1/4)/(1/4K-1/2L1/4M1/4)=16/1
K = 16L
291
Chapter Seven
Tangency Condition
Three equations and three unknowns.
Combining these, we can obtain the
long run demand functions for labor,
capital and materials:
• L(Q) = Q/8
• M(Q)= 2Q
• K(Q) = 2Q
Q = K1/2L1/4M1/4
292
Chapter Seven
Tangency Condition
Suppose that K* = 20. Is it the case that:
Ls(10,20) = L(10)
Ms(10,20) = M(10)?
Ls(10,20) = 100/(4(20) = 1.25
Ms(10,20) = 4(100)/20 = 20
L(10) = 10/8 = 1.25
M(10)= 2(10) = 20
293
Chapter Seven
Tangency Condition
Suppose that K* = 16 and L* =
256. The firm wishes to produce Q
= 48. What is the demand for
materials?
48 = (16)1/2(256)1/4M1/4
M = 81
294
Chapter Seven
Chapter Eight
Costs Curves
295
Chapter Eight
Chapter Eight Overview
1. Introduction: HiSense
2. Long Run Cost Functions
•
•
•
•
Shifts
Long run average and marginal cost functions
Economies of scale
Deadweight loss – "A Perfectly Competitive Market
Without Intervention Maximizes Total Surplus"
3. Short Run Cost Functions
4. The Relationship Between Long Run and
Short Run Cost Functions
296
Chapter Eight
Long Run Cost Functions
Definition: The long run total cost
function relates minimized total cost to
output, Q, to the factor prices (w and r).
TC(Q,w,r) = wL*(Q,w,r) + rK*(Q,w,r)
Where: L* and K* are the long run input
demand functions
297
Chapter Eight
Long Run Cost Functions
What is the long run total cost function for production function Q =
50L1/2K1/2?
L*(Q,w,r) = (Q/50)(r/w)1/2
K*(Q,w,r) = (Q/50)(w/r)1/2
TC(Q,w,r) = w[(Q/50)(r/w)1/2]+r[(Q/50)(w/r)1/2]
= (Q/50)(wr)1/2 + (Q/50)(wr)1/2
= (Q/25)(wr)1/2
What is the graph of the total cost curve when w = 25 and r = 100?
TC(Q) = 2Q
298
Chapter Eight
A Total Cost Curve
TC ($ per year)
TC(Q) = 2Q
$4M.
Q (units per year)
299
Chapter Eight
A Total Cost Curve
TC ($ per year)
TC(Q) = 2Q
$2M.
Q (units per year)
1 M.
300
Chapter Eight
A Total Cost Curve
TC(Q) = 2Q
TC ($ per year)
$4M.
$2M.
Q (units per year)
1 M.
2 M.
301
Chapter Eight
Long Run Total Cost Curve
Definition: The long run total cost curve
shows minimized total cost as output varies,
holding input prices constant.
Graphically, what does the total cost curve
look like if Q varies and w and r are fixed?
302
Chapter Eight
Long Run Total Cost Curve
303
Chapter Eight
Long Run Total Cost Curve
304
Chapter Eight
Long Run Total Cost Curve
305
Chapter Eight
Long Run Total Cost Curve
K
Q1
Q0
K1
K0
TC ($/yr)
0
•
•
TC = TC0
TC = TC1
L0 L1
L (labor services per year)
Q (units per year)
0
306
Chapter Eight
Long Run Total Cost Curve
K
Q1
Q0
K1
K0
TC ($/yr)
0
•
•
TC = TC0
TC = TC1
L0 L1
L (labor services per year)
LR Total Cost Curve
TC0 =wL0+rK0
Q (units per year)
0
Q0
307
Chapter Eight
Long Run Total Cost Curve
K
Q1
Q0
K1
K0
TC ($/yr)
0
•
•
L0 L1
TC = TC0
TC = TC1
L (labor services per year)
TC1=wL1+rK1
LR Total Cost Curve
TC0 =wL0+rK0
0
Q0
Q1 Q (units per year)
Chapter Eight
308
Long Run Total Cost Curve
Graphically, how does the
total cost curve shift if
wages rise but the price of
capital remains fixed?
309
Chapter Eight
A Change in Input Prices
K
TC0/r
0
L
310
Chapter Eight
A Change in Input Prices
K
TC1/r
TC0/r
-w1/r
-w0/r
0
L
311
Chapter Eight
A Change in Input Prices
K
TC1/r
B
TC0/r
•
•
A
-w1/r
-w0/r
0
L
312
Chapter Eight
A Change in Input Prices
K
TC1/r
B
TC0/r
•
•
A
Q0
-w1/r
-w0/r
0
L
313
Chapter Eight
A Shift in the Total Cost Curve
TC ($/yr)
TC(Q) post
Q (units/yr)
314
Chapter Eight
A Shift in the Total Cost Curve
TC ($/yr)
TC(Q) post
TC(Q) ante
Q (units/yr)
315
Chapter Eight
A Shift in the Total Cost Curve
TC ($/yr)
TC(Q) post
TC(Q) ante
TC0
Q (units/yr)
316
Chapter Eight
A Shift in the Total Cost Curve
TC ($/yr)
TC(Q) post
TC(Q) ante
TC1
TC0
Q (units/yr)
Q0
317
Chapter Eight
Input Price Changes
How does the total cost curve
shift if all input prices rise
(the same amount)?
For
example, suppose that all
input prices double:
318
Chapter Eight
All Input Price Changes
K (capital services/yr)
•
A
L (labor
services/yr)
0
319
Chapter Eight
All Input Price Changes
K (capital services/yr)
L (labor
-w/r
services/yr)
0
320
Chapter Eight
All Input Price Changes
K (capital services/yr)
•
A
Q0
L (labor
-w/r
services/yr)
0
321
Chapter Eight
All Input Price Changes
K (capital services/yr)
•
2
A
Q0
L (labor
-w/r
0
services/yr)
1
322
Chapter Eight
All Input Price Changes
Example:
TC(Q,w,r) = (wr)1/2Q/25
TC(Q, λw, λr) = (λw)1/2(λr)1/2Q/25 =
λ(wr)1/2Q/25 = λTC(Q,w,r)
323
Chapter Eight
Long Run Average Cost Function
Definition: The long run average
cost function is the long run total
cost function divided by output, Q.
That is, the LRAC function tells us
the firm’s cost per unit of output…
AC(Q,w,r) = TC(Q,w,r)/Q
324
Chapter Eight
Long Run Marginal Cost Function
Definition: The long run marginal
cost function measures the rate of
change of total cost as output varies,
holding constant input prices.
MC(Q,w,r) =
{TC(Q+Q,w,r) – TC(Q,w,r)}/Q
= TC(Q,w,r)/Q
where: w and r are constant
325
Chapter Eight
Long Run Marginal Cost Function
Recall that, for the
production function Q =
50L1/2K1/2, the total cost
function was TC(Q,w,r) =
(Q/25)(wr)1/2. If w = 25,
and r = 100, TC(Q) = 2Q.
326
Chapter Eight
Long Run Marginal Cost Function
a. What are the long run average and marginal cost
functions for this production function?
AC(Q,w,r) = (wr)1/2/25
MC(Q,w,r) = (wr)1/2/25
b. What are the long run average and marginal cost
curves when w = 25 and r = 100?
AC(Q) = 2Q/Q = 2.
MC(Q) = (2Q)/Q = 2.
327
Chapter Eight
Average & Marginal Cost Curves
AC, MC ($ per unit)
AC(Q) =
MC(Q) = 2
$2
Q (units/yr)
0
328
Chapter Eight
Average & Marginal Cost Curves
AC, MC ($ per unit)
AC(Q) =
MC(Q) = 2
$2
Q (units/yr)
0
1M
329
Chapter Eight
Average & Marginal Cost Curves
AC, MC ($ per unit)
AC(Q) =
MC(Q) = 2
$2
Q (units/yr)
0
1M
2M
Chapter Eight
330
Average & Marginal Cost Curves
Suppose that w and r are fixed:
When marginal cost is less than average
cost, average cost is decreasing in
quantity. That is, if MC(Q) < AC(Q),
AC(Q) decreases in Q.
331
Chapter Eight
Average & Marginal Cost Curves
When marginal cost is greater than
average cost, average cost is increasing in
quantity. That is, if MC(Q) > AC(Q),
AC(Q) increases in Q.
When marginal cost equals average cost,
average cost does not change with
quantity. That is, if MC(Q) = AC(Q),
AC(Q) is flat with respect to Q.
332
Chapter Eight
Average & Marginal Cost Curves
AC, MC ($/yr)
“typical” shape of AC
AC
Q (units/yr)
0
333
Chapter Eight
Average & Marginal Cost Curves
AC, MC ($/yr)
“typical” shape of AC
MC
AC
•
Q (units/yr)
0
334
Chapter Eight
Average & Marginal Cost Curves
AC, MC ($/yr)
“typical” shape of AC
MC
AC
•
AC at minimum when AC(Q)=MC(Q)
Q (units/yr)
0
335
Chapter Eight
Economies & Diseconomies of Scale
Definition: If average cost decreases as
output rises, all else equal, the cost
function exhibits economies of scale.
Similarly, if the average cost increases as
output rises, all else equal, the cost
function exhibits diseconomies of scale.
Definition: The smallest quantity at which
the long run average cost curve attains its
minimum point is called the minimum
efficient scale.
336
Chapter Eight
Minimum Efficiency Scale (MES)
AC ($/yr)
AC(Q)
Q (units/yr)
0
Q* = MES
337
Chapter Eight
MES – Selected Food & Beverages
Industry MES as % of US market output:
Beet Sugar (processed)
Cane Sugar (processed)
Flour
Breakfast Cereal
Baby food
1.87
12.01
.68
9.47
2.59
338
Chapter Eight
Returns to Scale & Economies of Scale
When the production function
exhibits increasing returns to
scale, the long run average cost
function exhibits economies of
scale so that AC(Q) decreases
with Q, all else equal.
339
Chapter Eight
Returns to Scale & Economies of Scale
• When the production function exhibits
decreasing returns to scale, the long run average
cost function exhibits diseconomies of scale so
that AC(Q) increases with Q, all else equal.
• When the production function exhibits constant
returns to scale, the long run average cost
function is flat: it neither increases nor decreases
with output.
340
Chapter Eight
Returns to Scale & Economies of Scale
CRS
IRS
DRS
Production Function Q = L Q = L2 Q = L1/2
Labor Demand
L*=Q L*=Q1/2 L*=Q2
Total Cost Function
TC=wQ wQ1/2 wQ2
Average Cost Function AC=w w/Q1/2 wQ
Economies of Scale
none
EOS
DOS
341
Chapter Eight
Output Elasticity of Total Cost
Definition: The percentage change in total
cost per one percent change in output is
the output elasticity of total cost, TC,Q.
TC,Q = (TC/Q)(Q/TC) =
= MC/AC
• If TC,Q < 1, MC < AC, so AC must be decreasing in Q.
Therefore, we have economies of scale.
• If TC,Q > 1, MC > AC, so AC must be increasing in Q.
Therefore, we have diseconomies of scale.
• If TC,Q = 1, MC = AC, so AC is just flat with respect to Q.
342
Chapter Eight
Output Elasticity of Total Cost
Example: For Selected Manufacturing Industries in India
Industry
TC,Q
Iron and Steel
Cotton Textiles
Cement
Electricity and Gas
0.553
1.211
1.162
0.3823
343
Chapter Eight
Short Run & Total Variable Cost Functions
Definition: The short run total cost function
tells us the minimized total cost of
producing Q units of output, when (at least)
one input is fixed at a particular level.
Definition: The total variable cost function
is the minimized sum of expenditures on
variable inputs at the short run cost
minimizing input combinations.
344
Chapter Eight
Total Fixed Cost Function
Definition: The total fixed cost function is a
constant equal to the cost of the fixed input (s).
STC(Q,K0) = TVC(Q,K0) + TFC(Q,K0)
Where: K0 is the fixed input and w and r are
fixed (and suppressed as arguments)
345
Chapter Eight
Key Cost Functions Interactions
TC ($/yr)
Example: Short Run Total Cost, Total
Variable Cost and Total Fixed Cost
TFC
Q (units/yr)
346
Chapter Eight
Key Cost Functions Interactions
TC ($/yr)
Example: Short Run Total Cost, Total
Variable Cost and Total Fixed Cost
TVC(Q, K0)
TFC
Q (units/yr)
347
Chapter Eight
Key Cost Functions Interactions
TC ($/yr)
Example: Short Run Total Cost, Total
Variable Cost and Total Fixed Cost
STC(Q, K0)
TVC(Q, K0)
TFC
Q (units/yr)
348
Chapter Eight
Key Cost Functions Interactions
TC ($/yr)
Example: Short Run Total Cost, Total
Variable Cost and Total Fixed Cost
STC(Q, K0)
rK0
TVC(Q, K0)
TFC
rK0
Q (units/yr)
349
Chapter Eight
Key Cost Functions Interactions
Suppose that the production
function is Q = K1/2L1/4M1/4.
Let w = 16, m = 1 and r = 2.
What is the short run total cost
curve when capital is fixed at level
K0? What is the (short run) total
variable cost curve? What is the
(short run) total fixed cost curve?
350
Chapter Eight
Key Cost Functions Interactions
Recall that the short run
input demand functions for
labor and materials are:
Ls (Q,K0) = Q2/(4K0) & Ms(Q,K0) = (4Q2)/K0
STC(Q,K0) = 16(Q2/(4K0))+ (4Q2)/K0 + 2K0
= (8Q2/K0) + 2K0
TVC(Q,K0) = (8Q2)/K0
TFC(K0) = 2K0
NB: for constant Q, TVC decreases in K0
351
Chapter Eight
Long and Short Run Total Cost Functions
The firm can minimize costs
at least as well in the long run
as in the short run because it is
“less constrained”.
Hence, the short run total cost
curve lies everywhere above
the long run total cost curve.
352
Chapter Eight
Long and Short Run Total Cost Functions
However, when the quantity is
such that the amount of the fixed
inputs just equals the optimal long
run quantities of the inputs, the
short run total cost curve and the
long run total cost curve coincide.
353
Chapter Eight
Long and Short Run Total Cost Functions
K
TC0/r
0
TC0/w
Chapter Eight
L
354
Long and Short Run Total Cost Functions
K
TC1/r
TC0/r
K0
0
•B
TC0/w TC1/w
Chapter Eight
L
355
Long and Short Run Total Cost Functions
TC2/r
TC1/r
K
Q1
•
TC0/r
K0
0
C
•
A
•B
TC0/w TC1/w TC2/w
Chapter Eight
L
356
Long and Short Run Total Cost Functions
TC2/r
TC1/r
K
Q1
Expansion Path
•
TC0/r
C
Q0
K0
0
•
A
Q0
B
•
TC0/w TC1/w TC2/w
Chapter Eight
L
357
Long and Short Run Total Cost Functions
Total Cost ($/yr)
STC(Q,K0)
TC(Q)
K0 is the LR cost-minimising
quantity of K for Q0
0
Q0
Q1
Q (units/yr)
358
Chapter Eight
Long and Short Run Total Cost Functions
STC(Q,K0)
Total Cost ($/yr)
TC(Q)
TC0
•
A
K0 is the LR cost-minimising
quantity of K for Q0
0
Q0
Q1
Q (units/yr)
359
Chapter Eight
Long and Short Run Total Cost Functions
STC(Q,K0)
Total Cost ($/yr)
TC(Q)
•C
TC1
TC0
•
A
K0 is the LR cost-minimising
quantity of K for Q0
0
Q0
Q1
Q (units/yr)
360
Chapter Eight
Long and Short Run Total Cost Functions
STC(Q,K0)
Total Cost ($/yr)
•
•C
TC2
B
TC1
TC0
TC(Q)
•
A
K0 is the LR cost-minimising
quantity of K for Q0
0
Q0
Q1
Q (units/yr)
361
Chapter Eight
Short Run Average Cost Function
Definition: The Short run average cost
function is the short run total cost
function divided by output, Q.
That is, the SAC function tells us the
firm’s short run cost per unit of output.
SAC(Q,K0) = STC(Q,K0)/Q
Where: w and r are held fixed
362
Chapter Eight
Short Run Marginal Cost Function
Definition: The short run marginal cost
function measures the rate of change of
short run total cost as output varies, holding
constant input prices and fixed inputs.
