2015 Summer II _ ECO 3320
Due on 7/31/2015
Chapter 9 HW
Name____________________________
R#____________________
Formulas: Oligopoly market (assume two firms)
Given a demand Function: P=a-b(Q1+Q2). Cost functions: C1(Q1)=c1Q1, C2(Q2)= c2Q2.
Cournot
Collusion
Stackelberg
Reaction function
Firm 1 output
Firm 2 output
𝑎 − 𝑐1 1
𝑎 − 𝑐2 1
𝑄1 =
− 𝑄2
𝑄2 =
− 𝑄1
2𝑏
2
2𝑏
2
𝑎−𝑐
𝑎−𝑐
𝑄1 =
𝑄2 =
4𝑏
4𝑏
𝑎 + 𝑐2 − 2𝑐1
𝑎 − 𝑐2 1
𝑄1 =
𝑄2 =
− 𝑄1
2𝑏
2𝑏
2
Q1: The market demand curve is P=50-(Q1+Q2). Cost functions: C1(Q1)=2Q1, C2(Q2)= 2Q2.
Marginal Cost functions: MC1(Q1)=2, MC2(Q2)= 2.
a. Show the reaction functions for each firm in the Cournot.
b. Show the reaction functions for each firm in the Stackelberg model.
c. Calculate each firms’ output level, profit and market price in each different Oligopoly
markets (Cournot, Collusion, Stackelberg and Betrand). Then compare each market price
and output level for each firm.
a. a=50, 𝒄𝟏 = 𝒄𝟐 = 𝟐 𝒂𝒏𝒅 𝒃 = 𝟏
Firm One’s best response function: Q1=24- ½ Q2
Firm Two’s best response function: Q2=24- ½ Q1
b.Firm One’s best response function: Q1=24
Firm Two’s best response function: Q2=24- ½ Q1
c. Cournot model: two firms have same marginal cost, therefore they produce same amount
in the equilibrium Q2=Q1; Use Firm One’s reaction function Q1=24- ½ Q1
Q1=Q2=16 P=18 Firm One’s profit=256, Firm Two’s profit=256
Collusion Model: Q1=Q2=12 P=26 Each firm’s profit=288
Stackelberg Model: Q1=24, Q2=12 P=14
Firm One’s profit=288, Firm Two’s profit=144
Betrand Model: P=MC=2 Q=48 Q1=Q2=24 Each firm’s profit is zero
1
Q2. Consider a market consisting of two firms where the inverse demand curve is given by P =
500 - 2Q1 - 2Q2. Each firm has a marginal cost of $50. Based on this information, we can
conclude that equilibrium price in the different oligopoly models will follow which of the
following orderings?
A. PBertrand < PStackelberg < PCournot < PCollusion
B. PStackelberg < PCollusion < PCournot < PBertrand
C. PCollusion < PCournot < PStackelberg < PBertrand
D. PBertrand < PCournot < PStackelberg < PCollusion
Q3. Which of the following are quantity-setting oligopoly models?
A. Stackelberg.
B. Cournot.
C. Bertrand.
D. Stackelberg and Cournot.
Q4. With linear demand and constant marginal cost, a Stackelberg leader's profits are
___________ the follower.
A. less than
B. equal to
C. greater than
D. either less than or greater than
Q5. If firms compete in a Cournot fashion, then each firm views the:
A. output of rivals as given.
B. prices of rivals as given.
C. profits of rivals as given.
D. All of the statements associated with this question are correct.
Q6. The Bertrand model of oligopoly reveals that:
A. capacity constraints are not important in determining market performance.
B. perfectly competitive prices can arise in markets with only a few firms.
C. changes in marginal cost do not affect prices.
D. All of the statements associated with this question are true.
Q7. A new firm enters a market which is initially serviced by a Bertrand duopoly charging a
price of $20. What will the new price be should the three firms coexist after the entry?
A. $25
B. $20
C. $15
D. None of the answers is correct.
2