Transcript Econ326 Intermediate Microeconomics

Econ326
Intermediate Microeconomics
Fall 2011
Instructor: Ginger Z. Jin
http://kuafu.umd.edu/~ginger
TA: Aaron Szott
Lecture 1
 Course
introduction
 Syllabus
 Teaching
style and expectations
 Textbook
Chapter 1, 2.1-2.3
Goal of the class

Teach you to think like a micro-economist
◦
◦
◦
◦
Labor market issues
Industrial organization
Public policies
International trade

Derive the major concepts and intuitions
from introductory microeconomics

We will emphasize analytic logic and
mathematical rigor.
Class will cover:

Consumer demand
◦
◦
◦
◦

Describe consumer preference
Derive consumer demand
Market vs. individual demand
Consumer welfare
Firm production
◦ Production technology
◦ Firm choice of input and output
◦ Cost and profit

How demand meets supply?
◦
◦
◦
◦
Exchange economy
Market structure
Market failures: monopoly, asymmetric info, externality
Policy interventions
Example: rental market in College Park

Product definition:
◦ one bedroom apt
◦ off-campus rental
◦ in College park

Players:
◦ tenants, landlords, city government? University?

Actions and incentives
◦ Tenants: reservation price/willingness to pay
◦ Landlords: cost, earn money if possible

Market outcomes:
 price, vacancy rate, tax revenue?
Monthly rent
supply
equilibrium
demand
Units available
Why is the demand downward sloping?
Monthly rent
supply
equilibrium
demand
Units available
When will we observe a fixed supply?
Market scenario 1: convert some
apartments to condos
supply
Monthly rent
demand
Units available
Both demand and supply get reduced, the effect on market
equilibrium price is unclear
Market scenario 2:
impose $50/month tax on landlord
supply
Monthly rent
demand
Units available
No change in demand and supply thus no change in price
ONLY TRUE with fixed supply
What happens if the supply is not fixed?
Market scenario 3:
non-discriminating monopoly
supply
Monthly rent
demand
Units available
The monopolist may want to restrict the supply so that he can charge
higher price  not efficient from the society point of view
What if the monopolist can charge different price on different tenants?
Market scenario 4:
rent control
supply
Monthly rent
demand
Keep the price down, but create excessive demand
How to allocate the limited supply to excessive demand?
lottery, ration, allow secondary market trade?
Units available
At the end of this class,
You know how to derive a simple demand
curve given individual preference
 You know how to derive the supply
decision of each firm
 You know how to compute market
equilibrium under different market
structures
 You can compute who gains and who
loses by how much under a simple policy
intervention

Syllabus

on my personal website
http://kuafu.umd.edu/~ginger/
click on Econ326

Also available on elms.umd.edu
Prerequisites – very strict rules by
Economics Department
◦ (1) have completed Econ300 with a grade of "C" (2.0) or
better,
OR
◦ (2) have completed or are concurrently taking Math 240
or Math 241.
If you satisfy either (1) or (2), you should have already completed
ECON200, ECON201, and Calculus I. But completion in these four
courses are not sufficient for enrollment in Econ326.
For those who do not meet the prerequisites but believe that an
exception could be made, please talk to Shanna Edinger in Tydings
3127B.
Syllabus
◦ Textbook:
 Pindyck and Rubenfeld, Microeconomics, Edition 7
◦ Evaluation

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Three problem sets, 10 points each
Two midterms, 20 points each
One cumulative final, 30 points
Five random in-class quizzes, 2 bonus points each
Total 110 points
Fixed grade definition
(No curve, no rounding)
F:
D:
D+
C-:
C:
C+:
B-:
B:
B+:
A-:
A:
A+:
<40
[40,45)
[45,50)
[50,55)
[55,60)
[60,65)
[65,70)
[70,75)
[75,80)
[80,90)
[90,100)
[100,110].
Important dates
Sept. 8:
Sept. 22
Oct. 4
Oct. 11
Oct. 28
Nov. 8
Nov. 15
Dec. 8
????
Handout problem set 1
Problem set 1 due
Midterm 1
Handout problem set 2
Problem set 2 due
Midterm 2
Handout problem set 3
Problem set 3 due
Final exam
There will be 5 in-class quizzes at unannounced
dates.
Exam policies
 If you miss exams for reasons in line with
university policy, you can take makeup
exams or roll over your missed points to
final
 For other reasons to miss the exam, you
are allowed to skip at most one midterm
(with points rolled over to final) upon
one-month written notice to the
Professor
Problem sets

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

Hard copy distributed in class, soft copy
available on elms
You can turn in problem sets in class or in
your TA’s mailbox (in 3105 Tydings) by 4pm
of due date.
Graded problem sets will be returned in TA
sessions
Collaborative discussion on problem sets is
ok but outright copying is cheating.
Everyone should turn in individual
problem sets.
Teaching Assistant: Aaron Szott

Office:
◦ 0124F Cole Field House

Office Hours
◦ Monday 2:15-3:15pm, Friday 2-3pm

Office Phone
◦ 301-305-9259
Change of office hours for
Sumedha
Teaching Style
Power point lecture notes are posted on
elms (subject to update)
 More details and examples may be
covered during the class
 Handouts, problem sets, answer keys will
be posted on elms. I will also distribute
handouts and problem sets in class
 Graded work will be returned in TA
sessions

Expectation on You

Attend the class
◦ Mute your cell phone at least
◦ If you have to use your computer, make sure it is
muted and you do not bother others

Read related textbook chapters
◦ date-specific chapter numbers are available in syllabus
Attend TA sessions (will be very useful)
 Sharpen your calculus
 Ask for help EARLY if you encounter difficulty
 Feel free to give us feedback any time so we can
improve during the class

Lecture 2
 Utility Theory
 Consumer
preferences
 Constructing Indifference curves
 Properties of Indifference curves
 Textbook
chapter 3.1-3.2
Intuition of consumer theory

How does a consumer choose the best
things that she can afford?
◦ What is the best
◦ Afford  budget constraint
◦ How to choose  constrained optimization

Examples:
◦ Individual choice of work time
◦ Apple rolls out iphone4
◦ Tax cut at the end of 2010
Axioms of preferences

Completeness
◦ A > B, B > A, A ~ B for all bundles A, B

Transitivity
◦ A > B and B > C => A > C
◦ Otherwise we won’t be able to tell which bundle is the
best

Non-satiation:
◦ more is preferred to less. Goods are always “good”
◦ Counter examples: bad (dislike), neutral goods (indifferent)

Balance:
◦ averages preferred to extremes
◦ Also called convex preference
Utility

Definition of Utility
◦ Numerical score representing the satisfaction
that a consumer gets from a given basket of
goods.

In what unit?
◦ ordinal versus cardinal
Marginal Utility

the increase in utility you get when you
consume one more unit of good X
Units of Apples
Total utility
(TU)
Marginal Utility
(MU)
0
0
1
5
5-0=5
2
9
9-5=4
3
12
12-9=3
4
14
14-12=2
5
15
15-14=1
One common property:
Diminishing marginal utility
Show MU in graph
Total
Utility U
Units of apples
(X)
Exercise:
compute MU, diminishing MU?

U=5(X+1)

U=5ln(X+1)

U=X0.3

U=100-X2

U=X0.4Y0.6
Ordinal vs Cardinal

Ordinal Utility
◦ the measurement of satisfaction that only requires a
RANKING of goods in terms of consumer
preference.
◦ This is the concept of utility that is embodied in the
so-called "utility function" that forms the basis of
CONSUMER THEORY…

Utility Function
◦ Utility function that generates a ranking of market
baskets in order of most to least preferred.
◦ This function is defined up to an order-preserving,
monotonic transformation
Exercise:
monotonic transformation of U function?