SMC(Q,K0)={STC(Q+Q,K0)–
STC(Q,K0)}/Q
= STC(Q,K0)/Q
where: w,r, and K0 are constant
363
Chapter Eight
Summary Cost Functions
Note: When STC = TC, SMC = MC
STC = TVC + TFC
SAC = AVC + AFC
Where:
SAC = STC/Q
AVC = TVC/Q (“average variable cost”)
AFC = TFC/Q (“average fixed cost”)
The SAC function is the VERTICAL
sum of the AVC and AFC functions
364
Chapter Eight
Summary Cost Functions
$ Per Unit
Example: Short Run Average
Cost, Average Variable Cost
and Average Fixed Cost
AFC
0
Q (units per year)
365
Chapter Eight
Summary Cost Functions
$ Per Unit
AVC
Example: Short Run Average
Cost, Average Variable Cost
and Average Fixed Cost
AFC
0
Q (units per year)
366
Chapter Eight
Summary Cost Functions
SAC
$ Per Unit
AVC
Example: Short Run Average
Cost, Average Variable Cost
and Average Fixed Cost
AFC
0
Q (units per year)
367
Chapter Eight
Summary Cost Functions
$ Per Unit
SMC
SAC
AVC
Example: Short Run Average
Cost, Average Variable Cost
and Average Fixed Cost
AFC
0
Q (units per year)
368
Chapter Eight
Long Run Average Cost Function
$ per unit
SAC(Q,K3)
AC(Q)
•
0
•
•
Q1
Q2
Q3
Q (units per year)
369
Chapter Eight
Long Run Average Cost Function
$ per unit
SAC(Q,K1)
AC(Q)
•
0
•
•
Q1
Q2
Q3
Q (units per year)
370
Chapter Eight
Long Run Average Cost Function
$ per unit
SAC(Q,K1)
SAC(Q,K2)
AC(Q)
•
0
•
•
Q1
Q2
Q3
Q (units per year)
371
Chapter Eight
Long Run Average Cost Function
$ per unit
SAC(Q,K3)
SAC(Q,K1)
SAC(Q,K2)
AC(Q)
•
0
•
•
Q1
Q2
Q3
Q (units per year)
372
Chapter Eight
Long Run Average Cost Function
Example: Let Q = K1/2L1/4M1/4 and let w
= 16, m = 1 and r = 2. For this production
function and these input prices, the long
run input demand curves are:
Therefore, the long run total cost curve is:
TC(Q) = 16(Q/8) + 1(2Q) + 2(2Q) = 8Q
The long run average cost curve is:
AC(Q) = TC(Q)/Q = 8Q/Q = 8
Chapter Eight
L*
(Q
)=
Q/
8
M
*(
Q)
=
2
Q
K
*(
Q)
=
2
373
Short Run Average Cost Function
Recall, too, that the short run total cost
curve for fixed level of capital K0 is:
STC(Q,K0) = (8Q2)/K0 + 2K0
If the level of capital is fixed at K0 what
is the short run average cost curve?
SAC(Q,K0) = 8Q/K0 + 2K0/Q
374
Chapter Eight
Cost Function Summary
$ per unit
MC(Q)
Q (units per
year)
0
375
Chapter Eight
Cost Function Summary
$ per unit
MC(Q)
AC(Q)
Q (units per
year)
0
376
Chapter Eight
Cost Function Summary
$ per unit
MC(Q)
AC(Q)
SAC(Q,K2)
•
•
SMC(Q,K )
1
Q (units per
0
Q1
Q2
year)
Q3
377
Chapter Eight
Cost Function Summary
$ per unit
MC(Q)
MC(Q)
SAC(Q,K3)
SAC(Q,K1)
AC(Q)
SAC(Q,K2)
•
•
SMC(Q,K )
1
•
Q (units per
0
Q1
Q2
year)
Q3
378
Chapter Eight
Cost Function Summary
$ per unit
MC(Q)
MC(Q)
SAC(Q,K3)
SAC(Q,K1)
AC(Q)
SAC(Q,K2)
•
•
SMC(Q,K )
1
•
Q (units per
0
Q1
Q2
year)
Q3
379
Chapter Eight
Chapter Nine
Perfectly
Competitive
Markets
380
Chapter Nine
Chapter Nine Overview
1. Introduction: Nakao Growers
2. Perfect Competition Defined
3. The Profit Maximization Hypothesis
4. The Profit Maximization Condition
5. Short Run Equilibrium
• Short Run Supply Curve for the Firm
• Short Run Market Supply Curve
• Short Run Perfectly Competitive Equilibrium
• Producer Surplus
6. Long Run Equilibrium
•
•
Long Run Equilibrium Conditions
Long Run Supply Curve
381
Chapter Nine
Perfectly Competitive Markets
A perfectly competitive market
consists of firms that produce identical
products that sell at the same price.
Each firm’s volume of output is so
small in comparison to the overall
market demand that no single firm has
an impact on the market price.
382
Chapter Nine
Perfectly Competitive Markets
A. Firms produce undifferentiated
products in the sense that consumers
perceive them to be identical
B.
Consumers
have
perfect
information about the prices all sellers
in the market charge
383
Chapter Nine
Perfectly Competitive Markets
C. Each buyer’s purchases are so
small that he/she has an imperceptible
effect on market price.
D. Each seller’s sales are so small that
he/she has an imperceptible effect on
market price.
Each seller’s input
purchases are so small that he/she
perceives no effect on input prices
E. All firms (industry participants and
new entrants) have equal access to
resources (technology, inputs).
384
Chapter Nine
Implications of Conditions
The Law of One Price: Conditions (a)
and (b) imply that there is a single price at
which transactions occur.
Price Takers: Conditions (c) and (d)
imply that buyers and sellers take the price
of the product as given when making their
purchase and output decisions.
Free Entry: Condition (e) implies that all
firms have identical long run cost functions
385
Chapter Nine
The Profit Maximization Hypothesis
Definition: Economic Profit
Sales Revenue-Economic (opportunity) Cost
Example:
• Revenues: $1M
• Costs of supplies and labor: $850,000
• Owner’s best outside offer: $200,000
386
Chapter Nine
The Profit Maximization Hypothesis
“Accounting Profit”: $1M - $850,000 = $150,000
“Economic Profit”: $1M - $850,000 - $200,000 = -$50,000
• Business “destroys” $50,000 of wealth of owner
387
Chapter Nine
The Profit Maximization Condition
Max (q) = Pq – TC(q)
q
Definition: A firm’s marginal revenue is the rate at which
total revenue changes with respect to output:
MR(q) = {TR(q + q)-TR(q)}/q =
(Pq)/q = P…the firm's "marginal benefit" from a sale
388
Chapter Nine
The Profit Maximization Condition
If P > MC then profit rises if output is increased
If P < MC then profit falls if output is increased.
Therefore, the profit maximization condition for a
price-taking firm is P = MC
389
Chapter Nine
The Profit Maximization Condition
390
Chapter Nine
The Profit Maximization Condition
Where these have been drawn for:
TC(q) = 242q - .9q2 + (.05/3)q3
MC(q) = 24 - 1.8q + .05q2
P = 15
At profit maximizing point:
1. P = MC
2. MC rising
“firm demand" = P (sells as much as likes at P)
“firm supply" defined by MC curve? Not quite:
391
Chapter Nine
Short Run Equilibrium
For the following, the short run is the
period of time in which the firm’s
plant size is fixed and the number of
firms in the industry is fixed.
STC(Q) = SFC + NSFC + TVC(q) for
q > 0 SFC for q = 0
392
Chapter Nine
Short Run Equilibrium
SFC is the cost of the firm’s fixed input that are unavoidable at q = 0
Output insensitive for q > 0 = Sunk
NSFC is the cost of the firm’s inputs that are avoidable if the firm
produces zero (salaries of some employees, for example)
Output insensitive for q > 0 = Non-sunk
TFC = SFC + NSFC
TVC(q) are the output sensitive costs (and are non-sunk)
393
Chapter Nine
Short Run Supply Curve (SRSC)
Definition: The firm’s Short run supply
curve tells us how the profit maximizing
output changes as the market price changes.
Case 1: Short Run Supply Curve:
NSFC=0
If the firm chooses to produce a positive
output, P = SMC defines the short run
supply curve of the firm. But…
394
Chapter Nine
Shut Down Price
The firm will choose to produce a positive
output only if:
(q) > (0) …or…
Pq – TVC(q) – TFC > -TFC 
Pq – TVC(q) > 0 
P > AVC(q)
Definition: The price below which the firm
would opt to produce zero is called the shut
down price, Ps. In this case, Ps is the
minimum point on the AVC curve.
395
Chapter Nine
Short Run Supply Function
Therefore, the firm’s short run supply
function is defined by:
1. P=SMC, where SMC slopes upward as
long as P > Ps
2. 0 where P < Ps
This means that a perfectly competitive firm
may choose to operate in the short run even
if economic profit is negative.
396
Chapter Nine
Short Run Supply Curve
$/yr
NSFC = 0
SMC
SAC
AVC
Ps
Quantity (units/yr)
397
Chapter Nine
Cost Considerations
At prices below SAC but above AVC, profits are
negative if the firm produces…but the firm loses less by
producing than by shutting down because of sunk costs.
Example:
STC(q) = 100 + 20q + q2
TFC = 100 (nb: this is sunk)
TVC(q) = 20q + q2
AVC(q) = 20 + q
SMC(q) = 20 + 2q
398
Chapter Nine
Cost Considerations
The minimum level of AVC is the point
where AVC = SMC or:
20+q = 20+2q
q=0
AVC minimized at 20
The firm’s short run supply curve is, then:
P < Ps = 20: qs = 0
P > Ps = 20: P = SMC 
P = 20+2q  qs = 10 + ½P
399
Chapter Nine
SRSC When All Costs are Non-Sunk
If the firm chooses to produce a positive
output, P = SMC defines the short run supply
curve of the firm. But the firm will choose to
produce a positive output only if:
(q) > (0) …or…
Pq – TVC(q) - TFC > 0 
P > AVC(q) + AFC(q) = SAC(q)
Now, the shut down price, Ps is the minimum
of the SAC curve
400
Chapter Nine
SRSC When All Costs are Non-Sunk
$/yr
SMC
SAC
Ps
AVC
Quantity (units/yr)
401
Chapter Nine
SRSC When All Costs are Non-Sunk
STC(q) = F + 20q + q2
F = 100, all of which is sunk:
AVC(q) = 20 + q
SMC(q) = 20 + 2q
SAC(q) = 100/q + 20 + q
SAC = SMC at q = 10
At any P > 40, the firm earns positive economic profit
At any P < 40, the firm earns negative economic profit.
402
Chapter Nine
Market Supply and Equilibrium
Definition: The market supply
at any price is the sum of the
quantities each firm supplies at
that price.
The short run market supply
curve is the horizontal sum of the
individual firm supply curves.
403
Chapter Nine
Short Run market & Supply Curves
404
Chapter Nine
Short Run Perfectly Completive Equilibrium
Definition: A short run perfectly competitive
equilibrium occurs when the market quantity
demanded equals the market quantity supplied.
ni=1 qs(P) = Qd(P)
and qs(P) is determined by the firm's individual
profit maximization condition.
405
Chapter Nine
Short Run Perfectly Completive Equilibrium
406
Chapter Nine
Deriving a Short Run Market Equilibrium
300 Identical Firms
Qd(P) = 60 – P
STC(q) = 0.1 + 150q2
SMC(q) = 300q
NSFC = 0
AVC(q) = 150q
407
Chapter Nine
Deriving a Short Run Market Equilibrium
Short Run Equilibrium
Profit maximization condition: P = 300q
qs(P) = P/300
Qs(P) = Qd(P)  P = 60 – P
P*= 30
q* = 30/300=.1
Q* = 30
408
Chapter Nine
Deriving a Short Run Market Equilibrium
Do firms make positive profits at the market
equilibrium?
SAC = STC/q = .1/q + 150q
When each firm produces .1, SAC per firm is:
.1/.1 + 150(.1) = 16
Therefore, P* > SAC so profits are positive
409
Chapter Nine
Producer Surplus
Definition: Producer Surplus is the area
above the market supply curve and below
the market price. It is a monetary measure
of the benefit that producers derive from
producing a good at a particular price.
…that the producer earns the price for every unit sold,
but only incurs the SMC for each unit. This is why the
difference between the P and SMC curve measures the
total benefit derived from production.
410
Chapter Nine
Producer Surplus
Further, since the market supply curve is
simply the sum of the individual supply
curves…which equal the marginal cost
curves the difference between price and
the market supply curve measures the
surplus of all producers in the market.
…that producer’s surplus
does not deduct fixed costs,
so it does not equal profit.
411
Chapter Nine
Producer Surplus
P
Market Supply Curve
P*
Producer Surplus
Chapter Nine
Q
412
Long Run Market Equilibrium
For the following, the long run is the period of time
in which all the firm’s inputs can be adjusted. The
number of firms in the industry can change as well.
The firm should use long run cost functions for
evaluating the cost of outputs it might produce in this
longer term period…i.e., decisions to modify plant
size, enter or exit, change production process and so
on would all be based on long term analysis
413
Chapter Nine
Long Run Market Equilibrium
MC
$/unit
P
AC
SMC0 SAC0
SAC1
Example: Incentive to
Change Plant Size
SMC1
For example, at P, this firm has an incentive to change plant size to level K1 from K0:
1.8
q
6
(000 units/yr)
414
Chapter Nine
Long Run Market Equilibrium
The firm’s long run supply curve:
P = MC for P > min(AC) = Ps
0 (exit) for P < min(AC) = Ps
A long run perfectly competitive equilibrium occurs
at a market price, P*, a number of firms, n*, and an
output per firm, q* that satisfies:
415
Chapter Nine
Long Run Market Equilibrium
Long run profit maximization with respect to
output and plant size:
P* = MC(q*)
Zero economic profit
P* = AC(q*)
Demand equals supply
Qd(P*) = n*q* …or…
n* = Qd(P*)/q*
416
Chapter Nine
Long Run Perfectly Competitive
$/unit
$/unit
n* = 10,000,000/50,000=200
MC
SAC
Market demand
AC
P*
SMC
q*=50,000
q
Q*=10M.
417
Chapter Nine
Q
Calculating Long Run Equilibrium
TC(q) = 40q - q2 + .01q3
AC(q) = 40 – q + .01q2
MC(q) = 40 – 2q + .03q2
Qd(P) = 25000-1000P
The long run equilibrium satisfies the following:
a. P* = 40 – 2q* - .03q*2
b. P* = 40 – q* + .01q*2
c. 25000-1000P* = q*n*
418
Chapter Nine
Calculating Long Run Equilibrium
Using (a) and (b), we have:
40 – 2q* + .03q*2 = 40-q*+.01q*2
q* = 50
P* = 15
Qd(P*) = 10000
Using (c ) we have:
n* = 10000/50 = 200
419
Chapter Nine
Calculating Long Run Equilibrium
Summarizing long run equilibrium – “If
anyone can do it, you can’t make money at it”
Or if the firm’s strategy is based on skills that
can be easily imitated or resources that can be
easily acquired, in the long run your economic
profit will be competed away.
420
Chapter Nine
Long Run Market Supply Curve
We have calculated a point at which the
market will be in long run equilibrium.
This is a point on the long run market
supply curve. This curve can be derived
explicitly, however.
Definition:
The Long Run Market
Supply Curve tells us the total quantity of
output that will be supplied at various
market prices, assuming that all long run
adjustments (plant, entry) take place.
421
Chapter Nine
Long Run Market Supply Curve
Since new entry can occur in the long run, we cannot obtain the long run
market supply curve by summing the long run supplies of current market
participants
Instead, we must construct the long run market supply curve.
We reason that, in the long run, output expansion or contraction in the industry
occurs along a horizontal line corresponding to the minimum level of long run
average cost.
If P > min(AC), entry would occur, driving price back to min(AC)
If P < min(AC), firms would earn negative profits and would supply nothing
422
Chapter Nine
Long Run Market Supply Curve
$/unit
$/unit
n** = 18M/52,000 = 360
SS0
SS1
D1
MC
23
15
SAC
D0
AC
LS
SMC
q (000s)
50 52
10
Chapter Nine
18
423
Q (M.)
Chapter Ten
Competitive
Markets:
Applications
424
Chapter Ten
Chapter Ten Overview
1. Motivation: Agricultural Price Supports
2. Deadweight Loss
•
A Perfectly Competitive Market Without Intervention
Maximizes Total Surplus"
3. Government Intervention – Who Wins and Who Loses?
4. Examples of Various Government Polices
•
•
•
•
Excise Taxes
Price Ceilings
Production Quotas
Import Tariffs
5. Conclusions
425
Chapter Ten
Deadweight Loss
At the Perfectly Competitive Equilibrium, (Q*,P*), Total Surplus is maximized.
