Economics 100B Microeconomics

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Economics 100BMicroeconomics
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Announcements

• Recall
• Midterm on Monday, February 13 (class time)
• Additional link to the course website
• http//www.princeton.edu/costinot/100B/100B.htm
• New on the course website
• Solution to Problem Set 3
• Problem Set 4 (solution will be posted Friday,
  February 10)
• Additional office hours this week check
  Updates on the course website

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Course Outline
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Todays Plan

• Monopoly (Chapter 13)
• Review for Midterm
• Oligopoly (Chapter 14)

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I. Monopoly

• Monopoly profit maximization (pp387-391)
• Monopoly and welfare (pp387-391)
• Price discrimination (pp397-404)
• Regulation of monopoly (pp404-407)

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A. Profits Maximization

• How does a monopolist behave to maximize profit?

Price
P1P(Q1)
D
Quantity
Q1Q(P1)
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Monopoly Profits

• Profit Revenue - Cost

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Profits Maximization (math)

• Choose the quantity to maximize profit

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Profits Maximization (graphical)
MC
Price
AC
D
MR
Quantity
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Monopoly Mark-up

• Elasticity of demand

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Monopoly Mark-up

• Assume C(Q) cQ
• Choose price to maximize profit

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Monopoly Mark-up

• First-order condition

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The Inverse Elasticity Rule

• The percent mark-up over marginal cost is
  inversely related to the elasticity of demand

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The Inverse Elasticity Rule

• A monopolist will choose to operate only in
  regions where the market demand curve is elastic

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Elasticity of Demand
Price
Is D or D' more elastic?
Has demand become more or less elastic if demand
increases from D to D''?
P
D''
D
D'
Quantity
Q
Q''
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Example with Linear Demand

• Consumer demand q100-(1/2)p
• Monopolists cost function c(q)q225

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B. Monopoly and Welfare

• Monopolies are associated with inefficient
  production

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Welfare Analysis
Price
Competitive market outcome (Q,P)
P
Monopoly outcome (Q,P)
MCAC
P
D
MR
Q
Q
Quantity
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Deadweight Loss
Price
Consumer surplus would fall
Producer surplus will rise
P
There is deadweight loss
MCAC
P
D
MR
Q
Q
Quantity
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C. Price Discrimination

• A monopoly may be able to increase profits
  through price discrimination charging different
  prices to different buyers
• Only feasible if can prevent arbitrage among
  buyers

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Perfect (first-degree) Price Discrimination

• The monopolist charges each buyer the maximum
  price he/she is willing to pay
• extracts all consumer surplus
• no deadweight loss

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Perfect Price Discrimination
The first buyer pays P1 for Q1 units
Price
The second buyer pays P2 for Q2-Q1 units
P1
P2
Continues until the marginal buyer is no longer
willing to pay the goods marginal cost
MC
D
Quantity
Q
Q1
Q2
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Third-degree Price Discrimination

• The monopolist separates its buyers into a few
  identifiable markets
• follows a different pricing policy in each market

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Third-degree Price Discrimination

• If the marginal cost is the same in all markets,

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Third-degree Price Discrimination
Price
The market with the less elastic demand will be
charged the higher price
P1
P2
MC
MC
D
D
MR
MR
Quantity in Market 2
Quantity in Market 1
Q2
Q1
0
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Third-degree Price Discrimination

• Profitability of the practice
• Example
• C(q) 800 4q
• q1 1000 100p1
• q2 1600 200p2

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Third-degree Price Discrimination

• Ambiguous welfare consequences relative to a
  single price policy

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Second-degree Price Discrimination

• Charge different prices for different quantities
• price schedule provides incentives for demanders
  to separate themselves according to how much they
  wish to buy

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Two-part Tariffs

• Buyers pay a fixed fee for the right to consume a
  good and a uniform price for each unit consumed
• T(q) a pq

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Two-part Tariffs

• Only feasible if those who pay low average prices
  cannot resell the good to those who must pay high
  average prices
• p' T/q a/q p

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Two-part Tariffs

• One feasible approach
• set p MC
• set a equal to the consumer surplus of the least
  eager buyer

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Two-part Tariffs

• Suppose there are two different buyers with the
  demand functions
• q1 24 - p1
• q2 24 - 2p2
• Could implement a two-part tariff by setting
• p1 p2 MC 6

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D. Regulation of Monopoly

• Governments often create and then regulate
  natural monopolies
• Trade-off Cost-efficiency versus Pareto
  inefficient output level