U=5X vs U=5(X+1)

U=5(X+1) vs U=5ln(X+1)

U=5X+5Y vs. U=5lnX+5lnY

U=X0.5Y0.5 vs U=XY

U=XY vs U=lnX+lnY

U=X+Y2 vs U=X+Y
Note:
1. monotonic
transformation
does not change
the order of
preference,
2. it may change the
property of MU
3. It does NOT
change the
relative tradeoff
between two
goods (MUx vs
MUy)
How to graph utility of two goods
U(X,Y)
U(X,Y)
Y
Y
0
X
0
X
Indifference curves

Definition of Indifference Curve:
◦ the set of consumption bundles among which
the individual is indifferent. That is, the bundles
all provide the same level of utility.
each indifference curve corresponds to a
specific utility level
 Indifference curves never cross each
other

Axioms of preferences

Completeness
◦ A > B, B > A, A ~ B for all bundles A, B

Transitivity
◦ A > B and B > C => A > C
◦ Otherwise we won’t be able to tell which bundle is the
best

Non-satiation:
◦ more is preferred to less. Goods are always “good”
◦ Counter examples: bad (dislike), neutral goods (indifferent)

Balance:
◦ averages preferred to extremes
◦ Also called convex preference
Examples of indifference curves

U(X,Y)=X * Y
point X
Y
U
1
1
1
1
2
2
2
4
3
3
3
9
4
4
4
16
5
1
4
4
6
4
1
4
7
2
3
6
8
3
2
6
Y
Typical convex preference
Satisfy all four axioms of preference
X
Examples of indifference curves

U(X,Y)=X + Y
point X
Y
U
1
1
1
2
2
2
2
4
3
3
3
6
4
4
4
8
5
1
4
5
6
4
1
5
7
2
3
5
8
3
2
5
Y
5
7
3
4
8
2
1
6
X
Perfect substitutes
Violate “balance” because avg is not better than extremes
MUx is a constant (not diminishing), so is MUY
Examples of indifference curves

U(X,Y)=min(X, Y)
point X
Y
U
1
1
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
1
4
1
6
4
1
1
7
2
3
2
8
3
2
2
Y
X
Perfect complements
Violate “non-satiation” sometimes
U is not always differentiable, MU is not well defined at the kinks
Lecture 3
Marginal rate of substitution
 Properties of indifference curves
 Shape of indifference curves

◦ Special examples
Textbook Chapter 3.1 & 3.2
 Assign problem set #1

Marginal rate of substitution (MRS)

Definition:
Marginal Rate of Substitution (of X for Y)
= -dy/dx | same satisfaction (i.e. same U)


How many units of Y would you like to give
up to get one more unit of X?
Can be interpreted as marginal willingness
to pay for X if Y is numeraire (money left for
other goods)
Marginal rate of substitution (MRS)
Y
A
Slope = - MRS at point A
X
Diminishing MRS
(MRS of X for Y diminishes with X)
Y
A lot of Y
relative to
X
Not much
Y rel to X
X
Consistent with diminishing marginal utility
Mathematical derivation of MRS
◦ U=U(X,Y)
◦ Total differentiation:
◦ dU = MUx * dX + MUy * dY =0
◦
◦ -dY/dX = MUx / MUy = MRS (of X for Y)
MRS and ordinal utility

Calculate MRS:
◦
◦
◦
◦
◦
◦

U=XY
U=lnX + lnY
U=X+Y
U=X+Y2
U=(X+1)(Y+2)
U=X2 Y2
Which and which are monotonic
transformations of each other?
Properties of indifference curves
for typical preferences

Indifferent curves are downward sloping
◦ Violate non-satiation if upward sloping

Indifference curves never cross
◦ Violate transitivity if they cross

Indifference curves are convex
◦ Violate balance if they are concave or linear
How would the indifference curves (on apples
and bananas) look like if:
Like apples and bananas
 Like apples up to a satiation level
 Like apples, but dislike bananas
 Like apples, but indifferent to bananas
 Must eat one apple with one banana
 Dislike apples, dislike bananas
 Like both apples and bananas up to a
satiation level

Like apples and bananas
bananas
U
apples
Like apples up to a satiation level
bananas
U
What happens if one likes both apple and banana up
to a satiation level?
apples
Like apples but dislike bananas
bananas
U
What if one dislikes both apples and bananas?
apples
Like apples but indifferent to bananas
bananas
U
apples
Must eat one apple with one banana
(perfect complements)
bananas
U
Locus line
What determines the locus line?
What if one must each two apples with one banana?
apples
Always willing to exchange one apple
for one banana (perfect substitutes)
bananas
U
What determines the slope of the indifference curve?
What if one is always willing to exchange two apples for one
banana?
apples
Cobb-Douglas Utility
Typical functional form:
U=Xc Yd
Transformations:
U=c*lnX + d*lnY
or
U= Xa Y1-a where a=c/(c+d)
Calculate MRS at point (X,Y)
Lecture 4:

Budget constraints
◦ definition
◦ Shocks to consumer budget
◦ Kinked consumer budget

Textbook Chapter 3.1 & 3.2
Budget constraints

Definition:
◦ The budget constraint presents the
combinations of goods that the consumer can
afford given her income and the price of
goods.
Equation: Px * X + Py * Y = I
 Rearrange: Y = I/ Py + (- Px / Py ) * X

intercept
slope
Graph budget constraint
Y
I/Py
Slope = - Px / Py
I/Px
X
Px/Py = the rate at which Y is traded for X in the marketplace
Unlike MRS, the price ratio does not depend on consumer psyche
Exercise
My 11-year-old son has 20 dollar
allowance each month.
 He likes bakugan balls and pokemon cards
 Bakugan ball is $5 each
 Pokemon card is $2 each
 Draw his budget line

What happens with income tax cut?

Tax cut  more income
Y
I/Py
• Does the intercept
on Y change?
• Does the intercept
on X change?
• Does the slope of
the budget line
change?
Slope = - Px / Py
I/Px
X
What happens if gasoline price goes up?
(assume gasoline is X)
 Px
increases
Y
I/Py
• Does the intercept
on Y change?
• Does the intercept
on X change?
• Does the slope of
the budget line
change?
Slope = - Px / Py
I/Px
X
Examples of kinked budget constraints
(if price depends on how many units to buy)
Assume income = $2000
 Two goods: X=food, Y=health care
 Prices:

◦ Px= $2,
◦ Py = $1 if Y<=500 (deductible $500)
◦ Py = $0.2 if Y> $500 (coinsurance 20%)
Y (health care)
8000
Slope = -Px /Py = -2/0.2=-10
Slope = -Px /Py = -2
500
750
1000
X (food)
Example 2: 1979 food stamp program
Income I=2000
 Two goods: food (X), other (Y)
 Px =1, Py = 1
 A household is granted $200 food stamp
 But the food stamp can only be used for
food

other
2000
2000
2200
food
What happens if there is a black market to trade
food stamps?
Example 3: role of financial market

#1: no financial market
Y (tomorrow)
2*I
I
I
2*I
X (today)
Y (tomorrow)
#2: a financial market
allows saving and
borrowing at interest
rate r
The opportunity cost of
not saving today makes
one feel as if today’s price
is increased to (1+r).
X (today)
Y (tomorrow)
Now we have a kink due
to the asymmetric terms
of borrowing and saving
X (today)
Recap so far
◦ Indifference curves describe consumer
preference
◦ Budget constraints describe what consumers
can afford
◦ Put the two together to determine the best
bundle one can afford
Graphical presentation
Y
MRS > Px/Py
I/Py
A
Slope = - Px / Py
C
B
MRS < Px/Py
I/Px
X
Px/Py = the rate at which Y is traded for X in the marketplace
MRS = the rate at which the consumer is willing to trade Y for X
At the best choice:
Must spend every penny (assume no
savings, goods are divisible)
 Equal Marginal Principle
 MRS = the rate at which the consumer is
willing to trade Y for one extra unit of X
 Px / Py = the rate at which Y is traded for
X in the market place
 MRS = Px / Py  MUx /Px = MUy /Py

Mathematical derivation
Max U(X,Y) by choosing X and Y
 Subject to I = Px * X + Py * Y
 Define Lagrangian function
 L = U(X,Y) + λ (I – Px * X – Py * Y)
 λ is an additional variable, now need to
choose X, Y, λ

Mathematical derivation


We get the equal marginal principle back!