Consumer's Surplus at (Q*,P*): ABC
Producer's Surplus at (Q*,P*) : DBC
Total Surplus at (Q*,P*): ADC
426
Chapter Ten
Deadweight Loss
Definition: A deadweight
loss is a reduction in net
economic benefits resulting
from an inefficient allocation
of resources.
427
Chapter Ten
Surplus Maximization in Competitive Equilibrium
P
Supply
A
Pd
C
P* B
Ps D
Demand
Q1
Q
Q*
428
Chapter Ten
Surplus Maximization in Competitive Equilibrium
P
Supply
A
Ps
P* B
Pd
C
D
Demand
Q*
Q2
Chapter Ten
Q
429
Economic Efficiency
Definition: Economic Efficiency means that the total
surplus is maximized.
"Every consumer who is willing to pay more than the
opportunity cost of the resources needed to produce
extra output is able to buy; every consumer who is not
willing to pay the opportunity cost of the extra output
does not buy.“
"All gains from trade (between buyers and suppliers)
are exhausted at the efficient point."
The perfectly competitive
economic efficiency.
equilibrium
attains
430
Chapter Ten
Government Intervention: Winners & Losers
Intervention
Type:
Effect on Effect on
Effect on
Effect on
(domestic) (domestic) (domestic) (domestic) Is a (domestic)
Quantity
Consumer Producer
Government Deadweight
Traded
Surplus
Surplus
Budget
Loss created?
Excise Tax
Falls
Falls
Falls
Positive
Yes
Subsidies to
Producers
Rises
Rises
Rises
Negative
Yes
Maximum Price
Ceilings for
Producers
Falls;
Excess
Demand
Rise or
Fall
Falls
Zero
Yes
Minimum Price
Floors for
Producers
Falls;
Excess
Supply
Falls
Rise or
Fall
Zero
Yes
Production
Quotas
Falls;
Excess
Supply
Falls
Rise or
Fall
Zero
Yes
Import Tariffs
Falls
Falls
Rises
Positive
Yes
Import Quotas
Falls
Falls
Rises
Zero
Yes
431
Chapter Ten
Policy: Excise Tax
Definition: An excise tax (or a specific
tax) is an amount paid by either the
consumer or the producer per unit of the
good at the point of sale.
(The amount paid by the demanders
exceeds the total amount received by the
sellers by amount T)
432
Chapter Ten
Policy: Excise Tax
S’
P
S
T
Pd
P*
Ps
Demand
Q
Q1 Q*
433
Chapter Ten
Key Definitions
Definition: The amount by which the
price paid by buyers, PD, rises over the
non-tax equilibrium price, P*, is the
incidence of the tax on consumers; the
amount by which the price received by
sellers, PS, falls below P* is called the
incidence of the tax on producers.
434
Chapter Ten
Incidence of Tax in Two Cases
P
Pd=P*+T
S’
T
Ps = P*
S
P
D
S
Q
Pd = P*
Ps = P*-T
T
Q
D
435
Chapter Ten
Back of the Envelope
"Back of the Envelope" method
calculate the incidence of a specific tax
to
Pd/Ps = /
where:  is the own-price elasticity of supply
 is the own-price elasticity of demand
436
Chapter Ten
Back of the Envelope
Why – consider a small tax applied to an
economy at point (Q*,P*)
 =(Q/Q*)/(Pd/P*)… Q/Q*=Pd/P*
 =(Q/Q*)/(Ps/P*)… Q/Q*=Ps/P*
but for market to clear, Q/Q* must be the
same for demand and supply, hence
Pd/P* = Ps/P*
437
Chapter Ten
Tax Affect
Example: Let  = -.5 and  = 2. What is the relative
incidence of a specific tax on consumers and producers?
Pd/Ps = 2/-.5 = -4
interpretation: "consumers pay four times as much as the
decrease in price producers receive. Hence, an excise tax
of $1 results in an increase in consumer price of $.8 and a
decrease in price received by producers of $.2"
Note: Subsidies are negative taxes.
438
Chapter Ten
Subsidies
P
S’
Ps
Pd
D
Q* Q2
Q
439
Chapter Ten
Subsidies
P
S
S’
T
Ps
Pd
D
Q* Q2
Q
440
Chapter Ten
Subsidies
P
S
S’
T
Ps
Pd
D
Q* Q2
Q
441
Chapter Ten
Policy: Price Ceilings
Definition: A price ceiling is a
legal maximum on the price per unit
that a producer can receive. If the
price ceiling is below the pre-control
competitive equilibrium price, then
the ceiling is called binding.
442
Chapter Ten
Policy: Price Ceilings
P
S
D
Q
443
Chapter Ten
Policy: Price Ceilings
P
S
PMAX
D
Q
444
Chapter Ten
Policy: Price Ceilings
P
S
PMAX
Excess
Demand
D
Qs Q* Qd
Q
445
Chapter Ten
Policy: Price Floor
Definition: A price floor is a
minimum price that consumers
can legally pay for a good. Price
floors sometimes are referred to
as price supports. If the price
floor is above the pre-control
competitive equilibrium price, it is
said to be binding.
446
Chapter Ten
Policy: Price Floor
P
S
D
Q
447
Chapter Ten
Policy: Price Floor
P
S
Excess
Supply
PMIN
D
Qd Q* Qs
Q
448
Chapter Ten
Policy: Production Quotas
Definition: A production quota
is a limit on either the number of
producers in the market or on
the amount that each producer
can sell. The quota usually has
a goal of placing a limit on the
total quantity that producers can
supply to the market.
449
Chapter Ten
Policy: Production Quotas
P
Original Supply
Demand
QMAX Q*
Q
450
Chapter Ten
Policy: Production Quotas
P
Supply with quota
Original Supply
P*
Demand
QMAX Q*
Q
451
Chapter Ten
Policy: Import Tariffs & Quotas
Definition: Tariffs are taxes levied by a
government on goods imported into the
government's own country.
Tariffs
sometimes are called duties.
Definition: An import quota is a limit
on the total number of units of a good
that can be imported into the country.
452
Chapter Ten
Import of a Good
P
A
Domestic Supply
D
Domestic Demand
Q
453
Chapter Ten
Import of a Good
P
A
Domestic Supply
P*
D
Domestic Demand
Q
454
Chapter Ten
Import of a Good
P
Domestic Supply
A
P*
PW
D
C
Q1
B
Q4
Foreign Supply
Domestic Demand
Q
455
Chapter Ten
Import of a Good – With Tariff
P
Domestic Supply
Domestic Demand
Q
456
Chapter Ten
Import of a Good – With Tariff
P
Domestic Supply
PW+T
PW
T
Domestic Demand
Q1 Q2
Q
Q3 Q4
457
Chapter Ten
Import of a Good – With Tariff
P
Domestic Supply
PW+T
PW D
A C
B
T
Domestic Demand
Q1 Q2
Q
Q3 Q4
458
Chapter Ten
Comparing a Tariff to a Quota
Let quota limit imports to Q3-Q2…the equilibrium
price would be the same as for the tariff…and the
(world) deadweight loss would be the same as well.
Is there a difference? The quota generates no
government revenue. Hence, while the total supply
and total price for the domestic market remains the
same under the two policies, domestic deadweight
loss is larger under the quota.
459
Chapter Ten
Chapter Eleven
Monopoly
&
Monopsony
460
Chapter Eleven
Chapter Eleven Overview
1. Introduction: Brush Wellman
2. The Monopolist’s Profit Maximization Problem
•
•
•
The Profit Maximization Condition
Equilibrium
The Inverse Pricing Elasticity Rule
3. Multi-plant Monopoly and Cartel Production
4. The Welfare Economics and Monopoly
461
Chapter Eleven
A Monopoly
Definition: A Monopoly Market consists of a
single seller facing many buyers.
The monopolist's profit maximization problem:
Max (Q) = TR(Q) - TC(Q) Q
where: TR(Q) = QP(Q) and P(Q) is the (inverse)
market demand curve.
462
Chapter Eleven
A Monopoly – Profit Maximizing
Profit maximizing condition for a monopolist:
TR(Q)/Q = TC(Q)/Q
MR(Q) = MC(Q)
The monopolist sets output so that marginal profit of
additional production is just zero.
Recall:
A perfect competitor sets P = MC…in other words,
marginal revenue equals price.
463
Chapter Eleven
A Monopoly – Profit Maximizing
Why is this not so for the monopolist?
TR = P1Q + Q0P =>
TR(Q0)/Q = P1 + Q0P/Q = MR(Q0)
and, as we let the change in output get very small, this approaches:
• MR(Q0) = P0 + Q0P/Q
• MR(Q0) < P0 for any Q0 > 0
• MR may be negative or positive for a perfect competitor, demand
was "flat" so MR = P
464
Chapter Eleven
Marginal Revenue
Price
Price
Competitive Firm
Monopolist
Demand facing firm
P0
Demand facing firm
P0
P1
A
B
q q+1
C
A
Firm output
B
Q0 Q0+1 Firm output
465
Chapter Eleven
Marginal Revenue Curve and Demand
Price
The MR curve lies below the demand curve.
P(Q0)
P(Q), the (inverse) demand curve
MR(Q0)
MR(Q), the marginal revenue curve
Quantity
Q0
Chapter Eleven
466
Market Power
Definition: An agent has Market Power if
s/he can affect, through his/her own
actions, the price that prevails in the
market. Sometimes this is thought of as
the degree to which a firm can raise price
above marginal cost.
467
Chapter Eleven
Market Power
P(Q) = a - bQ & linear demand
TR(Q) = QP(Q)
What is the equation of the marginal revenue curve?
P/Q = -b
MR(Q) = P + QP/Q = a - bQ + Q(-b) = a - 2bQ
twice the slope of demand for linear demand
468
Chapter Eleven
Market Power
What is the equation of the average
revenue curve?
AR(Q) = TR(Q)/Q = P = a - bQ
(you earn more on the average unit
than on an additional unit)
469
Chapter Eleven
Market Power
What is the profit-maximizing output if:
TC(Q) = 100 + 20Q + Q2
MC(Q) = 20 + 2Q
AVC(Q) = 20 + Q
AC(Q) = 100/Q + 20 + Q
P(Q) = 100 - Q
MR = MC => 100 - 2Q = 20 + 2Q
Q* = 20
P* = 80
470
Chapter Eleven
Shutdown Condition
In the short run, the monopolist shuts down if
the most profitable price does not cover AVC
(or average non-sunk costs). In the long run,
the monopolist shuts down if the most
profitable price does not cover AC. Here, P*
exceeds both AVC and AC.
* = 700 (= Q*P* - 100 - 20(Q*) - Q*2)
471
Chapter Eleven
Positive Profits for Monopolist
This profit is positive. Why? Because the
monopolist takes into account the pricereducing effect of increased output so that the
monopolist has less incentive to increase
output than the perfect competitor.
Profit can remain positive in the long run.
Why? Because we are assuming that there is
no possible entry in this industry, so profits
are not competed away.
472
Chapter Eleven
Positive Profits for Monopolist
Price
MC
100
AVC
80
MR
20
Demand Curve
20
50
Chapter Eleven
Quantity
473
Positive Profits for Monopolist
Price
MC
100
AVC
e
80
MR
20
Demand Curve
20
50
Chapter Eleven
Quantity
474
Positive Profits for Monopolist
Price
MC
100
AVC
e
80
AC
MR
20
Demand Curve
20
50
Chapter Eleven
Quantity
475
Equilibrium
A monopolist does not have a supply curve
(i.e., an optimal output for any exogenouslygiven price) because price is endogenouslydetermined by demand: the monopolist picks
a preferred point on the demand curve.
One could also think of the monopolist
choosing output to maximize profits subject
to the constraint that price be determined by
the demand curve.
476
Chapter Eleven
Inverse Elasticity Pricing Rule
We can rewrite the MR curve as follows:
MR = P + QP/Q
= P(1 + (Q/P)(P/Q))
= P(1 + 1/)
where:  is the price elasticity of demand, (P/Q)(Q/P)
477
Chapter Eleven
Inverse Elasticity Pricing Rule
Using this formula:
• When demand is elastic ( < -1), MR > 0
• When demand is inelastic ( > -1), MR < 0
• When demand is unit elastic ( = -1), MR= 0
478
Chapter Eleven
Elasticity Region of the Demand Curve
Price
a
Elastic region ( < -1), MR > 0
Unit elastic (=-1), MR=0
Inelastic region (0>>-1), MR<0
a/2b
a/b
Chapter Eleven
Quantity
479
Elasticity Region of the Demand Curve
Therefore:
The monopolist will always operate on the elastic region
of the market demand curve As demand becomes more
elastic at each point, marginal revenue approaches price
Example A:
QD = 100P-2
MC = $50
What is the monopolist's optimal price?
MR = MC  P(1+1/) = MC 
P(1+1/(-2)) = 50
P* = 100
480
Chapter Eleven
Elasticity Region of the Demand Curve
Example B:
Now, suppose that QD = 100P-b and MC = c (constant).
What is the monopolist's optimal price now?
P(1+1/-b) = c
P* = cb/(b-1)
We need the assumption that b > 1 ("demand is
everywhere elastic") to get an interior solution.
As b -> 1 (demand becomes everywhere less elastic), P*
-> infinity and P - MC, the "price-cost margin" also
increases to infinity.
As b -> , the monopoly price approaches marginal cost.
481
Chapter Eleven
The Lerner Index of Market Power
Definition: the Lerner Index of
market power is the price-cost
margin, (P*-MC)/P*.
This index
ranges between 0 (for the competitive
firm) and 1, for a monopolist facing a
unit elastic demand.
482
Chapter Eleven
The Lerner Index of Market Power
Restating the monopolist's profit maximization
condition, we have:
P*(1 + 1/) = MC(Q*) …or…
[P* - MC(Q*)]/P* = -1/
In words, the monopolist's ability to price above
marginal cost depends on the elasticity of demand.
483
Chapter Eleven
Multi-Plant Monopoly
Recall:
• In the perfectly competitive model, we could
derive firm outputs that varied depending on the
cost characteristics of the firms. The analogous
problem here is to derive how a monopolist
would allocate production across the plants
under its management.
Assume:
• The monopolist has two plants: one plant has
marginal cost MC1(Q) and the other has
marginal cost MC2(Q).
484
Chapter Eleven
Multi-Plant Monopoly – Production Allocation
Whenever the marginal costs of the two plants are not
equal, the firm can increase profits by reallocating
production towards the lower marginal cost plant and
away from the higher marginal cost plant.
Example:
Suppose the monopolist wishes to produce 6 units
3 units per plant =>
• MC1 = $6
• MC2 = $3
Reducing plant 1's units and increasing plant 2's units
raises profits
485
Chapter Eleven
Multi-Plant Monopoly – Production Allocation
Price
MC1
MCT
6
•
Example: Multi-Plant Monopolist
This is analogous to exit by higher
cost firms and an increase in entry
by low-cost firms in the perfectly
competitive model.
3
3
6
9
Chapter Eleven
Quantity
486
Multi-Plant Monopoly – Production Allocation
Price
MC2
MC1
MCT
6
3
•
Example: Multi-Plant Monopolist
This is analogous to exit by higher
cost firms and an increase in entry
by low-cost firms in the perfectly
competitive model.
•
3
6
9
Chapter Eleven
Quantity
487
Multi-Plant Marginal Costs Curve
Question: How much should the monopolist produce in total?
Definition: The Multi-Plant Marginal Cost Curve traces out
the set of points generated when the marginal cost curves of the
individual plants are horizontally summed (i.e. this curve shows
the total output that can be produced at every level of marginal
cost.)
Example:
For MC1 = $6, Q1 = 3
MC2 = $6, Q2 = 6
Therefore, for MCT = $6, QT = Q1 + Q2 = 9
488
Chapter Eleven
Multi-Plant Marginal Costs Curve
The profit maximization condition that
determines optimal total output is now:
• MR = MCT
The marginal cost of a change in output
for the monopolist is the change after all
optimal adjustment has occurred in the
distribution of production across plants.
489
Chapter Eleven
Multi-Plant Monopolistic Maximization
Price
MC1
MC2
MCT
P*
MR
Chapter Eleven
Quantity
490
Multi-Plant Monopolistic Maximization
Price
MC1
MC2
MCT
P*
Demand
Q*1 Q*2
Q*T
MR
Chapter Eleven
Quantity
491
Multi-Plant Monopolistic Maximization
Example:
P = 120 - 3Q …demand…
MC1 = 10 + 20Q1 …plant 1…
MC2 = 60 + 5Q2 …plant 2…
What are the monopolist's optimal total
quantity and price?