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Marginal Cost Pricing

• Require the firm to produce the socially-optimal
  output level and charge a price equal to marginal
  cost
• Problem operating revenues will not cover total
  costs

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Marginal Cost Pricing
An unregulated monopoly will maximize profit at
Q1 and P1
Price
If regulators force the monopoly to charge a
price of P2 and produce Q2, the firm will suffer
a loss
P1
C1
C2
AC
MR
MC
P2
Quantity
D
Q1
Q2
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Multi-price System
Allowed to charge a price of P1 to some users
Price
Other users are offered P2
P1
Profits from high-price sales balance losses on
low-price sales
C1
C2
AC
MC
P2
Quantity
D
Q1
Q2
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Average Cost Pricing

• Allow the monopoly to charge a price above
  marginal cost that is sufficient to earn a fair
  rate of return on investment

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Average Cost Pricing
Price
The equilibrium under average cost pricing would
be at Q3 and P3
P1
C1
P3C3
C2
AC
MR
MC
P2
Quantity
D
Q1
Q2
Q3
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Average Cost Pricing

• Regulator unlikely to have perfect information
  about costs
• Problem low incentives for cost efficiency
• Problem firm may over-capitalize

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Average Cost Pricing

• Suppose that a regulated utility has a production
  function of the form
• q f (k,l)
• The firm rate of return on capital is set by
  regulation to be

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Average Cost Pricing

• The Lagrangian for the firms constrained profit
  maximization problem is
• L pf (k,l) wl vk ?wl s0k pf (k,l)
• The first-order condition for capital is

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Average Cost Pricing

• The firm over-capitalizes
• Because s0gtv and ?lt1, this means that
• pfk lt v

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Dynamic Views of Monopoly

• Monopoly profits can play a beneficial role in
  the process of economic development

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II. Review for Midterm

• Logistics
• Ledden Auditorium, class time
• Exam lasts 90 minutes
• No calculators or other aids allowed
• Bring a blue book (we will reassign blue books
  before the exam)
• Exam is worth a total of 100 points
• Allocate your time wisely

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Topics Covered

• Consumer demand
• Constrained utility maximization
• Firm supply
• Cost minimization
• Profit maximization
• Firm-level supply curve
• Perfectly competitive market equilibrium
• Very short run, short run, long run

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Topics Covered

• Social surplus
• Deadweight loss of interventions
• Taxes
• Price ceilings and floors
• Import tariffs and quotas
• General equilibrium pricing
• In an exchange economy
• In a production economy

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Topics Covered

• Efficiency of perfect competition
• Exchange efficiency
• Technical (production) efficiency
• Product-mix efficiency
• Equity and perfect competition

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Topics Covered

• Monopoly
• Profit maximization
• Monopoly and welfare
• Price discrimination
• Regulation

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III. Oligopoly Pricing of Homogenous Goods

• A relatively small number of firms produce a
  single homogenous product
• Consumers will always choose the lowest price
  product

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Basic Model

• The output of each of n identical firms is
• qi (i1,,n)
• Barriers to entry (n is fixed)
• The inverse demand function depends on the level
  of industry output
• P f(Q) f(q1q2qn)

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Basic Model

• Each firms goal is to choose the quantity to
  produce to maximize profits
• ?i f(Q)qi Ci(qi)
• ?i f(q1q2qn)qi Ci(qi)

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Oligopoly Pricing Models

• Quasi-competitive model assumes price-taking
  behavior by all firms
• P is treated as fixed
• Cartel model assumes that firms can collude
  perfectly in choosing industry output and price

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Oligopoly Pricing Models

• Cournot model assumes that firm i treats firm j
  s output as fixed in its decisions
• ?qj /?qi 0
• Conjectural variations model assumes that firm
  js output will respond to variations in firm is
  output
• ?qj /?qi ? 0

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A. Cartel Model

• Assumes that firms coordinate their decisions so
  as to achieve monopoly profits

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Cartel Model

• Cartel chooses qi for each firm so as to maximize
  total industry profits

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Cartel Model

• The first-order conditions for a maximum are that

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Cartel Model
Price
MC
D
MR
Quantity
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Cartel Model

• Three problems with the cartel solution
• monopolistic decisions may be illegal
• large informational requirement
• unstable
• each firm has an incentive to expand output
  because MRi gt MCi

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Duopoly Example

• Assume the following
• Inverse demand curve f(Q) P 1 Q
• Firm 1s cost function C(q1) 0
• Firm 2s cost function C(q2) 0
• Total output Q q1 q2