λ is the shadow price of the budget
constraint
◦ Tell us how much the objective function will
increase if the budget constraint is relaxed by
one dollar ((dL/dI = dU/dI when I is binding)
◦ Therefore, λ is also called the marginal utility
of income when utility is maximized
Exercise: find the best choice when
U (Food, Clothes) = ln (F) + ln (C)
 Price of food = $2
 Price of clothes =$1
 Income=100
 Answer: F=25, C=50

Lecture 5

Consumer’s optimal choice
◦ Inner solution, corner solution
Cobb-Douglas utility
 Price and consumer choice
 Income and consumer choice
 Normal, inferior and giffen goods


Textbook Chapter 4 appendix, 4.1-4.4
Typically: Inner solution
Y
I/Py
At the optimal choice:
MRS = Px/Py
I=Px * X + Py * Y
I/Px
X
What if the equal marginal principle
cannot be satisfied?
 corner solution
Y
I/Py
U
Spend every penny:
I=Px * X + Py * Y
Check which corner gives
higher utility
I/Px
X
Example 1 of corner solution:
perfect substitutes
Y
U
100
100
U=X+2Y
Px=10
Py=10
Income=1000
X
Example 2 of corner solution:
perfect complements
U
Y
U=min(X,2Y)
Px=10
Py=10
Income=1000
100
100
X
Demand

Optimal choice
◦ X=f(Px, Py, Income)

Properties:
◦ Homogenous degree of zero
◦ Typically depends on income, own price, price
of other goods
Special example:
Cobb-Douglas Utility

Two
equations
Solve for
two
unknowns
(X and Y)

Demand only
depends on own
price, not price of
other goods
Homothetic
preferences:
MRS only depends
on the ratio of X
and Y
Fixed share of
income for each
good
Graph consumer choice in response to:
Price changes
 Income changes

Two goods:
food, clothing
Price of food drops
Two goods:
food, clothing
Income increases
Note that incomeconsumption curve is
not necessarily linear

Normal goods
◦ Consumers want to buy more quantity of
normal goods as their incomes increase.

Inferior goods
◦ Consumers want to buy fewer quantity of
inferior goods as their incomes increase.

Examples?
Hamburger is a normal good from A to B,
but an inferior good from B to C
Engel curve
Giffen goods
Normal and inferior goods are defined by
how consumer choice changes in
response to income change
 Giffen goods depend on price change

◦ Typical goods have downward sloping demand
curve
◦ Giffen goods have upward sloping demand
curve: as price increases, consumers buy
more; as price decreases, consumers buy less.
Lecture 6
Decompose income and substitution
effects in response to price change
 Slusky Equation
 Textbook chapter: 4.3-4.4
 Handout #1: an example




Food price falls
Initial choice A  new choice B
Imaginary D: same utility as A, but face new price
Slusky Equation

Total effects
Substitution
effects
Income
effects
What if X is an inferior good?
 income effect works against the substitution effect
What if X is a Giffen good?
 income effect works against and more than
cancels off the substitution effect
Example 1:

Example 2: Introduction of health
insurance
X=food,Y=health care, Px=$2, Py=$1 if no
insurance, Income=2000
 Benchmark: no insurance
 Scenario #1: insurers pay 80% of the cost of
any medical service
 Scenario #2: insurers pay 80% after $500
deductible

10000
Y (health care)
A: choice with no
insurance
C: choice with
insurance
Slope = -Px /Py = -2/0.2=-10
C
A to B: substitution
effect
B to C: income effect
B
A
Slope = -Px /Py = -2
1000
Scenario #1: insurers pay 80% of the cost of any medical service
X (food)
Scenario #2:
insurers pay 80% after
$500 deductible
Y (health care)
8000
Slope = -Px /Py = -2/0.2=-10
Slope = -Px /Py = -2
500
750
1000
X (food)
How would the insurance coverage affect those who are healthier and do not
need more than $500 health care before the insurance coverage?
Lectures 7-8
Application to labor supply
 Individual and market demand
 Demand elasticity and cross elasticity
 Textbook chapter: 4.3-4.4

Individual demand

A consumer’s optimal choice of a good
depends on
◦ The price of this good
◦ The price of other goods
◦ Income
Example


Two goods
Income
C
(24w+y)/Pc
C*
L*
24
24+y/w
L
w
1
0.5
4.8 8
24
L
Pc
1
0.5
19.2
42.7
C
More generally:
Market demand Q(P)= sum of individual demand Qi(P)
Textbook example of market demand

How to summarize market demand?

Meaning of demand elasticity

Classify demand by demand elasticity

Market demand

Q(P)
P
If you are the
producer, why do
you want to know
demand elasticity?
50

Example:
◦ Q=100-2P
100
◦ What is demand elasticity at p=10,20,30?
◦ At what price is the demand isoelastic?
Q
Special cases
P
Completely inelastic
demand
Infinitely elastic demand
Q
Other elasticities

Example

More on cross elasticity

X and Y are substitutes
◦ If an increase in Px leads to an increase in the quantity
demanded of Y.

X and Y are complements
◦ If an increase in Px leads to a decrease in the quantity
demanded of Y.

X and Y are Independent
◦ If Px does not affect the quantity demanded of Y
◦ Cobb-Douglas utility  independent goods
Consumer surplus
Individual consumer surplus
= difference between what a
consumer is willing to pay
for a good and the amount
actually paid
Total consumer surplus
= sum of individual
consumer surplus
For six consumers, CS = $6+$5+$4+$3+$2+$1=$21
Total Consumer Surplus
= ½ *(20-14)*6500=19,500
Textbook example of market demand

Calculate the
demand elasticity of
total demand and
total consumer
surplus at p=18.
To summarize
Consumer preference (utility function)
Budget Constraint
 optimal choice X=X(Px, Py, I)
Income-consumption curve, priceconsumption curve, engel curve, demand
curve
 Income and substitution effects
 Sum of Individual demand=market demand
 Demand elasticity, income elasticity, cross
elasticity
 Consumer surplus




Lecture 11
Risk and Consumer behavior
Describe risk
 Preferences towards risk
 Demand for risky assets

Risk, Uncertainty, and Profit, by Frank Knight (1921)

Risk: random events that can be quantified in
probability

Uncertainty: random events that cannot be
quantified in probability

Today we focus on “risk” only
Describe risk

Outcome: a random event is associated
with multiple outcomes, for instance:
◦ head/tail when we flip a coin
◦ gain/loss when we invest in a risky asset
◦ Healthy or sick in the future
Probability: likelihood that a given
outcome will occur
 Payoff: value associated with a possible
outcome

