Before starting Chapter 9, lets review Chapter 8:

1
Textbook problems from Chapter 8

• Before starting Chapter 9, lets review Chapter
  8
• Problem 11, page 308.
• Chapter 8 covered three market environments.
  Which one describes Pizza Hut?
• Monopoly (just one firm)
• Perfect competition (firms producing perfect
  substitutes)
• Monopolistic competition (firms producing close
  substitutes)
• Problem 15, page 308.
• Chapter 8 covered how the decision to produce
  depends on cost. (In the short-run, definitely
  produce if p gt AVC in the long-run, definitely
  produce if p gt AC.) Does that accounting data
  tell you exactly what you need to know? A full
  answer discusses the difference between fixed
  cost and variable cost.
• Is labor a fixed cost? Variable cost?
• Is depreciation a fixed cost? Variable cost?

2
Lesson overview

• Chapter 9 Basic Oligopoly Models
• Lesson II.3 Managing in Oligopolistic Markets
• When are markets oligopolistic?
• What is strategic interaction?
• Sweezy (kinked-demand) model
• Anticipating current strategies
• Cournot model
• Review Problems
• Lesson II.4 More Oligopolistic Models

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When are markets oligopolistic?

• When are markets oligopolistic?
• Few firms, usually less than 10.
• Duopoly - two firms
• Triopoly - three firms
• The products firms offer can be either
  differentiated (close but not perfect
  substitutes) or homogeneous (perfect
  substitutes).
• Firms decisions affect one another.
• Different strategic variables (quantity, price,
  ) are modeled
• There is no single oligopoly model.
• The model is defined by the environment.

4
Role of Strategic Interaction
Role of Strategic Interaction

• Your actions affect the profits of your rivals.
• Your rivals actions affect your profits.
• Central question How will rivals respond to your
  actions?

5
Role of Strategic Interaction

• An Example
• You and another firm sell differentiated (close
  but not perfect substitute) products. ---
  Example?
• How does the quantity demanded for your product
  change when you change your price?

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Role of Strategic Interaction
D2 (Rival matches your price change)
P
PH
PL
D1 (Rival holds its price constant)
Q
7
Role of Strategic Interaction
Demand if Rivals Match Price Reductions but not
Price Increases
D
8
Role of Strategic Interaction

• General conclusion
• The effect of a price reduction on the quantity
  demanded of your product depends upon whether
  your rivals respond by reducing their prices,
  too.
• The effect of a price increase on the quantity
  demanded of your product depends upon whether
  your rivals respond by increasing their prices,
  too.
• Strategic interdependence You arent in complete
  control of your profit.

9
Sweezy (Kinked-Demand) Model

• Sweezy (Kinked-Demand) Model Environment
• Few firms in the market serving many consumers.
• Firms produce differentiated products.
• Barriers to entry.
• Each firm believes rivals will match (or follow)
  price reductions, but wont match (or follow)
  price increases.
• Unusual implication of Sweezy Model
• Price-Rigidity.

10
Sweezy Demand and Marginal Revenue
Sweezy (Kinked-Demand) Model
P
DS Sweezy Demand
Q
MRS Sweezy MR
11
Sweezy Profit-Maximizing DecisionThe same price
and quantity for a variety of marginal cost.
Sweezy (Kinked-Demand) Model
P
D2 (Rival matches your price change)
D1 (Rival holds price constant)
Q
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Sweezy (Kinked-Demand) Model

• Sweezy Oligopoly Summary
• Firms believe rivals match price cuts, but not
  price increases.
• Firms operating in a Sweezy oligopoly maximize
  profit by producing where
• MRS MC.
• The kinked-shaped marginal revenue curve implies
  that there exists a range over which changes in
  MC will not affect the profit-maximizing level of
  output.
• Therefore, the firm will not change price or
  quantity provided marginal cost remains in a
  given range.

13
Anticipating Current Strategies

• Outcomes of any strategic decisions depend on the
  strategies chosen by your opponents, in
  particular output or pricing decisions made by
  rival firms. So you should predict your
  opponents strategies before you choose your own.
  When your opponents strategies (outputs or
  prices) are chosen at the same time as yours, you
  must predict what your opponent will do now,
  recognizing that your opponent is doing the same.
  How is that possible?

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Anticipating Current Strategies

• Guess 2/3 of the average
• No talking or other communication between
  players.
• Players secretly write a real number between 0
  and 100.
• The winner is the one closest to 2/3 of the
  average.
• The winner in this class gets 1.00. If there is
  a tie, the 1.00 will be evenly divided.
• Why did you choose your particular number?
• Will you play differently next time?

15
Cournot Model

• Cournot Model Environment
• A few firms produce goods that are either
  homogeneous (perfect substitutes) or
  differentiated (close but not perfect
  substitutes).
• Firms decision variable is output, rather than
  price.
• Each firm believes their rivals will hold output
  constant if it changes its own output (The output
  of rivals is viewed as given or fixed).
• For example, firms decide output at the same
  time.
• For example, Walmart and Target simultaneously
  deciding between a regular (low output) and a
  superstore (high output).
• Barriers to entry exist.