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Duopoly Example

• Cartel solution
• Firms maximize joint profits

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Duopoly Example

• Cartel solution
• Profits under equal division

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Duopoly Example

• Cartel solution
• Incentive to expand output

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B. Cournot Model

• Firms make quantity choices simultaneously and
  independently

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Cournot Model

• Each firm recognizes that its own decisions about
  qi affect price
• ?P/?qi ? 0
• Each firm believes that its decisions do not
  affect those of any other firm
• ?qj /?qi 0 for all j ?i

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Cournot Model

• The firms profit maximization problem

• The first-order conditions for profit
  maximization are

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Cournot Model

• Each firms output will exceed the cartel output
• the firm-specific marginal revenue is larger than
  the market marginal revenue
• P(Q) qi ? (?P/?qi) gt P(Q) Q ? (?P/?qi)
• Each firms output will fall short of the
  competitive output
• qi ? ?P/?qi lt 0

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Cournot Model
Under the Cournot solution, MRi MCi and an
intermediate output and price (QA , PA ) will
prevail
Price
PM
PA
MC
PC
D
MR
Quantity
QM
QC
QA
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Duopoly Example

• Cournot solution
• The two firms profits are given by
• ?1 P(Q)q1 (1 - q1 - q2)q1
• q1 - q12 - q1q2
• ?2 P(Q)q2 (1 - q1 - q2) q2
• q2 - q22 - q1q2

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Duopoly Example

• Cournot solution

Price
Conditional on a given quantity for firm 2, firm
1 faces the residual demand
1
1-q2
P(Q)1-Q
P(q1q2)1-q1-q2
Quantity
1-q2
1
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Duopoly Example

• Cournot solution
• First-order conditions for a maximum are

• these equations are called reaction functions

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Duopoly Example

• Cournot solution
• In Nash equilibrium (NE), each firm takes the
  action that maximizes its profits given the
  actions of all other firms
• For two firms, (q1, q2) is a NE if
• q1 maximizes p1 given q2
• AND
• q2 maximizes p2 given q1

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Duopoly Example

• Cournot solution

q1
1
q2(q1) (1-q1)/2
1/2
q1(q2) (1-q2)/2
1/2
1
q2
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Duopoly Example

• Cournot solution

q1
Nash equilibrium q1q1(q2) q2q2(q1)
1
q2(q1)
1/2
Nash equilibrium point
q1
q1(q2)
q2
1/2
1
q2
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Duopoly Example

• Cournot solution
• Solve the reaction functions simultaneously

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Duopoly Example
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Duopoly Example

• Cournot solution
• Steps to solve for the Nash equilibrium
• Find inverse demand p(q1q2)
• Write pi p(q1q2)qi - c(qi)
• Maximize profits to obtain reaction functions
  q1(q2) and q2(q1)
• Find the combination of quantities that jointly
  solves these two equations

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C. Conjectural Variations Model

• In markets with only a few firms, we can expect
  there to be strategic interaction among firms
• Consider the assumptions that firm i might make
  about how its decisions affect those of other
  firms
• For each firm i, we are concerned with the
  assumed value of ?qj /?qi for i?j

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Conjectural Variations Model

• The first-order condition for profit maximization
  becomes

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Price Leadership CV Model

• Suppose that the market is composed of a single
  price leader (firm 1) and a fringe of
  quasi-competitors
• firms 2,,n are price takers
• firm 1 has a more complex reaction function that
  takes other firms actions into account

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Price Leadership CV Model
Price
SC
SC represents the supply decisions of all of the
n-1 firms in the competitive fringe
Quantity
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Price Leadership CV Model
The demand for the leader (D) is constructed by
subtracting what the fringe will supply from
total market demand
Price
SC
P1
PL
The leader will set MR MC and produce QL at a
price of PL
D
P2
MC
D
MR
Quantity
QL
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Price Leadership CV Model
Price
Market price will then be PL
SC
P1
The competitive fringe will produce QC and total
industry output will be QT
PL
D
P2
MC
D
MR
Quantity
QL
QC
QT
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Price Leadership CV Model

• This model does not explain how the price leader
  is chosen or what happens if a member of the
  fringe decides to challenge the leader

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Assignment

• Read Nicholson Chapter 14
• Problem Set 4
• Available on the course website
• Solution will be posted on Friday, February 10 in
  order to give you time to study before the
  midterm
• Recall
• Midterm MONDAY, FEBRUARY 13 (class time)