Describe risk

Expected value: probability-weighted average of
the payoffs associated with all possible
outcomes
◦ E(X)=Prob1*X1+ Prob2*X2 +…+ Probn*Xn

Variance: Extent to which possible outcomes of
a risky event differ
◦ Var(X)= Prob1*(X1-E(X))2
◦
+ Prob2*(X2 -E(X))2 +…+ Probn*(Xn -E(X))2

Standard deviation: square root of variance,
same unit as X
Example

Job1:
◦ 50% probability with income $2000
◦ 50% probability with income $1000

Job2
◦ 99% probability with income $1510
◦ 1% probability with income $1500

Calculate expected values, variance,
standard deviation
Job1 is riskier
Preferences toward risk


For outcome Xi, utility = U(Xi)
Expected utility
◦ EU=Prob1*U(X1)+ Prob2*U(X2)
◦
+….+Probn*U(Xn)



Risk averse: prefers a certain given outcome to a risky
event with the same expected value: EU(X)<U(E(X))
Risk neutral: indifferent between a certain given
outcome and a risky event with the same expected
value: EU(X)=U(E(X))
Risk loving: prefer a risky event to a certain outcome
with the same expected value: EU(X)>U(E(X))
Example
Eric now has a job with annual income
$15000
 He is considering a new job:

◦ 50% prob with income $30,000
◦ 50% prob with income $10,000
Risk averse (EU(X)?, U(E(X))?)
Risk neutral (EU(X)?, U(E(X))?)
Risk loving (EU(X)?, U(E(X))?)
Risk premium: maximum amount of money that
a risk averse person will pay to avoid taking the
risk
Indifference curves for a risk averse person


Like higher expected value,
But dislike risk (measured in standard
deviation)
U
How would the
indifference curves
look like if the person
is risk neutral?
What if he is risk
loving?
How to reduce risk?

Diversification
◦ Practice of reducing risk by allocating
resources to a variety of activities whose
outcomes are not closely related
◦ Most effective if the activities are negatively
correlated (examples?)

Insurance
◦ Pay insurance premium to avoid risky
outcomes
◦ Actuarially fair: the insurance premium is
equal to the expected payout
Choosing between risk and return
Risk free asset: Rf
Asset with market risk: Rm, m
( Rm – Rf )
Portfolio p: Rp= Rf +-------------- * p
m

Choice of a risk averse person
Exercise: Chapter 5, Question 7





Suppose two investments have the same three payoffs, but the
probability of each payoff differs:
payoff
Prob (investment A)
Prob (investment B)
$300
0.10
0.30
$250
0.80
0.40
$200
0.10
0.30
Find the expected return and standard deviation of each
investment.
Jill has the utility function U=5*X where X denotes the payoff.
Which investment will she choose?
Ken’s utility function is U=5*X0.5, which investment will he
choose?
For Ken, what’s the risk premium of investment A? What’s the
risk premium of investment B?
Lectures 12, 13

Technology of production
◦
◦
◦
◦

Production function
Average product, marginal product
Law of diminishing marginal return
Malthus and the food crisis
Production with two inputs
◦ Isoquant curve
◦ Marginal rate of technical substitution
◦ Returns to scale
Technology of Production

Production function: shows the highest
output that a firm can produce for each
specified combination of inputs
◦ Single input (labor): q=F(L)
◦ Two inputs (capital, labor): q=F(K,L)
Short-run: time in which quantities of one
or more inputs cannot be changed
 Long-run: time needed to make all
production inputs variable.

Single-input production q=F(L)
Average product: q /L
 Marginal product: dq /dL

L
q
0
1
2
3
4
5
0
10
30
60
80
95
Avg product
q/L
Marginal product
dq/dL
Graphically:
Marginal Product (MP) and Average Product (AP)
Total product q = q (L)
Marginal Product = dq / dL
Average Product = q / L
Question: How does AP change with L?
𝑞
𝑑𝑞
𝑑𝐿
∙
𝐿
−
𝑞
𝑑(𝐴𝑃)
𝑀𝑃 − 𝐴𝑃
𝐿
𝑑𝐿
𝑑𝐿
=
=−
=
2
𝑑𝐿
𝑑𝐿
𝐿
𝐿
𝑑
If MP>AP, AP increases with L
If MP<AP, AP decreases with L
AP=MP at the maximum of AP
Law of diminishing marginal returns
As the use of an input increases with other inputs
fixed, the resulting additions to output (i.e. marginal
product) will eventually decrease.
 This is different from technological improvement

Example: Malthus
and the food crisis
How to describe production with more
than one inputs?
Isoquant curve: shows all possible combinations
of inputs that yield the same output
 Similar to “indifference curve” for consumer
utility

Marginal rate of technical substitution
(MRTS)
Amount by which the quantity of one
input can be reduced when one extra unit
of another input is used so that output
remains constant.
 MRTS of L for K = - dK/dL | same q =
MPL / MPk
 MRTS = - slope of isoquant curve
 Diminishing MRTS
 Similar to MRS in consumer utility

Example

Plot isoquant curve for K=2, L=1,
calculate marginal product of labor,
marginal product of capital and MRTS at
this point
◦ q=3KL
◦ q=3K+L
◦ q=min(3K, L)
Diminishing MRTS
Special case #1:
K and L are perfect substitutes if production
function is linear, MRTS is always a constant
Special case #2:
K and L are perfect complements if production
function is min(f(K), g(L), MRTS is not well
defined at the kink (i.e when f(K)=g(L))
Cardinal vs Ordinal

Consumer utility is ordinal because we only
care about the relative preference on bundles
and it is hard to compare utility across
individuals

Production function is cardinal because the
absolute scale matters

Cobb-Douglas production:
𝑞 = 𝐴 ∙ 𝐾 𝛼 ∙ 𝐿𝛽
𝐴: technological factor
𝛼 + 𝛽: return to scale
Returns to scale

Rate at which output increases as ALL inputs
are increased proportionally
◦ Note it is different from marginal product
◦ It is a property of a given production function,
also different from technological improvement

Simple rule of thumb: will the output double
when all the inputs double?
◦ q more than double  Increasing returns to scale
◦ q exactly double  Constant returns to scale
◦ q less than double  Decreasing returns to scale
Constant return to scale
Increasing return to scale
Can you think of any real-world examples that have
constant, increasing or decreasing returns to scale?
Cobb-Douglas production
Why does 𝛼 + 𝛽 represent returns to scale?
𝑞 = 𝐴 ∙ 𝐾 𝛼 ∙ 𝐿𝛽
Suppose K increases to xK, L increases to xL
Let q’ denote the new production by xK and xL
𝑞 ′ = 𝐴 ∙ 𝑥𝐾 𝛼 ∙ 𝑥𝐿 𝛽
= 𝑥 𝛼+𝛽 ∙ 𝐴 ∙ 𝐾 𝛼 𝐿𝛽
= 𝑥 𝛼+𝛽 ∙ 𝑞
If 𝛼 + 𝛽 < 1, decreasing returns to scale
If 𝛼 + 𝛽 = 1, constant returns to scale
If 𝛼 + 𝛽 > 1, increasing returns to scale
Example: are these production functions
decreasing, increasing or constant returns to
scale?
◦ q=3KL
◦ q= K0.5L0.3
◦ q=0.5lnK + 0.8lnL
◦ q=3K+L
◦ q=min(3K, L)
◦ q= 3KL + 3KL2
Lecture 14, 15 and 16
Cost functions