Step 1: Derive MCT as the horizontal
sum of MC1 and MC2. Inverting
marginal cost (to get Q as a function of
MC), we have:
Q1 = -1/2 + (1/20)MCT
Q2 = -12 + (1/5)MCT
492
Chapter Eleven
Multi-Plant Monopolistic Maximization
Let MCT equal the common marginal cost level in the
two plants. Then:
• QT = Q1 + Q2 = -12.5 + .25MCT
And, writing this as MCT as a function of QT:
• MCT = 50 + 4QT
Using the monopolist's profit maximization condition:
• MR = MCT => 120 - 6QT = 50 + 4QT
• QT* = 7
• P* = 120 - 3(7) = 99
493
Chapter Eleven
Multi-Plant Monopolistic Maximization
Example:
P = 120 - 3Q …demand…
MC1 = 10 + 20Q1 …plant 1…
MC2 = 60 + 5Q2 …plant 2…
What is the optimal division of output
across the monopolist's plants?
MCT* = 50 + 4(7) = 78
Therefore,
Q1* = -1/2 + (1/20)(78) = 3.4
Q2* = -12 + (1/5)(78) = 3.6
494
Chapter Eleven
Cartel
Definition: A cartel is a group
of firms that collusively
determine the price and output
in a market. In other words, a
cartel acts as a single monopoly
firm that maximizes total
industry profit.
495
Chapter Eleven
Cartel
The problem of optimally allocating output
across cartel members is identical to the
monopolist's problem of allocating output
across individual plants.
Therefore, a cartel does not necessarily
divide up market shares equally among
members: higher marginal cost firms
produce less.
This gives us a benchmark against which
we can compare actual industry and firm
output to see how far the industry is from
the collusive equilibrium
496
Chapter Eleven
The Welfare Economies of Monopoly
Since the monopoly equilibrium output
does not, in general, correspond to the
perfectly competitive equilibrium it
entails a dead-weight loss.
Suppose that we compare a monopolist
to a competitive market, where the
supply curve of the competitors is equal
to the marginal cost curve of the
monopolist
497
Chapter Eleven
The Welfare Economies of Monopoly
CS with competition: A+B+C CS with monopoly: A
PS with competition: D+E PS with monopoly:B+D
A
MC
PM
B
PC
DWL = C+E
C
E
D
Demand
QM
MR
QC
Chapter Eleven
498
Natural Monopolies
Dead-weight loss in a Natural Monopoly Market
Definition: A market is a natural monopoly if the
total cost incurred by a single firm producing output
is less than the combined total cost of two or more
firms producing this same level of output among
them.
Benchmark: What would be the market outcome if
the monopolist produced according to the same rule
as a perfect competitor (i.e., P = MC)?
499
Chapter Eleven
Natural Monopolies
Price
Demand
Quantity
Chapter Eleven
500
Natural Monopolies
Price
Natural Monopoly
falling average costs
AC
Demand
Quantity
Chapter Eleven
501
Natural Monopolies
P = MC cannot be the appropriate
benchmark here to calculate deadweight
loss due to monopoly…P = AC may be a
better benchmark. For small outputs,
this is a natural monopoly – for large
outputs, it is not.
P = MC is the appropriate benchmark
for these types of natural monopolies.
502
Chapter Eleven
Natural Monopolies – With Rising Average Cost
Price
AC
1.2
4.5
12
Chapter Eleven
Demand
Quantity
503
Natural Monopolies – With Rising Average Cost
Price
1.4
1.2
1
4.5
6
9
12
Chapter Eleven
Demand
Quantity
504
Natural Monopolies – With Rising Average Cost
Price
1.4
1.2
1
AC
4.5
6
9
12 Demand
Chapter Eleven
Quantity
505
Chapter Twelve
Capturing
Surplus
506
Chapter Twelve
Chapter Twelve Overview
1. Introduction: Airline Tickets
2. Price Discrimination
• First Degree
• Second Degree
• Third Degree
3. Tie-in Sales
• Requirements Tie-ins
• Package Tie-ins (Bundling)
507
Chapter Twelve
Airline Ticket Prices
Ticket Price
Number of
Passengers
 $2000
18
Average
Advance
Purchase
12 days
$1000-$1999
15
14 days
$800-$999
23
32 days
$600-$799
49
46 days
$400-$599
23
65 days
$200-$399
23
35 days
$1-$199
34
26 days
$0
19
508
Chapter Twelve
Uniform Price Vs. Price Discrimination
Definition: A monopolist charges a uniform price if
it sets the same price for every unit of output sold.
While the monopolist captures profits due to an
optimal uniform pricing policy, it does not receive the
consumer surplus or dead-weight loss associated with
this policy.
The monopolist can overcome this by charging more
than one price for its product.
Definition: A monopolist price discriminates if it
charges more than one price for its output.
509
Chapter Twelve
Uniform Price Vs. Price Discrimination
Price
Uniform Price Monopoly 1st Degree P.D. Monopoly
MC
MR
D
Quantity
Chapter Twelve
510
Uniform Price Vs. Price Discrimination
Uniform Price Monopoly 1st Degree P.D. Monopoly
Price
CS: E+F
PS: G+H+K+L
TS: E+F+G+H+K+L
DWL: J+N
0
E+F+G+H+J+K+L+N
E+G+G+H+J+K+L+N
0
PU E F
H
G
P1
K
MC
J
N
L
MR
D
Quantity
Chapter Twelve
511
Forms of Price Discrimination
Definition: A policy of first degree (or
perfect) price discrimination prices
each unit sold at the consumer's
maximum willingness to pay. This
willingness to pay is directly
observable by the monopolist.
Definition: The consumer's maximum
willingness to pay is called the
consumer's reservation price.
512
Chapter Twelve
“Willingness to Pay” Curve
Think of the demand curve as a
"willingness to pay" curve. If the
monopolist can observe the willingness
to pay of each customer (based on, for
example, residence, education, "look",
etc), then the monopolist can observe
demand perfectly and can "perfectly"
price discriminate.
513
Chapter Twelve
Is it Reasonable?
The monopolist will continue selling units until the
reservation price exactly equals marginal cost.
Therefore, a perfectly price discriminating
monopolist will produce and sell the efficient
quantity of output.
Note: Only if the monopolist can prevent resale
can the monopolist capture the entire surplus.
514
Chapter Twelve
Pricing Surplus – Monopoly
MC = 2
P = 20 - Q
What is producer surplus if uniform pricing is followed?
MR = P + (P/Q)Q = 20 - Q - Q = 20 - 2Q
MR = MC => 20 - 2Q = 2 =>
Q* = 9
P* = 11
PS= Revenue-TVC = PQ-2Q = 11(9)-2(9) = 81
515
Chapter Twelve
Pricing Surplus – Monopoly
What will producer surplus be if the
monopolist perfectly price discriminates?
P = MC => 20 - Q = 2 =>Q* = 18
Revenue - TVC = [18(20-2)(1/2) + 18(2)]18(2) = 162
This is a gain in captured surplus of 81!
516
Chapter Twelve
First Degree Price Discrimination
Price
20
11
MC
2
9
18
D
20
Quantity
MR (uniform pricing)
517
Chapter Twelve
Second Degree Price Discrimination
What is the marginal revenue curve for a perfectly price
discriminating monopolist?
When the monopolist sells an additional unit, it does not
have to reduce the price on the other units it is selling.
Therefore, MR = P. (i.e., the marginal revenue curve
equals the demand curve.)
Definition: A policy of second degree price
discrimination allows the monopolist to charge a
different price to different consumers. While different
consumers pay different prices, the reservation price of
any one consumer cannot be directly observed.
518
Chapter Twelve
Two Part Tariff
Definition: A monopolist charges a two part
tariff if it charges a per unit fee, r, plus a lump
sum fee (paid whether or not a positive number
of units is consumed), F.
This, effectively, charges demanders of a low
quantity a different average price than
demanders of a high quantity.
Example: hook-up charge plus usage fee for a
telephone, club membership, or the like.
519
Chapter Twelve
Two Part Tariff
P
100
Example:
All customers are identical and have demand
• P = 100 - QI
• MC = AC = 10
4050
10
90 100
Chapter Twelve
Q
520
Two Part Tariff
What is the optimal two-part tariff?
Two steps:
(1) maximize the benefits to the consumers by
charging r = MC = 10.
(2) capture this benefit by setting F = consumer
benefits = 4050.
521
Chapter Twelve
Two Part Tariff
Any higher usage charge would result in a deadweight loss that could not be captured by the
monopolist. Any lower usage charge would
result in selling at less than marginal cost.
In essence, the monopolist maximizes the size of
the "pie", then sets the lump sum fee so as to
capture the entire "pie" for itself.
The total surplus captured is the same as in the
case of perfect price discrimination.
522
Chapter Twelve
Block Tariff
Definition: If a consumer pays
one price for one block of output
and another price for another
block of output, the consumer
faces a block tariff
523
Chapter Twelve
Block Tariff
• P = 100 - Q
• MC = AC = 10
Let Q1 be the largest quantity for which the first
block rate applies so that p1(Q1) = 100 - Q1.
Let Q2 be the largest quantity purchased (so that the
second block rate will apply between Q1 and Q2) so
that p2(Q2) = 100 - Q2
524
Chapter Twelve
Block Tariff
Then:
 = p1(Q1)Q1 + p2(Q2)(Q2-Q1) - TC(Q2)
= (100 - Q1)Q1 + (100 - Q2)(Q2-Q1) - 10Q2
and we must choose Q1 and Q2 to maximize this profit…
MR1 = (100 - Q1) - Q1 - (100 - Q2) = 0
MR2 = (100 - Q2) - Q2 + Q1 = MC = 10
525
Chapter Twelve
Key Equations
These are two equations in two
unknowns that can be solved to obtain:
• Q1* = 30
• Q2* = 60
• P1* = 70
• P2* = 40 (a quantity discount)
526
Chapter Twelve
Block Pricing
P
100
Demand
450
70
450
40
2700
450
10
0
30
60
100 Q
527
Chapter Twelve
Block Pricing
P
100
P
100
Demand
Demand
450
70
1012.5
55
450
40
2700
450
10
0
2025
30
60
100 Q
0
Chapter Twelve
1012.5
45 MR
MC
100
Q
528
Block Pricing
If the monopolist could set a
different block price for each
customer, it would capture the same
amount of surplus as a perfectly
price discriminating monopolist.
529
Chapter Twelve
Utility Pricing
D - small
D - large
MC
Chapter Twelve
Q
530
Utility Pricing
D - small
D - large
Additional CS
P1
Additional PS
P2
MC
Q1s
Q1L Q2L
Q
531
Chapter Twelve
Third Degree Price Discrimination
Definition: A policy of third degree price
discrimination offers a different price for each
segment of the market (or each consumer group)
when membership in a segment can be observed.
Example: Movie ticket sales to older people or
students at discount
• Suppose that marginal costs for the two markets
are the same. How does a monopolist maximize
profit with this type of price discrimination?
532
Chapter Twelve
Optimal Pricing
Set the marginal revenue in each market equal to marginal
cost. (i.e., the monopolist maximizes total profits by
maximizing profits from each group individually.)
This implies that MR1 = MC = MR2 at the optimum.
Otherwise, the monopolist could raise revenues by switching
sales from the low MR group to the high MR group.
MC = AC = 20
Example
P1 = 100 - Q1
P2 = 80 - 2Q2
533
Chapter Twelve
Optimal Pricing
MR1 = 100 - 2Q1 = MC = 20
MR2 = 80 - 4Q2 = MC = 20
Q1* = 40
Q2* = 15
Example
P1* = 60
P2* = 50
534
Chapter Twelve
Third Degree Price Discrimination
P
100
Market 1
Demand 1
60
20
0
MR1
100
Q
535
Chapter Twelve
Third Degree Price Discrimination
P
P
100
Market 2
Market 1
Demand 1
80
60
Demand 2
50
20
0
MR1
100
Q
0
Chapter Twelve
20
40
MR2
Q
536
Tie-in Sales – Requirements
Definition: A tie-in sale occurs if customer can
buy one product only if they agree to purchase
another product as well.
• Requirements tie-in sales occur when a firm
requires customers who buy one product from the
firm to buy another product from the firm.
A requirements tie-in sale may be used in place
of price discrimination when the firm cannot
observe the relative willingness to pay of
different customers.
537
Chapter Twelve
Tie-in Sales – Bundling
• Package tie-in sales (or bundling) occur
when goods are combined so that customers
cannot buy either good separately.
Bundling may be used in place of price
discrimination to increase producer surplus
when consumers have different willingness to
pay for the goods sold in the bundle.
But bundling does not always pay…
538
Chapter Twelve
Tie-in Sales – Bundling
Reservation Price
Computer
Monitor
Customer 1
$1,200
$600
Customer 2
$1,500
$400
Marginal Cost $1,000
$300
539
Chapter Twelve
Tie-in Sales – Bundling
Optimal Pricing Policy
Without bundling: pc = $1500 pm = $600
• Profit cm = $800
With bundling: pb = $1800
• Profit b = $1000
540
Chapter Twelve
Tie-in Sales – Bundling
Reservation Price
Computer
Monitor
Customer 1
$1,200
$400
Customer 2
$1,500
$600
Marginal Cost $1,000
$300
541
Chapter Twelve
Tie-in Sales – Bundling
Optimal Pricing Policy
Without bundling: pc = $1500 pm = $600
• Profit cm = $800
With bundling: pb = $2100
• Profit b = $800
In general, bundling a pair of goods only pays if their
demands are negatively correlated (customers who
are willing to pay relatively more for good A are not
willing to pay as much for good B).
542
Chapter Twelve
Reservation Price
The reason is that the price is
determined by the purchaser with the
lowest reservation price.
If reservation prices for the two goods
are negatively correlated, bundling
reduces the dispersion of reservation
prices and so raises the price at which
additional units can be sold.
543
Chapter Twelve
Chapter Thirteen
Market Structure
And Competition
544
Chapter Thirteen
Chapter Thirteen Overview
1. Introduction: Cola Wars
2. A Taxonomy of Market Structures
3. Monopolistic Competition
4. Oligopoly – Interdependence of Strategic Decisions
•
Bertrand with Homogeneous and Differentiated Products
5. The Effect of a Change in the Strategic Variable
•
•
•
•
Theory vs. Observation
Cournot Equilibrium (homogeneous)
Comparison to Bertrand, Monopoly
Reconciling Bertrand, and Cournot
6. The Effect of a Change in Timing: Stackelberg Equilibrium
545
Chapter Thirteen
A Taxonomy Market Structures
• The number of sellers
• The number of buyers
• Entry conditions
• The degree of product differentiation
546
Chapter Thirteen
Product Differentiation
Definition: Product Differentiation
between two or more products exists
when the products possess attributes that,
in the minds of consumers, set the
products apart from one another and make
them less than perfect substitutes.
Examples: Pepsi is sweeter than Coke,
Brand Name batteries last longer than
"generic" batteries.
547
Chapter Thirteen
Product Differentiation
• "Superiority" (Vertical Product Differentiation)
i.e. one product is viewed as unambiguously better
than another so that, at the same price, all
consumers would buy the better product
• "Substitutability"
(Horizontal
Product
Differentiation) i.e. at the same price, some
consumers would prefer the characteristics of
product A while other consumers would prefer the
characteristics of product B.
548
Chapter Thirteen
A Taxonomy Market Structures
Approach
Degree of
Product
Differentiation
Firms produce
identical
products
Firms produce
differentiated
products
Many
Few
One
Dominant
One
Perfect
Oligopoly with Dominant
Monopoly
Competition homogeneous firm
products
Monopolistic Oligopoly with
Competition differentiated
----------------------products
549
Chapter Thirteen
Chamberlinian Monopolistic Competition
Market Structure
• Many Buyers
• Many Sellers
• Free entry and Exit
• (Horizontal) Product Differentiation
When firms have horizontally differentiated
products, they each face downward-sloping
demand for their product because a small
change in price will not cause ALL buyers to
switch to another firm's product.
550
Chapter Thirteen
Monopolistic Competition – Short Run
1. Each firm is small each takes the observed "market
price" as given in its production decisions.
2. Since market price may not stay given, the firm's
perceived demand may differ from its actual demand.
3.If all firms' prices fall the same amount, no
customers switch supplier but the total market
consumption grows.
