Economics 100B Microeconomics

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Economics 100BMicroeconomics
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Announcements

• Midterms can be picked up in my office during
  office hours (Th 12-1.30)

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Course Outline
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Todays Plan (Chapter 14)

• Basic Model
• Cartel Model
• Cournot Model

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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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I. 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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II. 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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III. 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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Assignment

• Read Nicholson Chapter 14