Firm decision
◦
◦
◦
◦
Given production technology
Given input prices of input
 firm decides on optimal choice of inputs
 cost function
 Short run
 Long run
Cost
w = wage rate
 r = capital rental cost

◦ Both could be opportunity cost
Cost function C (q) = w*L(q) + r*K(q)
 Firm’s decision does not include “sunk
cost” after the cost is sunk

◦ Example?
Fixed vs. Variable Cost
w = wage rate
 r = capital rental cost
 In the long run when every input is
variable
𝐶 𝑞 = 𝑤 ∗ 𝐿 𝑞 + 𝑟 ∗ 𝐾(𝑞)
 In the short run, if K is fixed at 𝐾,
𝐶 𝑞 =𝑤∗𝐿 𝑞 +𝑟∗𝐾

Variable cost
fixed cost
How to determine cost with only
one variable input?
𝑞 = 𝐹 𝐾, 𝐿  𝐿 = 𝐹 −1 (𝐾, 𝑞)
𝐶 𝑞 =𝑤∗𝐿+𝑟∗𝐾
= 𝑤 ∗ 𝐹 −1 𝐾, 𝑞 + 𝑟 ∗ 𝐾


Example: 𝑞 = 𝐾 ∙ 𝐿0.5
𝐶 =𝑤∗𝐿+𝑟∗𝐾 =𝑤∗
𝑞 2
𝐾
+𝑟∗𝐾
More generally
Total production
function
Total cost function
Marginal cost (MC) and avg cost (AC)
Total cost function
Marginal cost MC = dC/dq
Average Variale cost = VC/q
Average total cost = TC/q =
(VC + FC)/q
When MC=AC, it is the minimum
of AC
How to determine cost with two
variable inputs?
Choose L and K in order to
minimize 𝐶 𝑞 = 𝑤 ∗ 𝐿 + 𝑟 ∗ 𝐾
Subject to
𝑞 = 𝐹 𝐾, 𝐿
Define Lagrangian function
𝐺 = 𝑤𝐿 + 𝑟𝐾 − 𝜆 𝑞 − 𝐹 𝐾, 𝐿
First order conditions
𝜕𝐺
𝜕𝐹
=𝑤+𝜆
=0
𝜕𝐿
𝜕𝐿
𝜕𝐺
𝜕𝐹
=𝑟+𝜆
=0
𝜕𝐾
𝜕𝐾
𝜕𝐺
= 𝑞 − 𝐹(𝐾, 𝐿) = 0
𝜕𝜆
𝜕𝐹
𝑤 −𝜆 𝜕𝐿 𝑀𝑃𝐿
=
=
= 𝑀𝑅𝑇𝑆
𝜕𝐹
𝑟 −𝜆
𝑀𝑃𝐾
𝜕𝐾
Graphically:
Isoquant curve at q
Isocost curves
Special case 1: when K and L are perfect
substitutes, we may get corner solutions
𝑤
If > 𝑀𝑅𝑇𝑆, capital is
𝑟
cheaper, hire all capital
and zero labor
𝑤
𝑟
If < 𝑀𝑅𝑇𝑆, labor is
cheaper, hire all labor and
zero capital
Special case 2: when K and L are perfect
complements, we always use the “perfect”
proportion of K and L
Optimal inputs are at the kink of the isoquant curve
Follow the previous example
𝑞 = 𝐾 ∙ 𝐿0.5
 In the short run when K = 𝐾, we find
𝑞 2
𝐶 =𝑤∗𝐿+𝑟∗𝐾 =𝑤∗
+𝑟∗𝐾
𝐾
 In the long run when both L and K are
variable:
𝑟𝑞
𝐶=𝑤∗
𝑤
2
3
+𝑟∗2
1
𝑤𝑞 2 3
𝑟
Long run AC and MC
Inflexibility of short run
Short run and long run costs
Exercise
Production function q=10KL
 Wage w=10, rental cost of capital r=20
 Total, average and marginal cost of
producing q units in the short run when
K is fixed at 5?
 Total, average and marginal cost of
producing q units in the long run?
 What happens if wage rate increases to
20?

Lectures 16 & 17
Profit Maximization of competitive firms
So far we know how to choose inputs
and derive cost function for a specific
level of production under a specific
technology, but how does a firm
determine how much to produce?
 This class:

◦ Competitive market
◦ Profit maximization of competitive firms
 Total revenue, marginal revenue
 Choice of output given market prices
Perfectly competitive market
◦ Homogenous goods
 must charge same price
◦ Free entry and exit of producers
◦ Price-taking:
 numerous firms in the market so no firm's
individual supply decision affects price.
 All firms face perfectly elastic demand
◦ Any example that violates the above
assumption(s)?
Individual firms vs. the industry
Demand curve faced
by a competitive firm
(perfectly elastic)
Demand curve faced
by the industry
Profit-maximizing firms

We assume a for-profit firm aims to
maximize profit

Total profit = total revenue – total cost
𝜋 𝑞 = 𝑇𝑅 𝑞 − 𝑇𝐶 𝑞

The firm chooses q to maximize total
profit
Graphic illustration of profit
maximization
Algebraically:

Choose q in order to maximize
𝜋 𝑞 = 𝑇𝑅 𝑞 − 𝑇𝐶 (𝑞)

First order condition:
𝑑𝜋 𝑑𝑇𝑅(𝑞) 𝑑𝑇𝐶 𝑞
=
−
= 𝑀𝑅 − 𝑀𝐶 = 0
𝑑𝑞
𝑑𝑞
𝑑𝑞

At the optimal choice of q, MR=MC

For a competitive firm, price-taking
implies:
𝑇𝑅 𝑞 = 𝑝 ∙ 𝑞
𝑀𝑅 𝑞 = 𝑝

At the optimal choice of q
𝑀𝑅 = 𝑀𝐶 =⇒ 𝑝 = 𝑀𝐶
About fixed cost
𝜋 𝑞 = 𝑇𝑅(𝑞) − 𝑇𝐶 𝑞
In the short run, fixed cost does not vary
by q, so it does not affect the optimal
choice of q, what matters is marginal cost
(MC).
 In the long run, fixed cost occurs if and
only if the firm enters the market. So it
may affect the entry decision.

Graphic example
Exercise
Output price p=10
 Total cost = 100 + q + 0.5 * q2
 Write down FC, VC, AC and MC.
 How much should the firm choose to
produce in the short run (after it incurs
FC)?
 Should the firm shut down in the long
run?
 At what price will the firm enter the
market?