4. If only one firm's price falls, it steals customers
from other firms as well as increases total market
consumption
551
Chapter Thirteen
Perceived vs. Actual Demand
Price
d (PA=20)
Quantity
552
Chapter Thirteen
Perceived vs. Actual Demand
Price
Demand assuming no price matching
d (PA=50)
d (PA=20)
Quantity
553
Chapter Thirteen
Perceived vs. Actual Demand
Price
Demand (assuming price matching by all firms)
50
•
Demand assuming no price matching
d (PA=50)
d (PA=20)
Quantity
554
Chapter Thirteen
Market Equilibrium
The market is in equilibrium if:
• Each firm maximizes profit taking
the average market price as given
• Each firm can sell the quantity it
desires at the actual average market
price that prevails
555
Chapter Thirteen
Short Run Chamberlinian Equilibrium
Price
d(PA=43)
Quantity
Chapter Thirteen
556
Short Run Chamberlinian Equilibrium
Price
Demand assuming no price
matching
d (PA=50)
d(PA=43)
Quantity
Chapter Thirteen
557
Short Run Chamberlinian Equilibrium
Price
Demand (assuming price matching by all firms P=PA)
•
•
Demand assuming no price
matching
d (PA=50)
d(PA=43)
Quantity
Chapter Thirteen
558
Short Run Chamberlinian Equilibrium
Price
Demand (assuming price matching by all firms P=PA)
50
43
•
•
15
Demand assuming no price
matching
mc
57
d (PA=50)
d(PA=43)
Quantity
MR43
Chapter Thirteen
559
Short Run Monopolistically Competitive Equilibrium
Computing Short Run
Monopolistically Competitive Equilibrium
• MC = $15
• N = 100
• Q = 100 - 2P + PA
• Where: PA is the average market
price N is the number of firms
560
Chapter Thirteen
Short Run Monopolistically Competitive Equilibrium
A. What is the equation of d40? What is the equation of D?
• d40: Qd = 100 - 2P + 40 = 140 - 2P
• D: Note that P = PA so that
• QD = 100 - P
B. Show that d40 and D intersect at P = 40
• P = 40 => Qd = 140 - 80 = 60
QD = 100 - 40 = 60
C. For any given average price, PA, find a typical firm's profit
maximizing quantity
561
Chapter Thirteen
Inverse Perceived Demand
P = 50 - (1/2)Q + (1/2)PA
MR = 50 - Q + (1/2)PA
MR = MC => 50 - Q + (1/2)PA = 15
Qe = 35 + (1/2)PA
Pe = 50 - (1/2)Qe + (1/2)PA
Pe = 32.5 + (1/4)PA
562
Chapter Thirteen
Short Run Monopolistically Competitive Equilibrium
D. What is the short run equilibrium
price in this industry?
In equilibrium, Qe = QD at PA so that
100 - PA = 35 + (1/2)PA
PA = 43.33
Qe = 56.66
QD = 56.66
563
Chapter Thirteen
Monopolistic Competition in the Long Run
At the short run equilibrium P > AC so that
each firm may make positive profit.
Entry shifts d and D left until average
industry price equals average cost.
This is long run equilibrium is represented
graphically by:
MR = MC for each firm
D = d at the average market price
d and AC are tangent at average market price
564
Chapter Thirteen
Long Run Chamberlinian Equilibrium
Price
Residual Demand shifts
in as entry occurs
P*
Marginal Cost
P**
Average Cost
q**
q*
MR
Chapter Thirteen
Quantity
565
Oligopoly
Assumptions:
• Many Buyers and Few Sellers
• Each firm faces downward-sloping
demand because each is a large producer
compared to the total market size
• There is no one dominant model of
oligopoly. We will review several.
566
Chapter Thirteen
Bertrand Oligopoly (homogeneous)
Assumptions:
• Firms set price*
• Homogeneous product
• Simultaneous
• Non-cooperative
*Definition: In a Bertrand
oligopoly, each firm sets its
price, taking as given the
price(s) set by other firm(s),
so as to maximize profits.
567
Chapter Thirteen
Simultaneously vs. Non-cooperatively
Definition: Firms act simultaneously if
each firm makes its strategic decision at the
same time, without prior observation of the
other firm's decision.
Definition: Firms act non-cooperatively if
they set strategy independently, without
colluding with the other firm in any way
568
Chapter Thirteen
Setting Price
• Homogeneity implies that consumers will
buy from the low-price seller.
• Further, each firm realizes that the demand
that it faces depends both on its own price
and on the price set by other firms
• Specifically, any firm charging a higher
price than its rivals will sell no output.
• Any firm charging a lower price than its
rivals will obtain the entire market demand.
569
Chapter Thirteen
Residual Demand
Definition: The relationship between the
price charged by firm i and the demand
firm i faces is firm is residual demand
In other words, the residual demand of
firm i is the market demand minus the
amount of demand fulfilled by other
firms in the market: Q1 = Q - Q2
570
Chapter Thirteen
Residual Demand Curve – Price Setting
Price
Market Demand
Residual Demand Curve
•
(thickened line segments)
Quantity
0
571
Chapter Thirteen
Residual Demand Curve – Price Setting
• Assume firm always meets its residual demand (no
capacity constraints)
• Assume that marginal cost is constant at c per unit.
• Hence, any price at least equal to c ensures nonnegative profits.
572
Chapter Thirteen
Price Setting – Homogeneous Products
Reaction Function of Firm 1
Price charged
by firm 2
45° line
Reaction Function of Firm 2
p2*
•
Price charged by firm 1
0
p1*
573
Chapter Thirteen
Best Response Function
Thus, each firm's profit maximizing response to the
other firm's price is to undercut (as long as P > MC)
Definition: The firm's profit maximizing action as a
function of the action by the rival firm is the firm's
best response (or reaction) function
Example:
2 firms
Bertrand competitors
Firm 1's best response function is P1=P2- e
Firm 2's best response function is P2=P1- e
574
Chapter Thirteen
Equilibrium
If we assume no capacity constraints and
that all firms have the same constant
average and marginal cost of c then:
For each firm's response to be a best
response to the other's each firm must
undercut the other as long as P> MC
Where does this stop? P = MC (!)
575
Chapter Thirteen
Equilibrium
1. Firms price at marginal cost
2. Firms make zero profits
3. The number of firms is irrelevant to the price
level as long as more than one firm is present: two
firms is enough to replicate the perfectly
competitive outcome.
Essentially, the assumption of no capacity
constraints combined with a constant average and
marginal cost takes the place of free entry.
576
Chapter Thirteen
Bertrand Competition – Differentiated
Assumptions:
Firms set price*
Differentiated product
Simultaneous
Non-cooperative
*As before, differentiation means that
lowering price below your rivals' will not
result in capturing the entire market, nor will
raising price mean losing the entire market so
that residual demand decreases smoothly
577
Chapter Thirteen
Bertrand Competition – Differentiated
Q1 = 100 - 2P1 + P2 "Coke's demand"
Q2 = 100 - 2P2 + P1 "Pepsi's demand"
MC1 = MC2 = 5
What is firm 1's residual demand when
Firm 2's price is $10? $0?
Q110 = 100 - 2P1 + 10 = 110 - 2P1
Q10 = 100 - 2P1 + 0 = 100 - 2P1
578
Chapter Thirteen
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Coke’s
Price
100
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Pepsi’s price = $0 for D0 and $10 for D10
MR0
0
Coke’s Quantity
Chapter Thirteen
579
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Coke’s
Price
110
100
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Pepsi’s price = $0 for D0 and $10 for D10
D10
D0
0
Coke’s Quantity
Chapter Thirteen
580
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Coke’s
Price
110
100
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Pepsi’s price = $0 for D0 and $10 for D10
MR10
0
MR0
D10
D0
Coke’s Quantity
Chapter Thirteen
581
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Coke’s
Price
110
100
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Pepsi’s price = $0 for D0 and $10 for D10
D10
5
0
MR10
MR0
D0
Coke’s Quantity
Chapter Thirteen
582
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Coke’s
Price
110
100
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Pepsi’s price = $0 for D0 and $10 for D10
30
27.5
D10
MR10
5
0
45
50 MR0
D0
Coke’s Quantity
Chapter Thirteen
583
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Example:
MR110 = 55 - Q110 = 5
Q110 = 50
P110 = 30
Therefore, firm 1's best response to a price of
$10 by firm 2 is a price of $30
584
Chapter Thirteen
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
Example:
• Solving for firm 1's reaction function for
any arbitrary price by firm 2
P1 = 50 - Q1/2 + P2/2
MR = 50 - Q1 + P2/2
MR = MC => Q1 = 45 + P2/2
585
Chapter Thirteen
Key Concepts
Residual Demand, Price Setting, Differentiated Products
Each firm maximizes profits based on its residual demand by
setting MR (based on residual demand) = MC
And, using the demand curve, we have:
• P1 = 50 + P2/2 - 45/2 - P2/4 or
• P1 = 27.5 + P2/4 the reaction function
586
Chapter Thirteen
Equilibrium and Reaction Functions
Pepsi’s
Price (P2)
Price Setting and Differentiated Products
P2 = 27.5 + P1/4
(Pepsi’s R.F.)
27.5
Coke’s
Price (P1)
587
Chapter Thirteen
Equilibrium and Reaction Functions
Pepsi’s
Price (P2)
Price Setting and Differentiated Products
P1 = 27.5 + P2/4
(Coke’s R.F.)
P2 = 27.5 + P1/4
(Pepsi’s R.F.)
•
27.5
27.5
P1 = 110/3
Coke’s
Price (P1)
588
Chapter Thirteen
Equilibrium and Reaction Functions
Pepsi’s
Price (P2)
P2 =
110/3
Price Setting and Differentiated Products
P1 = 27.5 + P2/4
(Coke’s R.F.)
Bertrand
Equilibrium
P2 = 27.5 + P1/4
(Pepsi’s R.F.)
•
27.5
27.5
P1 = 110/3
Coke’s
Price (P1)
589
Chapter Thirteen
Equilibrium
Equilibrium occurs when all
firms simultaneously choose
their best response to each
others' actions.
Graphically, this amounts to
the point where the best
response functions cross.
590
Chapter Thirteen
Equilibrium
Example: Firm 1 and Firm 2, continued
• P1 = 27.5 + P2/4
• P2 = 27.5 + P1/4
Solving these two equations in two unknowns.
• P1* = P2* = 110/3
Plugging these prices into demand, we have:
• Q1* = Q2* = 190/3
• 1* = 2* = 2005.55
•  = 4011.10
591
Chapter Thirteen
Equilibrium
Profits are positive in equilibrium since
both prices are above marginal cost!
Even if we have no capacity constraints,
and constant marginal cost, a firm cannot
capture all demand by cutting price.
This blunts price-cutting incentives and
means that the firms' own behavior does
not mimic free entry
592
Chapter Thirteen
Equilibrium
Only if I were to let the number of firms
approach infinity would price approach
marginal cost.
Prices need not be equal in equilibrium if
firms not identical (e.g. Marginal costs
differ implies that prices differ)
The reaction functions slope upward:
"aggression => aggression"
593
Chapter Thirteen
Theory vs. Observation
US Manufacturing
Industries
CR8
>70
<70
Average Profit Rate
12.1%
6.9%
Source: Bain, Joe S., "Relation of Profit Rate to Industry
Concentration: American Manufacturing, 1936-1940,"
Quarterly Journal of Economics, v. 65 (August 1951), pp.
293-324 and Barriers to New Competition (Cambridge:
Harvard University Press, 1956).
594
Chapter Thirteen
Cournot Oligopoly
Assumptions
• Firms set outputs (quantities)*
• Homogeneous Products
• Simultaneous
• Non-cooperative
*Definition: In a Cournot game, each firm sets its output
(quantity) taking as given the output level of its competitor(s),
so as to maximize profits.
Price adjusts according to demand.
Recall our reasoning from the Bertrand case…
Residual Demand: Firm i's guess about its rival's output
determines its residual demand.
595
Chapter Thirteen
Residual Demand
Price
10 units
Residual Marginal Revenue when q2 = 10
Residual Demand when q2 = 10
MC
Demand
0
Quantity
q1*
596
Chapter Thirteen
Profit Maximization
Profit Maximization: Each firm acts as a
monopolist on its residual demand curve,
equating MRR to MC.
MRR = p + q1(p/q) = MC
Best Response Function:
The point where (residual) marginal revenue equals marginal cost
gives the best response of firm i to its rival's (rivals') actions.
For every possible output of the rival(s), we can determine firm i's
best response. The sum of all these points makes up the best
response (reaction) function of firm i.
597
Chapter Thirteen
Profit Maximization
q2
Example: Reaction Functions, Quantity Setting
Reaction Function of Firm 1
0
q1
Chapter Thirteen
598
Profit Maximization
q2
Example: Reaction Functions, Quantity Setting
Reaction Function of Firm 1
q2*
0
•
q1*
Reaction Function of Firm 2
q1
Chapter Thirteen
599
Equilibrium
Equilibrium: No firm has an incentive to deviate in equilibrium in
the sense that each firm is maximizing profits given its rival's output
Example A:
P = 100 - Q1 - Q2
MC = AC = 10
What is firm 1's profit-maximizing
output when firm 2 produces 50?
Firm 1's residual demand:
• P = (100 - 50) - Q1
• MR50 = 50 - 2Q1
• MR50 = MC  50 - 2Q1 = 10
• Q150 = 20
600
Chapter Thirteen
Profit Maximization
Example B:
What is the equation of firm 1's reaction function?
Firm 1's residual demand:
• P = (100 - Q2) - Q1
• MRr = 100 - Q2 - 2Q1
• MRr = MC  100 - Q2 - 2Q1 = 10
• Q1r = 45 - Q2/2 firm 1's reaction function
601
Chapter Thirteen
Profit Maximization
Example C:
Similarly, one can compute that Q2r = 45 - Q1/2.
Now, calculate the Cournot equilibrium.
• Q1 = 45 - (45 - Q1/2)/2
• Q1* = 30
• Q2* = 30
• P* = 40
• 1* = 2* = 30(30) = 900
602
Chapter Thirteen
Cournot, Bertrand, and Monopoly Equilibriums
P > MC for Cournot competitors, but P < PM:
If the firms were to act as a monopolist (perfectly
collude), they would set market MR equal to MC:
• P = 100 - Q
• MC = AC = 10
• MR = MC => 100 - 2Q = 10 => QM = 45
• PM = 55
• M= 45(45) = 2025
• c = 1800
603
Chapter Thirteen
Cournot, Bertrand, and Monopoly Equilibriums
A perfectly collusive industry takes into account that an increase in
output by one firm depresses the profits of the other firm(s) in the
industry. A Cournot competitor takes into account the effect of the
increase in output on its own profits only.
Therefore, Cournot competitors "overproduce" relative to the collusive
(monopoly) point. Further, this problem gets "worse" as the number of
competitors grows because the market share of each individual firm
falls, increasing the difference between the private gain from increasing
production and the profit destruction effect on rivals.
Therefore, the more concentrated the industry in the Cournot case, the
higher the price-cost margin.
604
Chapter Thirteen
Cournot, Bertrand, and Monopoly Equilibriums
Homogeneous product Bertrand resulted in
zero profits, whereas the Cournot case resulted
in positive profits. Why?
The best response functions in the Cournot
model slope downward. In other words, the
more aggressive a rival (in terms of output), the
more passive the Cournot firm's response.
The best response functions in the Bertrand
model slope upward. In other words, the more
aggressive a rival (in terms of price) the more
aggressive the Bertrand firm's response.
605
Chapter Thirteen
Cournot, Bertrand, and Monopoly Equilibriums
Cournot: Suppose firm j raises its
output…the price at which firm i can sell
output falls. This means that the incentive
to increase output falls as the output of the
competitor rises.
Bertrand: Suppose firm j raises price the
price at which firm i can sell output rises.
As long as firm's price is less than firm's,
the incentive to increase price will depend
on the (market) marginal revenue.
606
Chapter Thirteen
Cournot, Bertrand, and Monopoly Equilibriums
What if one firm moves before the other?
Call the first mover the “leader” and the second
mover the “follower”. Let both firms choose
quantities once and for all.
The second firm is in the same situation as a
Cournot firm: it takes the leader’s output as
given and maximizes profits accordingly, using
its residual demand.
The second firm’s behavior can, then, be
summarized by a Cournot reaction function.
607
Chapter Thirteen
Stackelberg Equilibrium vs. Cournot
q2
A
Profit for firm 1 at A…0
at B…0
at C…1012.5
at Cournot Eq…900
•
Former Cournot Equilibrium
•
•
C
B
(q1= 90)
•
Chapter Thirteen
Follower’s Cournot
Reaction Function
q1
608
Summary
1. Market structures are characterized by the number of
buyers, the number of sellers, the degree of product
differentiation and the entry conditions.