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Cournot Model

• Inverse Demand in a Cournot Duopoly
• Linear market demand in a homogeneous-product
  Cournot duopoly is
• P a b(Q1 Q2)
• Thus, each firms marginal revenue depends on the
  output produced by the other firm. Precisely, for
• R1 (a b(Q1 Q2)) Q1
• R2 (a b(Q1 Q2)) Q2
• MR1 dR1 /dQ1 a bQ2 - 2bQ1
• MR2 dR2 /dQ2 a bQ1 - 2bQ2

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Cournot Model

• Best-Response Function
• Since a firms marginal revenue in a homogeneous
  Cournot oligopoly depends on both its output and
  its rivals, each firm needs a way to respond to
  any change in their belief about their rivals
  output decisions.
• Firm 1s best-response (or reaction) function is
  a schedule summarizing the amount of Q1 firm 1
  should produce in order to maximize its profits
  for each quantity of Q2 firm 1 believes will be
  produced by firm 2.
• Since the products are perfect substitutes, an
  increase in firm 2s output leads to a decrease
  in the profit-maximizing amount of firm 1s
  product.

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Cournot Model

• Best-Response Function for a Cournot Duopoly
• To find a firms best-response function, equate
  its marginal revenue to marginal cost and solve
  for its output as a function of its rivals
  output.
• Just consider the simple case of constant
  marginal cost.
• Firm 1s best-response function is (c1 is firm
  1s MC)
• MR1 a bQ2 - 2bQ1 c1 implies
• Firm 2s best-response function is (c2 is firm
  2s MC)

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Graph of Firm 1s Best-Response Function
Cournot Model
Q2
(a-c1)/b
Q2
(Firm 1s Reaction Function)
r1
Q1
Q1M
Q1
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Cournot Model

• Cournot Equilibrium
• When where each firm produces the output that
  maximizes its profits, given the output of rival
  firms.
• No firm can gain by unilaterally changing its own
  output to improve its profit.
• A point where the two firms best-response
  functions intersect.

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Graph of Cournot Equilibrium
Cournot Model
Q2
(a-c1)/b
r1
Numerical Solution Q1 (4/3)(a-c1)/(2b)
(2/3)(a-c2)/(2b) Q2 (4/3)(a-c2)/(2b)
(2/3)(a-c1)/(2b)
Q2M
Q2
r2
Q1
(a-c2)/b
Q1
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How do Firms get to Cournot Equilibrium? Trial
and error.
Cournot Model

• What does Firm 1 think?
• Firm 1 believes Q2 0, and so sets monopoly Q1M
• Firm 1 believes Firm 2 believes Q1 Q1M, and so
  sets Q2 at b. In particular, the belief Q2 0
  is wrong.
• Firm 1 believes Q2 is at b, and so sets Q1 at c
• Firm 1 believes Firm 2 believes Q1 is at c, and
  so sets Q2 at b. And so on.

Q2
(a-c1)/b
r1
Q2M
Q2
d
b
c
r2
Q1
a Q1M
(a-c2)/b
Q1
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Getting to Cournot Equilibrium, by trial and error
Cournot Model

• What does Firm 1 think?
• Eventually, Firm 1 believes Q2 Q2, and so sets
  Q1 Q1
• Firm 1 believes Firm 2 believes Q1 Q1M, and so
  sets Q2 Q2. In particular, the belief Q2
  Q2 is rationalized.
• Likewise, Firm 2s belief Q1 Q1 is also
  rationalized.

Q2
(a-c1)/b
r1
Q2M
Q2
d
b
c
r2
Q1
a Q1M
(a-c2)/b
Q1
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Cournot Model

• Summary of Cournot Equilibrium
• The output Q1 maximizes firm 1s profits, given
  that firm 2 produces Q2.
• The output Q2 maximizes firm 2s profits, given
  that firm 1 produces Q1.
• Neither firm has an incentive to change its
  output, given the output of the rival.
• Beliefs are consistent
• In equilibrium, each firm thinks rivals will
  stick to their current output and they do.

25
Graphing the Effect of Rising Costs on Equilibrium
Cournot Model
Q2
Firm 1s reaction function given c1,
Q1
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Collusion Incentives in Cournot
OligopolyMonopoly profit is higher than the
total of all profits in Cournot Oligopoly, so
there is an incentive for all firms to merge,
either through a legal merger or illegal
collusion.
Cournot Model
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Review Problems

• Question about making predictions with the
  Cournot Duopoly model (should you sell your
  secrets?)
• Exam 2 Version A, Question 3
• http//faculty.pepperdine.edu/jburke2/ba445/Exam2/
  Exam2aAnswers.pdf
• Answer
• Compute and compare profit when c1 1 and c2
  2 with profit when c1 1 and c2 1.

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End of Lesson II.3
BA 445

Managerial Economics