Short run supply curve of a
competitive firm
How will the supply curve change in the long run?
Industry supply curve in the short run
Producer surplus

Sum over all units produced by a firm of
differences between the market price of a
good and the marginal cost of production
𝑞
𝑃𝑆 𝑞 =
𝑝 − 𝑀𝐶 𝑥 𝑑𝑥
𝑥=0
= 𝑝𝑞 − 𝑇𝑉𝐶 𝑞 = 𝑝 − 𝐴𝑉𝐶 𝑞
Producer surplus for a firm
Producer surplus for the industry in
the short run
Long run profit maximization for an
individual firm
•
•
More flexible in input choices  production can
be more cost-efficient in the long run
Can shut down and exit the market if the
expected profit is lower than the fixed cost
Long run competitive equilibrium
for the industry – three conditions
1. All firms are maximizing profit.
2. No firm has an incentive to entry or exit
because all firms earn zero economic profit
• Zero economic profit represents a
competitive return for the firm’s
investment of financial capital
3. The price of the product is such that the
quantity supplied by the industry is equal to
the quantity demanded by consumers.
Continue the previous example for the whole
industry
start with p=40
The industry’s long run supply curve
•
Constant cost industry
• All firms face same cost
• Every firm is small as compared to the market
• Long run supply curve is horizontal
The industry’s long run supply curve
•
increasing cost industry
• The prices of some or all inputs increase as
the industry expands
• Long run supply curve is upward sloping
Is it possible for the industry’s long
run supply curve to be downward
sloping?
•
Yes, for decreasing cost industry
• The prices of some or all inputs may fall
as the industry expands and takes
advantage of the industry size to obtain
cheaper inputs
Price elasticity of supply
𝑒𝑠𝑢𝑝𝑝𝑙𝑦
𝑑𝑄/𝑄
=
𝑑𝑃/𝑃
• In a constant cost industry, 𝑒𝑠𝑢𝑝𝑝𝑙𝑦 is
infinitely large.
• In an increasing cost industry, 𝑒𝑠𝑢𝑝𝑝𝑙𝑦
is positive and finite, with magnitude
depending on the extent to which
input costs increase as the market
expands.
Exercise
Suppose that a competitive firm has a total cost
function 𝐶 𝑞 = 450 + 15𝑞 + 2𝑞2 .
 If the market price is P=$115 per unit, find the
level of output produced by the firm, the level
of profit and the level of producer surplus.
 Suppose all firms are identical. At P=115, is the
industry in long-run equilibrium? If not, find the
price and every firm’s production associated
with long-run equilibrium .

Lecture 18
Competitive market equilibrium
Demand equal to supply
 Consumer surplus
 Producer surplus
 Dead weight loss
 Consequence of price regulations

Competitive market equilibrium
Every consumer is a price-taker and a
utility-maximizer
 Every firm is a price-taker and a profitmaximizer
 Free entry and exit
 Demand equal to supply

Consumer surplus and producer surplus

Consumer surplus = sum of (consumer willingness to pay –
𝑄
price paid) over all units sold = 0 𝑊𝑇𝑃 − 𝑃 𝑑𝑥

Producer surplus = sum of (market price – marginal cost)
𝑄
over all units sold = 0 𝑃 − 𝑀𝐶 𝑑𝑥
Price control #1:
impose a maximum price that is below
the market clearing price
Price control #2:
impose a minimum price that is above
the market clearing price
Regulating price away from free-market
price (in either direction) will introduce
some deadweight loss.
Exercise:
Demand: P=100-Q
 Supply: P=1+2Q
 Calculate market price, quantity sold,
consumer surplus, producer surplus and
total welfare
 Suppose the government imposes a price
ceiling of $50. How would market price,
quantity sold, consumer surplus, producer
surplus and total welfare change? How
much is the dead weight loss?

More about price regulation
Price regulation will distort the market and generate
dead weight loss in total welfare
 Price regulation will also generate a redistribution
between consumers and producers
 What if you care more about consumer surplus than
about producer surplus?
◦ Lower price may lead consumers to suffer a net loss
if the demand is sufficiently inelastic

With price ceiling,
new CS=old CS-B+A
Example:
the market of kidney and the National
Organ Transplantation Act
Market clearing price is 20,000. The law makes the price zero.
At market price, total welfare=(D+B+…)+(A+C)
At regulated price, total welfare=(D+.A+..)+0
Other regulations: supply restriction
Limited taxi licenses
 Trade barriers

At world price, buy
Qs from domestic,
and import Qd-Qs
If import is not
allowed, price rises
to P0
How much is the
deadweight loss?
How much is the loss
of consumer
surplus?
What if there is an import quota?
At world price, buy
Qs from domestic,
and import Qd-Qs
If import is only
allowed up to the
quota, price rises to
P*
How much is the
deadweight loss?
How much is the loss
of consumer
surplus?
What about domestic
and foreign
producers?
What about we impose a lump sum
tax on gasoline?
Changes in CS?
Changes in PS?
Gov revenue?
Impact of tax depend on demand
and supply elasticity
Lecture 19 Exchange economy
Edgeworth box
 Determination of trade price and trade
amount
 Contract curve
 Textbook: Chapter 16

Edgeworth box
2 individuals
 No production, exchange only
 Every one is price taker

Contract curve
Pareto optimal (pareto efficient)
There is no way to make one better off
and the others not worse off
 Every point on the contract curve is
pareto optimal.

Competitive equilibrium
Example: Handout
Two individuals: A and B
 Two goods: X and Y
 Endowment: each one has 5 unites of X
and 5 units of Y
 Utility: UA=XA*YA, UB=XB2*YB.
 Question: is there a trade? How much to
trade? Market price?

Lecture 20
First welfare theorem
 Reasons for market failure
 Monopoly: Marginal revenue = MC
 Monoposony: Marginal expenditure = MC

First theorem of welfare economics:
Competitive equilibrium is the best!
 More formally, textbook Page 597:

◦ If everyone trades in the competitive
marketplace, all mutually beneficial trades will
be completed and the resulting equilibrium
allocation of resources will be economically
efficient.
Three reasons for market failure

Market power: some party is not price
taker
◦ Monopoly: one seller, non price taker
◦ Monoposony: one buyer, non price taker
Asymmetric information
 Externality

Monopoly
Keep market demand as given
 A single seller (or a group of colluding
sellers)
 Maximize profit by choosing output

𝜋 = 𝑝 𝑞 ∙ 𝑞 − 𝑇𝐶(𝑞)
Total revenue
Total cost
• First order condition:
𝑀𝑅 = 𝑝 + 𝑝′ 𝑞 ∙ 𝑞 = 𝑀𝐶
Marginal revenue < price
 restrict supply
Monopoly choice
competitive choice
MC
The Principle of Monopoly pricing

𝑀𝑅 = 𝑝
𝑝 1+

𝑑𝑝
+
𝑑𝑞
𝑑𝑝
𝑝
𝑑𝑞
𝑞
∙𝑞 =𝑝 1+
=𝑝 1
1
+
𝜀
𝑑𝑝 𝑞
∙
𝑑𝑞 𝑝
=
= 𝑀𝐶
Rewrite it, we get
𝑝 − 𝑀𝐶
1
=−
𝑝
𝜀
Mark up
Inverse of demand elasticity
This implies:

The more elastic the demand is, the lower
the monopoly mark up.
◦ Demand elasticity limits the monopolist’s
market power

Monopolist will always choose to operate
at an elastic part of the demand curve.
Example
Demand: P=100-Q
 Total cost: TC = 20+4Q
 Competitive P and Q?
 Monopoly P and Q? Demand elasticity at
this point? Confirm the Lerner rule.
 Loss of CS due to monopoly?
 Change of PS due to monopoly?
 Total welfare changes?

Exercise:
Drug innovation needs FC=5 billion
 Demand per month P=100-0.0001Q
 Marginal cost =$2
 If we grant X years of monopoly power
for the inventor, what should X be?

Lecture 21 Price discrimination

Price discrimination – the practice of selling a
particular good at different prices to groups
with different valuations.