2. Product differentiation alone or a small number of
competitors alone is not enough to destroy the long run
zero profit result of perfect competition. This was
illustrated with the Chamberlinian and Bertrand models.
3. Chamberlinian) monopolistic competition assumes
that there are many buyers, many sellers, differentiated
products and free entry in the long run.
609
Chapter Thirteen
Summary
4. Chamberlinian sellers face downward-sloping demand but are
price takers (i.e. they do not perceive that their change in price will
affect the average price level). Profits may be positive in the short
run but free entry drives profits to zero in the long run.
5. Bertrand and Cournot competition assume that there are many
buyers, few sellers, and homogeneous or differentiated products.
Firms compete in price in Bertrand oligopoly and in quantity in
Cournot oligopoly.
6. Bertrand and Cournot competitors take into account their strategic
interdependence by means of constructing a best response schedule:
each firm maximizes profits given the rival's strategy.
610
Chapter Thirteen
Summary
7. Equilibrium in such a setting requires that all firms be on
their best response functions.
8. If the products are homogeneous, the Bertrand equilibrium
results in zero profits. By changing the strategic variable from
price to quantity, we obtain much higher prices (and profits).
Further, the results are sensitive to the assumption of
simultaneous moves.
9. This result can be traced to the slope of the reaction
functions: upwards in the case of Bertrand and downwards in
the case of Cournot. These slopes imply that "aggressivity"
results in a "passive" response in the Cournot case and an
"aggressive" response in the Bertrand case.
611
Chapter Thirteen
Chapter Fourteen
Game Theory and
Strategic Behavior
612
Chapter Fourteen
Chapter Fourteen Overview
1. Motivation: Honda and Toyota
2. Nash Equilibrium
3. The Prisoner's Dilemma
4. Dominant Strategy Equilibrium
5. Limitations of the Nash Equilibrium
6. Sequential Moves Games
• The Value of Limiting One’s Opinion
613
Chapter Fourteen
Capacity Expansion Game
What is the likely outcome of this game?
Toyota
Honda
Build a new
plant
Do not Build
Build a new
plant
16,16
20,15
Do not Build
15,20
18,18
614
Chapter Fourteen
Capacity Expansion Game
Game Elements
Players: agents participating in the game (Toyota, Honda)
Strategies: Actions that each player may take under any possible
circumstance (Build, Don't build)
Outcomes: The various possible results of the game (four, each
represented by one cell of matrix)
Payoffs: The benefit that each player gets from each possible
outcome of the game (the profits entered in each cell of the matrix)
615
Chapter Fourteen
Capacity Expansion Game
Information: A full specification of who
knows what when (full information)
Timing: Who can take what decision when
and how often the game is repeated
(simultaneous, one-shot)
Solution concept of the game: "What is
the likely outcome"? (Dominant Strategy
Equilibrium, Nash Equilibrium)
616
Chapter Fourteen
Nash Equilibrium
Definition: A Nash Equilibrium occurs
when each player chooses a strategy that
gives him/her the highest payoff, given
the strategy chosen by the other player(s)
in the game. ("rational self-interest")
Toyota vs. Honda:
A Nash equilibrium: Each Firm Builds a
New Plant
617
Chapter Fourteen
Nash Equilibrium
• Given Toyota builds a new plant, Honda's
best response is to build a new plant.
• Given Honda builds a new plant, Toyota's
best response is to build a plant.
• Why is the Nash Equilibrium plausible?
• It IS "self enforcing” Even though it DOES
NOT necessarily maximise collective interest.
618
Chapter Fourteen
Prisoner's Dilemma
Definition: If a game is such that the players choose a set of
payoffs that is Pareto dominated by another set of payoffs,
the game is called a Prisoner's Dilemma.
Ron
Confess
Don't Confess
-5,-5
0,-10
Don't Confess -10,0
-1,-1
Confess
619
Chapter Fourteen
Other Considerations
Nash Equilibrium: both confess Pareto Dominant Point:
Neither confesses
Example: Bertrand and Cournot Equilibriums
Example: The Prisoner's Dilemma and Excessive Litigation
Definition: A dominant strategy is a strategy that is better
than any other strategy that a player might choose, no matter
what strategy the other player follows.
Note: When a player has a dominant strategy, that strategy will be the
player's Nash Equilibrium strategy.
620
Chapter Fourteen
Dominant Strategy Equilibrium
Definition: A Dominant Strategy Equilibrium occurs when
each player uses a dominant strategy.
Example: Game Matrix 1, Game Matrix 2
Toyota
Build a
Don’t
New Plant Build
Honda
Build a
12,4
New Plant
20,3
Don’t
Build
18,5
15,6
621
Chapter Fourteen
Dominated Strategy
Game Matrix 3: Capacity Expansion: Revisited
Honda does not have a dominant strategy, but a Nash
Equilibrium exists: Toyota builds, Honda Doesn't
Definition: A player has a dominated strategy when the
player has another strategy that gives it a higher payoff no
matter what the other player does.
Example: "Do not build" in Game Matrix 1.
Example: "Do not build" for Toyota only in Game Matrix 3.
622
Chapter Fourteen
Dominant or Dominated Strategy
Why look for dominant or dominated strategies?
A dominant strategy equilibrium is particularly
compelling as a "likely" outcome
Similarly, because dominated strategies are unlikely
to be played, these strategies can be eliminated from
consideration in more complex games. This can
make solving the game easier.
623
Chapter Fourteen
Dominated Strategy
Game Matrix 4: Dominated Strategies
Toyota
Build
Large
Build
Small
Do Not
Build
Build Large 0,0
12,8
18,9
Build Small
8,12
16,16
20,15
Do Not
Build
9,18
15,20
18,18
Honda
"Build Large" is dominated for each player
By eliminating the dominated strategies, we can reduce the game to matrix #1!
624
Chapter Fourteen
Nash Equilibrium Limitations
Game Matrix 4: Dominated Strategies Limitations of Nash Equilibrium
The Nash Equilibrium need not be unique
Slick
Luke
Swerve
Stay
Swerve
0,0
-10,10
Stay
10,-10
-100,-100
625
Chapter Fourteen
Nash Equilibrium Limitations
In the above example, Nash Equilibriums: (Swerve, Stay)
and (Stay, Swerve). Now, compare to the following case:
Sirius
Stay
Exit
Stay
-200, -200
300,0
Exit
0,300
0,0
XM
626
Chapter Fourteen
Nash Equilibrium Limitations
Example: Bank Runs
Depositor 2
Withdraw
Don't
Withdraw
Withdraw
25,25
50,0
Don't
Withdraw
0,50
110,110
Depositor 1
627
Chapter Fourteen
Nash Equilibrium Limitations
Nash Equilibrium need not exist
Example: Matching Pennies
Game Matrix 6: Non-existence of Nash Equilibrium
Player 1
Heads
Tails
Heads
1,-1
-1,1
Tails
-1,1
1,-1
628
Chapter Fourteen
Sequential Move Games – Game Tree
Definition: A game tree shows
the different strategies that each
player can follow in the game and
the order in which those
strategies get chosen.
629
Chapter Fourteen
Sequential Move Games – Game Tree
Game Tree 1: Toyota and Honda, Revisited
630
Chapter Fourteen
Sequential Move Games – Game Tree
Game trees often are solved by starting at the end of the tree and, for each
decision point, finding the optimal decision for the player at that point.
Keeps analysis manageable. Ensures optimality at each point.
The solution to the revisited game differs from that of the simultaneous
game. Why – the first mover can force second mover's hand Illustrates the
value of commitment (i.e. limiting one's own actions) rather than flexibility
Example: Irreversibility of Business Decisions in the Airline Industry.
631
Chapter Fourteen
Summary
1. Game Theory is the branch of economics concerned
with the analysis of optimal decision making when all
decision makers are presumed to be rational, and each is
attempting to anticipate the actions and reactions of the
competitors
2. A Nash Equilibrium in a game occurs when each
player chooses a strategy that gives him/her the highest
payoff, given the strategies chosen by the other players
in the game.
3. The Nash Equilibrium may be a good predictor when
it coincides with the Dominant Strategy Equilibrium.
632
Chapter Fourteen
Summary
4. When there are multiple Nash Equilibriums,
we must appeal to other concepts to choose
the "likely" outcome of the game.
5.An analysis of sequential move games
reveals that moving first in a game can have
strategic value if the first mover can gain from
making a commitment.
633
Chapter Fourteen
Chapter Fifteen
Risk and
Information
634
Chapter Fifteen
Chapter Fifteen Overview
1. Introduction: Amazon.com
2. Describing Risky Outcome – Basic Tools
•
•
•
Lotteries and Probabilities
Expected Values
Variance
3. Evaluating Risky Outcomes
•
Risk Preferences and the Utility Function
4. Avoiding and Bearing Risk
•
•
•
The Demand for Insurance and the Risk Premium
Asymmetric Information and Insurance
The Value of Information and Decision Trees
635
Chapter Fifteen
Tools for Describing Risky Outcomes
Definition: A lottery is any event with an uncertain
outcome.
Examples: Investment, Roulette, Football Game.
Definition: A probability of an outcome (of a
lottery) is the likelihood that this outcome occurs.
Example: The probability often is estimated by the
historical frequency of the outcome.
636
Chapter Fifteen
Probability Distribution
Definition: The probability distribution of the lottery depicts all
possible payoffs in the lottery and their associated probabilities.
Property:
• The probability of any particular outcome is between 0
and 1
• The sum of the probabilities of all possible outcomes
equals 1.
Definition: Probabilities that reflect subjective beliefs about risky
events are called subjective probabilities.
637
Chapter Fifteen
Probability Distribution
Probability
1
.90
.80
.70
.60
.50
.40
.30
.20
.10
0
67% chance of losing
Payoff
$25
638
Chapter Fifteen
Probability Distribution
Probability
1
.90
.80
.70
.60
.50
.40
.30
.20
.10
0
67% chance of losing
33% chance of winning
$25
$100
Payoff
639
Chapter Fifteen
Expected Value
Definition: The expected value of a lottery is a
measure of the average payoff that the lottery
will generate.
EV = Pr(A)xA + Pr(B)xB + Pr(C)xC
Where: Pr(.) is the probability of (.) A,B, and C
are the payoffs if outcome A, B or C occurs.
640
Chapter Fifteen
Expected Value
In our example lottery, which pays $25
with probability .67 and $100 with
probability 0.33, the expected value is:
EV = .67 x $25 + .33 x 100 = $50.
Notice that the expected value need not
be one of the outcomes of the lottery.
641
Chapter Fifteen
Variance & Standard Deviation
Definition: The variance of a lottery is the
average deviation between the possible
outcomes of the lottery and the expected
value of the lottery. It is a measure of the
lottery's riskiness.
Var = (A - EV)2(Pr(A)) + (B - EV)2(Pr(B))
+ (C - EV)2(Pr(C))
Definition: The standard deviation of a
lottery is the square root of the variance. It is
an alternative measure of risk
642
Chapter Fifteen
Variance & Standard Deviation
For the example lottery
The squared deviation of winning is:
• ($100 - $50)2 = 502 = 2500
The squared deviation of losing is:
• ($25 - $50)2 = 252 = 625
The variance is:
• (2500 x .33)+ (625 x .67) = 1250
643
Chapter Fifteen
Evaluating Risky Outcomes
Example: Work for IBM or Amazon.Com?
Suppose that individuals facing risky alternatives attempt
to maximize expected utility, i.e., the probability-weighted
average of the utility from each possible outcome they
face.
Note:
EV(Amazon) =
.5($4000)+.5($104,000) = $54,000
U(IBM) = U($54,000) = 230
U(Amazon) =
• .5xU($4,000) + .5xU($104,000) = .5(60) + .5(320) = 190
644
Chapter Fifteen
Evaluating Risky Outcomes
Utility
Utility function
U(104) = 320
0
4
104
Income (000 $ per year)
645
Chapter Fifteen
Evaluating Risky Outcomes
Utility
Utility function
U(104) = 320
U(54) = 230
.5u(4) + .5U(104)
= 190
U(4) = 60
0
4
54
104
Income (000 $ per year)
646
Chapter Fifteen
Risk Preferences
Notes:
• Utility as a function of yearly income only
• Diminishing marginal utility of income
Definition: The risk preferences can be classified as follows:
An individual who prefers a sure thing to a lottery with the same
expected value is risk averse
An individual who is indifferent about a sure thing or a lottery
with the same expected value is risk neutral
An individual who prefers a lottery to a sure thing that equals the
expected value of the lottery is risk loving (or risk preferring)
647
Chapter Fifteen
Risk Preferences
Suppose that an individual must decide between buying one of two stocks:
the stock of an Internet firm and the stock of a Public Utility. The values that
the shares of the stock may take (and, hence, the income from the stock, I)
and the associated probability of the stock taking each value are:
Internet firm
Public Utility
I Probability
I
$80
.3
$80
$100
.4
$100
$120
.3
$120
Probability
.1
.8
.1
648
Chapter Fifteen
Risk Preferences
Which stock should the individual buy if she has
utility function U = (100I)1/2? Which stock
should she buy if she has utility function U = I?
EU(Internet) = .3U(80) + .4U(100) + .3U(120)
EU(P.U.) = .1U(80) + .8U(100) + .1U(120)
a. U = (100I)1/2:
• U(80) = (8000)1/2 = 89.40
• U(100) = (10000)1/2 = 100
• U(120) = (12000)1/2 = 109.5
649
Chapter Fifteen
Risk Preferences
 EU(Internet) = .3(89.40)+.4(100)+.3(109.50) = 99.70
 EU(P.U.) =
.1(89.40) + .8(100) + .1(109.50) = 99.9
The individual should purchase the public utility stock
650
Chapter Fifteen
Risk Preferences
U = I:
 EU(Internet) = .3(80)+.4(100)+.3(120)=100
 EU(P.U.)
.1(80) + .8(100) + .3(120) = 100
This individual is indifferent between the two stocks.
651
Chapter Fifteen
Utility Function – Risk Averse Decision Maker
Utility
Utility function
U(100)
U(50)
U(25)
0
$25
$50
$100
Income
652
Chapter Fifteen
Utility Function – Risk Averse Decision Maker
Utility
Utility function
U(100)
U(50)
•A
U(25)
0
$25
$100
$50
Income
653
Chapter Fifteen
Utility Function – Risk Averse Decision Maker
Utility
Utility function
U1
I
0
I
Income
654
Chapter Fifteen
Utility Function – Risk Averse Decision Maker
Utility
Utility function
U2
U1
I
0
I
Income
655
Chapter Fifteen
Utility Function – Two Risk Approaches
Risk Neutral Preferences
Risk Loving Preferences
Utility
Utility
Utility Function
0
Utility Function
Income
Income
656
Chapter Fifteen
Avoiding Risk - Insurance
Utility
Risk premium = horizontal distance $17000
Utility function
U(104) = 320
U(54) = 230
E
•
.5u(4) + .5U(104)
= 190
17000
•D
U(4) = 60
0
4
37
54
104
Income (000 $ per year)
657
Chapter Fifteen
Risk Premium
Definition: The risk premium of a lottery is the necessary difference
between the expected value of a lottery and the sure thing so that the
decision maker is indifferent between the lottery and the sure thing.
pU(I1) + (1-p)U(I2) = U(pI1 + (1-p)I2 - RP)
The larger the variance of the lottery,
the larger the risk premium
658
Chapter Fifteen
Computing Risk Premium
Example: Computing a Risk Premium
• U = I1/2; p = .5
• I1 = $104,000
• I2 = $4,000
659
Chapter Fifteen
Computing Risk Premium
A. Verify that the risk premium for this lottery is approximately $17,000
.5(104,000)1/2 + .5(4,000)1/2 = (.5(104,000) + .5(4,000) - RP)1/2
$192.87 = ($54,000 - RP)1/2
$37,198 = $54,000 - RP
RP = $16,802
660
Chapter Fifteen
Computing Risk Premium
B.
Let I1 = $108,000 and I2 = $0. What is the risk premium now?
.5(108,000)1/2 + 0 = (.5(108,000) + 0 - RP)1/2
.5(108,000)1/2 = (54,000 - RP)1/2
RP = $27,000
(Risk premium rises when variance rises, EV the same…)
661
Chapter Fifteen
The Demand for Insurance
Lottery:
$50,000 if no accident (p = .95)
$40,000 if accident (1-p = .05)
(i.e. "Endowment" is that income in the good state
is 50,000 and income in the bad state is 40,000)
EV = .95($50000)+.05($40000) = $49,500
662
Chapter Fifteen
The Demand for Insurance
Insurance:
Coverage = $10,000
Price = $500
$49,500 sure thing.