When does price discrimination occur?
1. The seller has some market power (i.e. facing
downward demand)
2. Sellers can distinguish different types of consumers
3. No arbitrage
Types of Price discrimination
◦ 1st degree
 charge each consumer their maximum willingness
to pay
◦ 2nd degree
 don’t know who is willing to pay more, offer a menu
of deals to sort out consumers
◦ 3rd degree: offer
 different prices according to consumers’ observable
attributes (age, gender, …)
Can you think of examples for each?
Third degree of price discrimination

Two types of demand:
𝑝1 = 𝑓1 𝑞1
𝑝2 = 𝑓2 𝑞2

Monopolist’s profit:
𝜋 = 𝑝1 𝑞1 + 𝑝2 𝑞2 − 𝑇𝐶 𝑞1 + 𝑞2

Profit maximization leads to:
𝑀𝑅1 = 𝑀𝑅2 = 𝑀𝐶
Third degree of price discrimination
Profit maximization leads to:
𝑀𝑅1 = 𝑀𝑅2 = 𝑀𝐶
 Which type of consumers get charged
more?


Who benefits from price discrimination?

Who loses?
Example: Chapter 11, Exercise 8
Sal’s satellite company broadcasts TV to
subscribers in Los Angeles and New York. The
demand functions for each group are:
 𝑄𝑁𝑌 = 60 − 0.25𝑃𝑁𝑌
 𝑄𝐿𝐴 = 100 − 0.50𝑃𝐿𝐴
 Cost of production:
𝐶 = 100 + 40𝑄 𝑤ℎ𝑒𝑟𝑒 𝑄 = 𝑄𝐿𝐴 + 𝑄𝑁𝑌
 Price and quantity with price discrimination?
 What if the firm must charge the same price for
NY and LA?

Recap on competitive equilibrium and monopoly

Competitive equilibrium:
◦ Both sellers and buyers are price-takers
◦ Demand = supply
◦ P=MC

Monopoly
◦ Buyers are price takers, but the seller is not
◦ MR=MC>P
◦ Seller has market power, will push price up to
consumer willingness to pay (i.e. the demand
curve)
Lecture 22 Monoposony


Monopoly
◦ one seller vs. competitive buyers
◦ The seller realizes his power to set market price
◦ This power is only useful when demand is
downward sloping (rather than horizontal)
Monopsony:
◦ one buyer vs. competitive sellers
◦ The buyer realizes his power to set market price
◦ This power is only useful when supply is upward
sloping (rather than horizontal)
Mathematically

Monopsony tries to maximize
𝑁𝑒𝑡 𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠 𝑓𝑟𝑜𝑚 𝑏𝑢𝑦𝑖𝑛𝑔 𝑞
= 𝑇𝑜𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑞 − 𝑇𝑜𝑡𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑞
= sum of WTP for each unit − p ∙ 𝑞

First order condition:
𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑞 = 𝑚𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑞
Willingness to pay for the
marginal unit of q =
inverse demand p(q)
𝑑[𝑝 ∙ 𝑞] 𝑑[𝑀𝐶(𝑞) ∙ 𝑞]
=
𝑑𝑞
𝑑𝑞
𝑑𝑀𝐶(𝑞)
= 𝑀𝐶 +
∙𝑞
𝑑𝑞
> 𝑀𝐶 if MC is upward sloping
 inverse demand p(q) = 𝑀𝐶
𝑑𝑀𝐶(𝑞)
+
𝑑𝑞
∙𝑞
Graphically
-> marginal
expenditure >MC
-> supply
curve MC
-> demand
curve
Compare monopsony with monopoly
Monopoly
pushes price to
demand curve
Monopsony
pushes price to
supply curve
Monopoly is
more powerful
if demand is
inelastic
Monopsony is
more powerful
if supply is
inelastic
Monopsony leads to dead weight loss
Exercise:






Walmart is a monopsony of apparel in China. There
are many sellers of apparel in China.
Based on US demand for apparel, Walmart is willing
to pay P=500-0.1Q for Q units of apparel.
The supply of apparel is P=80+0.2Q
Calculate P and Q in competitive equilibrium
Calculate P and Q in monopsony equilibrium
Welfare consequence of monopsony
Lectures 23 and 24
Imperfect competition

Recall conditions for perfect competition
◦ Homogenous goods
◦ Every one is price taker
◦ Free entry and exit
We talked about two extremes: perfect
competition and monopoly (monopsony)
 Between the two extremes:

◦ Monopolistic competition
◦ Oligopoly
Monopolistic competition
large number of small firms
 freedom of entry and exit
 perfect info
 Differentiated products
What does this imply?
1. Every firm faces downward sloping
demand  have some power is setting
price above MC
2. Every firm earns zero economic profit

Monopolistic competition in shortrun and long-run
Short run
Long run
Inefficiency in monopolistic
competition

Downward sloping demand  market
power to set price above MC  dead
weight loss

P>MC and Zero profit in the long run 
operate at AC>MC  extra capacity,
economy of scale not fully exploited
Oligopoly

a market structure in which
◦ a small number of firms serve market
demand.
◦ The industry is characterized by limited entry.
◦ Homogenous goods

Simplest case
◦ duopoly (i.e. only two sellers)
◦ Each aware of the existence of the other firm
◦ Compete instead of collude  each firm has
market power less than monopolist

Examples?
Nash Equilibrium
Each firm is doing the best it can given
what its competitors are doing.
 No one has incentive to deviate at the
equilibrium

Cournot model of Duopoly
Two profit maximizing firms produce the
same goods (e.g. gasoline)
 Both firms try to set its own output
separately and simultaneously
 each firm treats the output level of its
competitor as fixed when deciding its
own output

Solve Cournot equilibrium
Reaction curves:
 𝑄1 = 𝑓1 𝑄2 , 𝑄2 = 𝑓2 𝑄1

Example: textbook p453
Market demand: P=30-Q
 MC=0 for both firms
 How much to produce in Cournot
equilibrium? What is the market price?
 What if the two firms collude so they
together act like a monopolist?
 Compare these two cases with
competitive equilibrium

Cournot: firm 1’s point of view
𝜋1 = 𝑃 ∙ 𝑄1 − 𝐶1 = (30 − 𝑄1 - 𝑄2 ) ∙ 𝑄1 − 0
First order condition with respect to Q1
while taking Q2 as given:
𝑑𝜋1
= 30 − 2𝑄1 − 𝑄2 = 0
𝑑𝑄1
Firm 1’s reaction curve:
𝑄1 = 15 − 𝑄2 /2
Cournot: firm 2’s point of view
𝜋2 = 𝑃 ∙ 𝑄2 − 𝐶2 = (30 − 𝑄1 - 𝑄2 ) ∙ 𝑄2 − 0
First order condition with respect to Q2
while taking Q1 as given:
𝑑𝜋2
= 30 − 𝑄1 − 2𝑄2 = 0
𝑑𝑄2
Firm 1’s reaction curve:
𝑄2 = 15 − 𝑄1 /2
Put the two together:
𝑄1 = 15 − 𝑄2 /2
𝑄2 = 15 − 𝑄1 /2
𝑄1 = 𝑄2 = 10
 𝑃 = 30 − 𝑄 = 30 − 10 + 10 = 10

Compare to monopoly if the two
firms collude
MR=P+P’(Q)*Q=30-Q-Q=30-2Q
 MR=MC  30-2Q=0  Q=15
 The two firms together produce 15, so
each produce 7.5.
 P=30-Q=15.

Compare to perfect competition

P=MC  30-Q=0  Q=30, P=0.
Graphically
Variation 1: What if the two firms do not
choose output simultaneously?