Why?
In a good state, receive 50000-500 = 49500
In a bad state, receive 40000+10000-500=49500
663
Chapter Fifteen
The Demand for Insurance
If you are risk averse, you prefer to insure this way
over no insurance. Why?
Full coverage ( no risk so prefer all else equal)
Definition: A fairly priced insurance policy is one
in which the insurance premium (price) equals the
expected value of the promised payout. i.e.:
500 = .05(10,000) + .95(0)
664
Chapter Fifteen
The Supply of Insurance
Insurance company expects to break even and assumes all risk
– why would an insurance company ever offer this policy?
Definition:
Adverse Selection is
opportunism characterized by an
informed person's benefiting from
trading or otherwise contracting with
a less informed person who does not
know
about
an
unobserved
characteristic of the informed person.
665
Chapter Fifteen
Insurance & Moral Hazard
Definition: Moral Hazard is
opportunism characterized by an
informed person's taking advantage
of a less informed person through
an unobserved action.
666
Chapter Fifteen
Adverse Selection & Market Failure
Lottery:
• $50,000 if no blindness (p = .95)
• $40,000 if blindness (1-p = .05)
• EV = $49,500
(fair) insurance:
• Coverage = $10,000
• Price = $500
• $500 = .05(10,000) + .95(0)
667
Chapter Fifteen
Adverse Selection & Market Failure
Suppose that each individual's probability of
blindness differs  [0,1]. Who will buy this policy?
Now, p' = .10 so that:
EV of payout = .1(10,000) + .9(0) = $1000 while
price of policy is only $500. The insurance company
no longer breaks even.
668
Chapter Fifteen
Adverse Selection & Market Failure
Suppose we raise the price of policy to $1000.
Now, p'' = .20 so that.
EV of payout = .2(10,000) + .8(0) = $2000. So
the insurance company still does not break
even and thus the Market Fails.
669
Chapter Fifteen
Decision Trees
Definition: A decision tree is a diagram
that describes the options available to a
decision maker, as well as the risky events
that can occur at each point in time.
1.
2.
3.
4.
Decision Nodes
Chance Nodes
Probabilities
Payoffs
We analyze decision problems by working backward along the
decision tree to decide what the optimal decision would Be.
670
Chapter Fifteen
Decision Trees
671
Chapter Fifteen
Decision Trees
Steps in constructing and analyzing the tree:
1.
2.
3.
4.
5.
6.
Map out the decision and event sequence
Identify the alternatives available for each decision
Identify the possible outcomes for each risky event
Assign probabilities to the events
Identify payoffs to all the decision/event combinations
Find the optimal sequence of decisions
672
Chapter Fifteen
Perfect Information
Definition: The value of perfect
information is the increase in the
decision maker's expected payoff
when the decision maker can -- at no
cost -- obtain information that reveals
the outcome of the risky event.
673
Chapter Fifteen
Perfect Information
Example:
• Expected payoff to conducting test: $35M
• Expected payoff to not conducting test: $30M
The value of information: $5M
The value of nformation reflects the value of
being able to tailor your decisioins to the
conditions that will actually prevail in the future.
It should represent the agent's willingness to pay
for a "crystal ball".
674
Chapter Fifteen
Summary
1. We can think of risky decisions as lotteries.
2. We can think of individuals maximizing
expected utility when faced with risk.
3. Individuals differ in their attitudes towards risk:
those who prefer a sure thing are risk averse.
Those who are indifferent about risk are risk
neutral. Those who prefer risk are risk loving.
4. Insurance can help to avoid risk. The optimal
amount to insure depends on risk attitudes.
675
Chapter Fifteen
Summary
5. The provision of insurance by individuals
does not require risk lovers.
6. Adverse Selection and Moral Hazard can
cause inefficiency in insurance markets.
7. We can calculate the value of obtaining
information in order to reduce risk by
analyzing the expected payoff to eliminating
risk from a decision tree and comparing this to
the expected payoff of maintaining risk.
676
Chapter Fifteen
Chapter Sixteen
General
Equilibrium
Theory
677
Chapter Sixteen
Chapter Sixteen Overview
1. General Equilibrium – Analysis I
• Partial Equilibrium Bias
2. Efficiency and Perfect Competition
3. General Equilibrium – Analysis II
•
•
•
•
The Efficiency if Competition
The Edgeworth Box
Analysis of Allocation: A Pure Exchange Economy
Analysis of Production
678
Chapter Sixteen
Partial vs. General Equilibrium
If there are spillover effects from one
market to another, then the effects of
a change in one market on the
economy must be analyzed by
examining its effect on all markets
679
Chapter Sixteen
Partial vs. General Equilibrium
Further, many exogenous events (or
policy changes) affect many markets
simultaneously (example: discovery of a
major oil deposit that raises the income
of all citizens in an economy and so
affects equilibrium in all markets).
If we do not take into account all
markets in our equilibrium calculation,
we induce a bias in our analysis
680
Chapter Sixteen
Partial vs. General Equilibrium
Definition: General Equilibrium analysis is
the study of how equilibrium is determined in
all markets simultaneously (e.g. product
markets and labor markets).
Definition: Partial Equilibrium analysis is the
study of how equilibrium is determined in only
a single market (e.g. a single product market).
681
Chapter Sixteen
Partial vs. General Equilibrium
Example: Equilibrium in two markets
Q1D = 12 – 3p1 + p2
Q2D = 4 – 2p2 + p1
Q1s = 2 + p1
Q2s = 1 + p2
What is the general equilibrium level of
prices and output in this economy?
Market 1 equilibrium:
• 12 – 3p1 + p2 = 2 + p1
• p1 = 10/4 + p2/4
Market 2 equilibrium:
• 4 – 2p2 + p1 = 1 + p2
• p2 = 1 + p1/3
682
Chapter Sixteen
Partial vs. General Equilibrium
Substituting
condition 1 into condition 2:
4 – 2p2 + 10/4 + p2/4 = 1 + p2
• 2 = p2e
• 3 = p1e
• Q1e = 5
• Q2e = 3
683
Chapter Sixteen
Equilibrium in Two Markets
P1
Market 1
4.67
P1 = 4 + P2/3 – QD1/3
14
Chapter Sixteen
Q1
684
Equilibrium in Two Markets
P1
P1 = Q1s - 2
Market 1
4.67
2
14
Chapter Sixteen
Q1
685
Equilibrium in Two Markets
P1
P1 = Q1s - 2
Market 1
4.67
e1
•
3
2
P1 = 4 + P2/3 - Q1D/3
5
14
Chapter Sixteen
Q1
686
Equilibrium in Two Markets
P2
P2 = Q2s - 1
Market 2
Q2
1
687
Chapter Sixteen
Equilibrium in Two Markets
P2
P2 = Q2s - 1
Market 2
5.5
P2 = 4 + P1/2 - Q2D/2
1
11
Q2
688
Chapter Sixteen
Equilibrium in Two Markets
P2
P2 = Q2s - 1
Market 2
5.5
e2
•
2
1
4
P2 = 4 + P1/2 - Q2D/2
11
Q2
689
Chapter Sixteen
Equilibrium in Two Markets
Suppose an exogenous shock increases
demand in market 1 to: Q1D = 22 – 3p1 +
p2 . What is the new general equilibrium?
• Market 1 equilibrium: p1 = 22/4 + p2/4
• Market 2 equilibrium: p2 = 1 + p1/3
• 32/11 = p2e
• 63/11 = p1e
• Q1e = 85/11
• Q2e = 43/11
690
Chapter Sixteen
Equilibrium in Two Markets
Suppose you used the partial equilibrium
price and output level in market 2 in order
to compute the market 1 equilibrium.
What would be the bias in your
conclusions for market 1?
If we re-solve for market 1 price with the
new demand but p2e = 2, we obtain p1e =
11/2 = 5.5 – but in part (b), p1e = 63/11 =
5.72. In other words, we would
underestimate the true price for good 1.
691
Chapter Sixteen
Efficiency and Competitive Markets
Definition: An economic situation is Pareto
Efficient if there is no way to make any person
better off without hurting somebody else.
Result 1 – Production Efficiency: A
perfectly competitive market produces a
Pareto efficient amount of output.
Because the price at which someone is
willing to buy an extra unit exactly equals
the price that must be paid to induce
someone else to sell an extra unit:
Or
692
Chapter Sixteen
Efficiency and Competitive Markets
Since price equals marginal cost at the
competitive equilibrium, consumers value the
last unit of output by exactly the amount that it
costs to produce (in the sense of opportunity
cost) so that no reallocation of consumption
towards this good or away from this good
could increase the value obtained from
resources in the economy.
693
Chapter Sixteen
Efficiency and Competitive Markets
As long as Pi > MCi, the total size of
the “economic pie” could be increased
by increased consumption of good i
since MRi reflects the opportunity cost
of producing i.
As long as Pi < MCi, the total size of
the “economic pie” could be increased
by decreased consumption of good i.
694
Chapter Sixteen
Efficiency and Competitive Markets
Result 2 – Allocative Efficiency: A
competitive market allocates goods in a
way that is Pareto efficient.
because it equalizes the marginal rates
of substitution across consumers.
i.e., If all consumers are willing to trade
goods at the same rate then it is not
possible for any pair to get together and
improve their joint utilities by
reallocating goods.
695
Chapter Sixteen
Summarizing Perfect Competition
Perfect competition maximizes the sum of consumers’
surplus plus producers’ surplus (minimizes deadweight loss)
and allocates that output in a Pareto Efficient way.
Is Prefect Competition Really Desirable?
We know that consumers’ surplus is not the “ideal” measure of consumer
benefit from consumption when there are income effects…but if income
affects the placement of demand, have we calculated our measure of
“efficiency” correctly? Where does “income” come from and does our
result depend on the allocation of income across consumers?
696
Chapter Sixteen
Summarizing Perfect Competition
Producers’ surplus measures producers’
benefits net of costs (i.e., costs affect the
placement of supply)…but what determines
these “opportunity costs”?
Our discussion has taken “income” and “costs”
as, at least partially, given. But these come, in
fact, from other markets (labor markets, for
example). Further, these concepts are related.
If we wish to make a stronger statement about
economic efficiency, we need to measure
economic efficiency while allowing income
and all costs to be endogenous.
697
Chapter Sixteen
Pure Exchange Economy Efficiency
Simplifying Assumptions
1. Consumers and producers are price takers.
2. There are only two individuals and two goods in the economy.
3. Individuals have fixed allocations (endowments) of goods that
they might trade. No production occurs for now.
4. Consumers maximize utility with usually-shaped indifference
curves (and non-satiation). Utilities are not interdependent.
698
Chapter Sixteen
Edgeworth Box Diagram
699
Chapter Sixteen
Edgeworth Box Diagram
700
Chapter Sixteen
Edgeworth Box Diagram
701
Chapter Sixteen
Edgeworth Box Diagram
1. The length of the side of the box measures the
total amount of the good available.
2. Person A’s consumption choices are measured
from the lower left hand corner, Person B’s
consumption choices are measured from the
upper right hand corner.
3. We can represent an initial endowment,
(wA1,wA2), (wB1,wB2) as a point in the box.
This is the allocation that consumers have before
any exchange occurs.
702
Chapter Sixteen
Edgeworth Box Diagram
4. Any other feasible consumption allocation is a
point in the box such that, for each individual:
"final demand" < "initial supply"
• xA1+xB1 < wA1 + wB1
• xA2+xB2 < wA2 + wB2
5. We can represent indifference curves of the
individuals between the goods in the standard
way measured from the appropriate corners.
703
Chapter Sixteen
Exchange
• Any voluntary barter trade (a point that
makes at least one consumer better off) must lie
in a “lens” formed by the indifference curves
that intersect the initial endowment.
• Allocation through trading that potentially
improves utility…but is infeasible: There is
excess demand for good 1 and excess supply of
good 2. Neither the market for good 1 nor the
market for good 2 is in equilibrium.
704
Chapter Sixteen
Edgeworth Box – Infeasible Allocation
705
Chapter Sixteen
Edgeworth Box – Infeasible Allocation
706
Chapter Sixteen
Edgeworth Box – Infeasible Allocation
707
Chapter Sixteen
Edgeworth Box –Allocation Can be Improved
708
Chapter Sixteen
Edgeworth Box –Allocation Can be Improved
709
Chapter Sixteen
Edgeworth Boxes
Trading will continue until no
mutually improving trades are
possible. (e.g. at M)
710
Chapter Sixteen
Edgeworth Box – Economically Efficient Allocation
711
Chapter Sixteen
Edgeworth Box – Economically Efficient Allocation
712
Chapter Sixteen
Edgeworth Box – Economically Efficient Allocation
713
Chapter Sixteen
Edgeworth Box – Economically Efficient Allocation
714
Chapter Sixteen
Pareto Set / Contract Curves
1. M is Pareto efficient
2. M is at a tangency point of the two individuals’
indifference curves
MRSA1,2 = MRSB1,2
3. Definition: The set of all Pareto efficient
points in the Edgeworth box is known as the Pareto
set or the Contract Curve.
This set typically will stretch from one corner to the other of the
box (M not unique). A subset of this set will contain the points
that are Pareto efficient with respect to the initial endowment.
715
Chapter Sixteen
The Contract Curve
716
Chapter Sixteen
The Contract Curve
717
Chapter Sixteen
The Contract Curve
718
Chapter Sixteen
The Contract Curve
719
Chapter Sixteen
Pure Exchange Economy
• A pure exchange economy in which
completely decentralized trading is allowed
such that agents have access to each other
and each is able to maximize utility subject
to a feasibility constraint gets the economy
to A Pareto Efficient Allocation.
• This requires each individual to have
information on his endowment and
preferences only
720
Chapter Sixteen
Calculating a Contract Curve
Two individuals, A and B with "Cobb-Douglas" utility
functions over 2 goods, X and Y.
UA = (XA)(YA)1-
UB = (XB)(YB)1-
MUYA = (1-)XAY-
MUXB = XA-1Y1-
MUYB = (1-)XAY-
XA + XB = 100 – This gives the size of the Edgeworth Box
YA + YB = 200
Therefore:
MRSX,YA = MUXA/MUYA = [/(1-)][YA/XA]
MRSX,YB = MUXB/MUYB = [/(1-)][YB/XB]
721
Chapter Sixteen
Calculating a Contract Curve
And
XA = 100 – XB – feasibility constraints
YA = 200 - YB
MRSX,YA = MRSX,YB – tangency condition for contract curve
[/(1-)][(200 – YB)/(100 – XB)] = [/(1-)][YB/XB]
Or
(-)YBXB - (1-)(100YB) + (1-)200XB = 0
or
(-)YAXA + (1-)(100YA) - (1-)200XA = 0
722
Chapter Sixteen
Calculating a Contract Curve
Draw the contract curve for
==½
The equations for the
contract curves simplify to:
YA = 2XA and YB = 2XB
723
Chapter Sixteen
The Role of Prices
Suppose that agents are presented with prices,
(p1,p2) that they take as given and can use to
value their initial endowment of goods
p1w1 + p2w2 = I
Hence, these prices define a budget constraint
for each individual…tangency with the budget
constraint determines where the individuals
will desire to consume:
724
Chapter Sixteen
Prices & Equilibrium
MRS = p1/p2
So that in the General Equilibrium – MRSA1,2 = MRSB1,2 = p1/p2
Definition: If, at the announced prices,
the amount that A wants to buy (sell) of
good 1 exactly equals the amount B
wants to sell (buy) of good 1 and if the
same holds for good 2 as well, the
market is in equilibrium.
725
Chapter Sixteen
Economically Efficient Price Allocation
726
Chapter Sixteen
Economically Efficient Price Allocation
727
Chapter Sixteen
Economically Efficient Price Allocation
728
Chapter Sixteen
Economically Efficient Price Allocation
729
Chapter Sixteen
Economically Efficient Price Allocation
• In other words, income is determined by the
value of the endowment and equilibrium holds
when, in every market, demand equals supply.
• Further, since the market equilibrium holds
where the marginal rates of substitution are
equal and the preferred bundles of each agent
lie above the budget set, the market
equilibrium is Pareto Efficient.
730
Chapter Sixteen
Economically Efficient Price Allocation
This means that society can achieve efficiency by
allowing competition
This equilibrium requires very little information (prices
only) or co-ordination.
In fact, any Pareto-efficient equilibrium can be obtained
by competition, given an appropriate endowment.
For example, any Pareto efficient allocation, x, can be
obtained as a competitive equilibrium if the initial
endowment is x.