Stackelberg model:
◦ One firm sets its output before other firms
do.  first move advantage

Difference between Cournot and
Stackelberg models
◦ The leading firm will consider how the other
firms adjust output according to his choice of
output
Continue the previous example
Demand: P=30-Q, MC=0 for both firms
 Firm 1 chooses Q1 first, firm 2 chooses
Q2 next
 Firm 2’s best choice of Q2 given Q1 
firm 2’s reaction curve 𝑄2 = 15 − 𝑄1 /2
 Firm 1 anticipates firm 2’s reaction curve
 𝜋1 = 𝑃 ∙ 𝑄1 − 𝐶1 = (30 − 𝑄1 - 𝑄2 ) ∙ 𝑄1 −
0 = (30 − 𝑄1 -15 + 𝑄1 /2) ∙ 𝑄1
 First order condition: 15 − 𝑄1 =0
 𝑄1 = 15, 𝑄2 = 7.5, 𝑃 = 7.5.

Variation 2: What if the two firms choose price
instead of output simultaneously?
Demand: P=30-Q, MC=0 for both firms
 As long as the other firm charges above
MC, this firm has incentive to undercut
 At the end, each charges MC and earns
zero profit!
 This is called Bertrand competition!
 What if the two firms have different cost,
say MC1=10, MC2=0?
  firm 2 takes the whole market, and
charges slightly under 10

Simple Game Theory
Nash Equilibrium: no one has incentive to
deviate given the other parties’ strategy.
 Dominant strategy: it is the player’s best
strategy no matter what strategy the
other players adopt
 Prisoner’s dilemma

Confess
Not confess
Confess
-10, -10
-5, -15
Not confess
-15, -5
-6, -6
Examples of prison’s dilemma
Two firms collude  each has incentive
to secretly cut price or expand output 
collusion is fundamentally unstable
 Any other example?


Pure strategy vs. Mixed strategy
◦ Mixed: randomize between strategies


Example: Inspection game
Detect
Not Detect
Comply
-5,-5
-5,0
Not comply
-10, 5
0, 0
No pure strategy equilibrium, the only
equilibrium is 50% probability detect, 50%
probability comply
Lecture 25 Asymmetric Information

Adverse Selection
◦ Problem
◦ solution

Moral Hazard
◦ Problem
◦ Solution

Adverse selection and Moral Hazard
Recall: Reasons for market failure

Imperfect competition
◦ Monopoly, monopsony, oligopoly,
◦ monopolistic competition

Asymmetric information
◦ Situation in which a buyer and a seller possess
different information about a transaction.

Externality
The market for lemons
Suppose used car quality is uniformly
distributed between 0 (completely
dysfunctional) and 1 (same as brand new)
 Suppose a typical buyer is willing to pay X
for quality X.
 Problem: the buyer cannot observe car
quality before purchase (no test drive….)

0
0.25
0.5
1
Adverse selection
Cause: Products of different qualities are
sold at a single price because sellers
observe product quality but buyers do
not
 Consequence: too much of the low
quality product (so called “lemons”) and
too little of the high quality product (so
called “peaches”) are sold.
 Other examples?

Solutions to adverse selection

Return and warranty
◦ Blanket return policy
◦ Hyundai offers 10-year warranty

Signaling
◦ workers may signal their ability by education

Reputation
◦ Reputable restaurants (e.g. McDonald) have
more to lose if they cheat

Third party certification
◦ Unraveling results
Moral hazard
One party engage in hidden actions
 This action affects the probability or
magnitude of a payment associated with
an event
 Example: principal-agent problem

Solutions to principal-agent problem
Close monitoring
 Incentive contract

◦ Textbook example: revenue from making watches
Bad Luck (50%)
Good Luck (50%)
Low effort (a=0)
$10,000
$20,000
High effort (a=1)
$20,000
$40,000
◦ Cost of low effort=0, cost of high effort=10,000
◦ What kind of contract can solicit high effort?
Incentive contract







Any fixed wage does not yield high effort.
Let wage conditional on revenue.
Consider: w=max(R-18000,0)
At low effort, expected wage is 0*0.5+(2000018000)*0.5=1000
At high effort, expected wage is (2000018000)*0.5+(40000-18000)*0.5=12000
The net gain to the worker with high effort = 1200010000=2000>1000, so the worker will commit to
high effort
When the worker engages in high effort, the
principal’s net gain = 20000*0.5+40000*0.512000=18000.
Adverse selection and moral hazard

They are different
◦ Adverse selection: info asymmetry before
contract
◦ Moral hazard: info asymmetry after contract

They can co-exist
◦ Unsecured consumer credit
◦ Insurance
◦ Employment
Lecture 26: Externality
Definition
 Negative externality
 Positive externality
 Solutions

Externality

Definition:
◦ Action by either a producer or a consumer
which affects other producers or consumers
but is not accounted for in the market price

Negative externality
◦ Examples?

Positive externality
◦ Examples?
Inefficiency of negative externality
MC: marginal cost facing the producer
 MSC: marginal social cost of production facing
the whole society
 MSC-MC=marginal external cost
 Externality  over production

Solution

Restrict production in light of negative
externality
◦ Emission standard
◦ How can EPA know the optimal standard?
◦ Enforcement cost is high
Charge emission fee
 Tradeable emissions permits

Example: Chapter 18 Exercise #6
Demand for paper: Qd=160,000-2000P
 Supply for paper: Qs=40,000+2000P
 Marginal external cost of effluent
dumpting: MEC=0.0006Qs
 Calculate P and Q assumption no
regulation on the dumping of effluent.
 Determine the socially efficient P and Q.

Inefficiency of positive externality




Consider home repair and landscaping
MB=Marginal benefits for the home owner
Marginal social benefits=MB+marginal external
benefit for neighbors
Positive externality  under provision of public
goods
Public goods




Definition: the marginal cost of provision to an
additional consumer is zero and people cannot be
excluded from consuming it
Two properties:
◦ Nonrival: zero cost to additional consumers
◦ Nonexclusive: cannot exclude people from using
the public goods
Examples: national defense, light house, air quality,
information
Private provision of public goods suffers from the
free-riding problem
A comprehensive example
Stephen J. Dubner and Steven D. Levitt’s
blog on 4/20/2008 titled “Not so-free
ride”
 http://www.nytimes.com/2008/04/20/maga
zine/20wwln-freakonomicst.html?pagewanted=1

Course overview

Three main blocks
◦ Consumer’s problem
◦ Producer’s problem
◦ Market equilibrium

Extras
◦ uncertainty, game theory, asymmetric
information, externality

The review below focuses on the most
basic points that you should master, it is
not meant to be exhaustive of all
materials subject to testing
Consumer’s problem







Utility function
Budget constraint
Write out and solve consumer’s utility maximization
problem
How does consumer choice change in response to
changes in price or income?
Derive individual demand and market demand
Calculate demand elasticity
Special cases: perfect substitutes and perfect
complements
Producer’s problem
Production function and related concepts
 Solve firm’s cost minimization problem
 How does firm’s choice change in light of
production change or input price change?
 Cost function and related concepts
 Derive individual and market supply in
perfect equilibrium

Market equilibrium
Perfect competition (demand = supply,
price=MR=MC)
 2-person exchange economy (Edgeworth
box)
 Monopoly (MR=MC<price)

◦ uniform pricing, price discrimination
Monoposony (ME=WTP>Price)
 Duopoly (Cournot, Bertrand,
Stackelberg)
 Monopolistic competition

Extras




Uncertainty
◦ Expected value, expected utility and risk preferences
Simple game theory
◦ Concept of Nash Equilibrium, dominant strategy,
mixed strategy
◦ Simple examples in class
Asymmetric Information
◦ Adverse selection
◦ Moral hazard
Externality
◦ Negative externality
◦ Positive externality, public goods, free-riding
Course evaluation please

CourseEvalUM.umd.edu OPEN in
the last two weeks of the semester
Thank you!