731
Chapter Sixteen
Economically Efficient Price Allocation
• This means that society can obtain a
particular efficient allocation by appropriately
redistributing endowments (income).
• This can be achieved through taxes/subsidies
to endowments (lump sum taxes) that do not
affect choice (prices)
• In fact, this redistribution could be viewed as
the main role of government in the perfectly
competitive model
732
Chapter Sixteen
At Equilibrium Prices:
1. Allocative Efficiency: MRSX,Y for all the
individuals must be equal
2. Private Utility Maximization: MRSX,Y for
each and every individual must equal pX/pY
3. Market Equilibrium: Qd = QS must hold for
each and every good.
4. Feasibility: Total supply must equal the
original endowment for each and every good.
733
Chapter Sixteen
Production
Suppose that all individuals in the economy have a dual
role: they are consumers, but they also are the
producers. In other words, the individual's role as a
producer will determine their income.
Definition: The production possibility frontier (PPF)
of an individual is the maximum combinations of goods
A and B that can be produced with the individual’s
input (e.g., labor) per unit of time.
Definition: An individual achieves efficiency in
production if s/he produces combinations of goods on
the PPF (so that there is no "slacking off").
734
Chapter Sixteen
Marginal Rate of Transformation
Definition: The slope of the production
possibility frontier is the marginal rate of
transformation (MRT).
The MRT tells us how much more of good Y
can be produced if the production of good X is
reduced by a small amount.
Or…the MRT tells us how much it costs to
produce one good in terms of foregone
production of the other good (opportunity cost).
735
Chapter Sixteen
Production Possibility Frontier (PPF)
Kate’s Production
Y
6
PPFK
MRTK= 2
2
3
X
736
Chapter Sixteen
Production Possibility Frontier
Kate’s Production
Y
Pierre’s Production
Y
6
PPFK
MRTK= 2
PPFP
2
MRTP= 1/2
3
3
X
2
6
X
737
Chapter Sixteen
Production Possibility Frontier
Kate’s Production
Y
Pierre’s Production
Joint Production
Y
Y
PPFJ
MRTJ= 1/2
6
6
MRTJ= 2
PPFK
MRTK= 2
PPFP
2
MRTP= 1/2
3
3
X
2
6
X
6
X
738
Chapter Sixteen
Joint PPF
Definition:
The joint PPF for all possible
technologies and all producers in the economy
depicts the maximum amount of each good that
could be produced in total by all producers.
Definition: A producer who, when producing one
good, reduces production of a second good less
compared to another producer is said to have a
comparative advantage in producing the first good.
739
Chapter Sixteen
Joint PPF
• If the MRT of two different producers
(and consumers) differs, then the
individuals can potentially gain from trade
• If many production methods are
available, the joint PPF takes a typically
“rounded” shape, representing the various
MRT’s available to the economy.
740
Chapter Sixteen
The Efficient Product Mix
• Now, let’s look at the efficient product
mix. At which point along the joint PPF
would society operate?
• Any individual consumer would prefer
production to occur at a point where the
consumer's indifference curve is just
tangent to the PPF.
741
Chapter Sixteen
The Efficient Product Mix
Y
Preference
Direction
PPFJ
X
742
Chapter Sixteen
The Efficient Product Mix
Y
Preference
Direction
IC
PPFJ
X
743
Chapter Sixteen
The Efficient Product Mix
Y
Preference
Direction
•
MRSX,Y = MRTX,Y
IC
PPFJ
X
744
Chapter Sixteen
The Efficient Product Mix
At this point, the consumer’s willingness to give up
good X in order to get good Y just equals the rate at
which a producer has to give up good X in order to
produce more of good Y.
MRTX,Y = MRSX,Y
But this must be true for all consumers if the
economy is to produce optimally for each consumer.
745
Chapter Sixteen
Comparative Markets & Optimality
Can the competitive market help us
to achieve this optimality?
At the Pareto efficient allocations,
it is true for all consumers that:
MRSX,Y = pX/pY
746
Chapter Sixteen
The Producers’ Problem
Suppose that the producers produce goods X and Y and
choose the product mix so as to maximize profits given the
prices pX and pY:
Max  = pXQX + pYQY – C*QX,QY
Where: we will suppose that the cost of production is fixed
whatever the optimal output mix (e.g., we just want to know
how to employ the labor we have contracted)
747
Chapter Sixteen
Isoprofit
Definition: an isoprofit line shows
the output combinations that result
in a given level of profit, 0
or
QY = (0 + C*)/pY – pXQX/pY
748
Chapter Sixteen
The Profit Maximizing Product Mix
Y
PPFJ
X
Chapter Sixteen
749
The Profit Maximizing Product Mix
Y
Isoprofit Lines
(0+C*)/PY
•
-pX/pY
PPFJ
X
Chapter Sixteen
750
The Profit Maximizing Product Mix
Y
Isoprofit Lines
(0+C*)/PY
Direction of
increasing profits
•
Profit maximising
product mix
-pX/pY
PPFJ
X
Chapter Sixteen
751
The Profit Maximizing Product Mix
Hence, If the firm maximizes profits, then,
it chooses the product mix that shifts out
the isoprofit line as much as possible while
remaining feasible. This is a tangency
point such that for all producers:
MRTX,Y = pX/pY
752
Chapter Sixteen
The Profit Maximizing Product Mix
In other words, in equilibrium, the price ratio will measure the
opportunity cost of production of one good in terms of
production of the other good.
Therefore
Because competition ensures that both the MRS and the MRT
equal the (same) price ratio for all producers and all consumers,
a competitive equilibrium achieves an efficient product mix for
all producers and all consumers
Earlier allocative efficiency results still hold with production
753
Chapter Sixteen
General Equilibrium
Y
PPF
X
754
Chapter Sixteen
General Equilibrium
Y
Ys
XeB
•
YeB
PPF
Xs
X
755
Chapter Sixteen
General Equilibrium
Y
Ys
XeB
•
•
Slope = -p1e/p2e
YeB
PPF
XeA
X
Xs
756
Chapter Sixteen
General Equilibrium
Y
Ys
YeA
XeB
•
•
Slope = -p1e/p2e
YeB
PPF
XeA
Xs
X
757
Chapter Sixteen
General Equilibrium
Ys and Xs are the amounts of X produced in
the economy; (XeA,YeA) is the amount of X and
Y consumed by person A and (XeB,YeB) is the
amount of X and Y consumed by person B.
• Efficiency in exchange (on contract curve)
• Efficiency in use of inputs (on PPF)
• Efficiency in product mix (tangency with PPF)
758
Chapter Sixteen
Summary
1. If there are spillover effects among markets
in the economy, we need to calculate
equilibrium by determining equilibrium in all
markets simultaneously. Otherwise, our results
for equilibrium prices and quantities will be
biased. This bias can be large.
2. In partial equilibrium analysis, a perfectly
competitive and allocates goods in a way
market produces a Pareto efficient amount of
output that is Pareto efficient.
759
Chapter Sixteen
Summary
3. We can make a similar statement about perfect
competition in a general equilibrium analysis. In
other words, taking into account that income is
determined endogenously and costs are determined
endogenously was well, we can still state that
perfect competition produces a Pareto efficient
amount of output and allocates it in a Pareto
efficient way.
4. More specifically, competitive allocations are
efficient in exchange, efficient in the use of inputs
in production, and efficient in the mix of outputs.
760
Chapter Sixteen
Chapter Seventeen
Externalities and
Public Goods
761
Chapter Seventeen
Chapter Seventeen Overview
1. Motivation
2. Inefficiency of Competition with Externalities
3. Allocation Property Rights to Restore Optimality
•
•
•
The Coase Theorem
Problems with the Coase Approach
Other Methods to Restore Optimality – Standards and Fees
4. Public Goods
•
•
•
A Taxonomy
Demand for Public Goods
Free Riders and the Supply of Public Goods
762
Chapter Seventeen
Externalities
Definition: If one agent's actions
imposes costs on another party, the
agent exerts a negative externality,
while if the agent's actions have
benefits for another party, the agent
exerts a positive externality.
• Network externalities, snob effects
• Wind chimes
When externalities are present, the competitive
market may not attain the Pareto Efficient outcome.
763
Chapter Seventeen
Inefficiency of Competition with Externalities
Competitive firms and consumers do not have to pay for the
harms of their negative externalities, they produce too many.
Since they are not compensated for the benefits of their positive
externalities, they create too little.
Example – Firm produces paper and harmful by-products:
1 ton paper  1 unit waste
• Private cost of production does not include harm from waste.
• Social cost of production includes the harm from the
externality and is, then, greater than the private cost.
764
Chapter Seventeen
Inefficiency of Competition with Externalities
MCS = MCP + MCW
Pp
($/ton)
MCP
MCW
Demand
0
Qp (tons/day)
W (units/day)
765
Chapter Seventeen
Inefficiency of Competition with Externalities
MCS = MCP + MCW
Pp
($/ton)
PS
MCP
•e
s
PC
•e
c
MCW
QS
0
Demand
QC
Qp (tons/day)
W (units/day)
766
Chapter Seventeen
Inefficiency of Competition with Externalities
MCS = MCP + MCW
Pp
($/ton)
MCP
A
PS
PC
•e
B
F
C
E
S
D
H
G
•e
•MC
C
MCW
P
• MC
Demand
W
QS
0
QC
Qp (tons/day)
W (units/day)
767
Chapter Seventeen
Inefficiency of Competition with Externalities
Social
Optimum
Private
Change
B+C+D
• Consumers Surplus
A
A+B+C+D
• Private Producers Surplus
PSP
B+C+F+G F+G+H H-B-C
• Externality Cost,
CG
• Social Producers Surplus
PSS = PSP-CG
• Welfare
W = CS + PSS
C+G
A+B+F
C+D+E+
G+H
B+F
D+E+H
F-C-D-E
-B-C-D-E
A+B+F-E -E=DWL
768
Chapter Seventeen
Competitive Market & Social Optimum
Competitive market: p = MPP
Social optimum:
p = MCS
Competitive market creates a dead-weight loss
(socially excessive negative externalities)
This is because the polluter does not have to pay
for pollution
Socially optimal amount of waste is non-zero.
How can we restore optimality?
769
Chapter Seventeen
Restoring Optimality
Definition: A property right is a legal rule
that describes what economic agents can do
with an object or idea.
Deed to parcel of land; patent on a method
770
Chapter Seventeen
Restoring Optimality – Paper Mill & Fishermen
Suppose that paper mill may reduce its emissions of gunk by installing filters
and fishermen can reduce emissions by installing a water treatment plant.
Mill
Fishermen
No
Treatment
treatment
No filter 500,100
500,200
filter
300,500
300,300
771
Chapter Seventeen
Restoring Optimality – Paper Mill & Fishermen
Case 1: No explicit rights allocation
• Nash outcome: no filter, treatment plant
• Joint payoff = 700 (not Pareto efficient)
772
Chapter Seventeen
Restoring Optimality – Paper Mill & Fishermen
Case 2: Fishermen have property right to no Pollution
(and so, set a fee of, say, $500 for receiving pollution)
Fishermen
Nash Outcome:
Filter, No treatment
Joint Payoff = 800
(Pareto Efficient)
Mill
No
Treatment
treatment
No filter 0,600
0,700
Filter
300,500
300,300
773
Chapter Seventeen
Restoring Optimality – Paper Mill & Fishermen
Case 3: Mill has right to pollute. Suppose the mill "sells"
right to fresh water (i.e. obligation to install filter) for $250:
Fishermen
Nash Outcome:
Filter, No Treatment
Joint Payoff = 800
(Pareto Efficient)
Mill
No
Treatment
treatment
No filter 500,100
500,200
filter
550,250
550,50
774
Chapter Seventeen
The Coase Theorem
• If there are no impediments to bargaining,
assigning property rights results in the efficient
outcome (at which joint profits are maximized).
• Efficiency is achieved regardless of who
receives the property rights.
• Who gets the property rights affects the income
distribution: the property rights are valuable.
(The party with the property rights is
compensated by the other party.)
775
Chapter Seventeen
The Coase Theorem
• Transaction Costs may be high;
• Large numbers of injured parties;
• Incomplete/Asymmetric Information.
e.g. What are the long run effects of genetic engineering?
776
Chapter Seventeen
Other Methods to Restore Optimality
Pp ($/ton)
MCS = MCP + MCW
Emissions Standards (quota)
MCP
MCW
Demand for Paper
Qp (tons/day)
W (units/day)
0
Chapter Seventeen
777
Other Methods to Restore Optimality
MCS = MCP + MCW
Pp ($/ton)
Emissions Standards (quota)
MCP
•e
What is the marginal cost of
pollution at the social optimum?
S
T
MCW
•MC
P
• MC
Demand for paper
G
0
Qp (tons/day)
W (units/day)
QS= Quota
Chapter Seventeen
778
Public Goods
Definition: Rivalry in consumption means that only
one person can consume a good: the good is used up
in consumption (it can be depleted).
Definition: Exclusion in consumption means that
others can be prevented from consuming a good.
779
Chapter Seventeen
Public Goods
Definition:
Private goods have properties of rivalry and
exclusion. Pure Public goods lack both rivalry and exclusion.
Club goods lack rivalry but have property of exclusion. Common
property lacks exclusion but does have the property of rivalry.
Exclusion
No exclusion
Rivalry
Pure Private Commons:
goods: Apple Fisheries
No Rivalry
Club goods:
concert
Pure public
good: clean
air
780
Chapter Seventeen
Demand for Public Goods
Because public goods lack rivalry,
the aggregate demand is the
aggregate willingness to pay curve:
the vertical sum of the individual
demand curves.
781
Chapter Seventeen
Efficient Provision of a Public Good
400
Price ($/unit)
300
200
100
D1
0
30
Quantity of Public Good
100
782
Chapter Seventeen
Efficient Provision of a Public Good
400
Price ($/unit)
300
200
100
D2
D1
0
30
100
Quantity of Public Good
200
Chapter Seventeen
783
Efficient Provision of a Public Good
400
Price ($/unit)
300
MC = 240
200
100
D2
MC = 50
D1
0
30
100
Quantity of Public Good
200
Chapter Seventeen
784
Efficient Provision of a Public Good
400
Price ($/unit)
MSB
300
MC = 240
200
100
D2
MC = 50
D1
0
30
100
Quantity of Public Good
200
Chapter Seventeen
785
Efficient Provision of a Public Good
400
MC = 400
Price ($/unit)
MSB
300
MC = 240
200
100
D2
MC = 50
D1
0
30
100
Quantity of Public Good
200
Chapter Seventeen
786
Efficient Provision of a Public Good
Example
Consumer 1: P1 = 100 - Q
Consumer 2: P2 = 200 - Q
How would we determine the efficient level of the
public god algebraically assuming the marginal cost
of the public good is $240?
Summing P1 and P2, we obtain
MSB = P1 + P2 = 100 - Q + 200 - Q =
300 - 2Q
787
Chapter Seventeen
Efficient Provision of a Public Good
Setting MSB = MC, we have:
300 - 2Q = 240
Or
Q* = 30
788
Chapter Seventeen
Free Rider
Definition: a free rider benefits from an action
of other (s) without paying for that action.
Solutions to the free rider problem
789
Chapter Seventeen
Summary
1. When one agent's actions affect another
agent, the agent exerts an externality.
2. When externalities are present the
competitive market may not attain the
Pareto Efficient outcome.
3. We can restore optimality by assigning
property rights to the cause of the
externality (The Coase Theorem).
4. If we follow this approach, efficiency is
achieved regardless of who receives the
property rights; however, the property
rights affect the income distribution.
790
Chapter Seventeen
Summary
5. When transaction costs are high or there
is asymmetric or incomplete information,
allocating property rights may not restore
optimality.
6. Other methods of restoring optimality
include standards and fees.
7. Private goods have the properties of
rivalry and exclusion. Other types of goods
exist that do not have these properties.
791
Chapter Seventeen
Summary
8. Goods that lack rivalry and exclusion
are called pure public goods.
9. The demand for pure public goods is
the vertical sum of the individual
willingness to pay for the good.
10.
Pure public goods tend to be
undersupplied by the market.
792
Chapter Seventeen
Index – Alphabetical Topics
Take me to
the Text:
Analyzing Economic Problems
Demand and Supply Analysis
Capturing Surplus
Competitive Markets: Applications
Consumer Choice
Consumer Preferences and the Concept of Utility
Costs and Cost Minimization
Cost Curves
Demand Theory
Equilibrium Theory
Externalities
Game Theory and Strategic Behavior
Inputs and Production Functions
Market Structure and Competition
Monopoly and Monopsony
Perfectly Competitive Markets
Public Goods
Risk and Information
793