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ECN211G : Intermidate Microeconomics
Problem Set 4 : Oligopoly, Monopolistic Competition
and Game Theory
Exercise 1 :
The market inverse demand function for good X is P = 10-Q. Suppose there are two identical
firms with cost function C(q) = q. Assume the two firms compete a la Cournot (i.e. firms
simultaneously choose quantities).
1. Compute the best response function of each firm and determine the equilibrium quantities produced by each firm and the equilibrium price.
2. Suppose now that the government is considering the introduction of a tax τ = e 3
per unit of production only on firm 2. What would be the impact of the tax on the
equilibrium quantity produced by each firm ? Compute the new equilibrium quantities,
the new equilibrium price and the new profits of each firm.
3. Suppose firm 2 knows that the government is planning to introduce the tax described
above. Suppose also that firm 2 can bribe a government official to prevent the introduction the tax. What is the maximum bribe firm 2 would be willing to pay ? Is this
bigger or smaller than the tax revenues that could be collected with the tax ? Why ?
4. Is firm 1 better off with or without the tax on firm 2’s production ? How about
consumers ? Compute and compare the consumer surplus with and without the tax.
Exercise 2 :
Consider a simplified model of the market for gasoline. There are two potential producers
of gasoline : firm A and firm B. Firm A has a marginal cost of e 40/barrel. Firm B has
discovered a new technology (that firm A does not have) that enables it to produce at a
much lower marginal cost of e 20/barrel. Assume there are no fixed costs. The demand for
gasoline (in barrels per day) in the US is :
Q = 25, 000 − 50P
1. Imagine that firms A and B engage in Cournot competition. What will be the market
clearing price of a barrel of oil ? How much does firm A produce ? How much does
firm B produce ?
2. Now the government starts a new program where they send firm A a check of e
20/barrel for each barrel it produces. (Firm A’s lobbyists successfully convince politicians that this subsidy is required to “help it compete”). What is the new quantity
produced by each firm, and what is the new market-clearing price ?
3. Without doing any math, is it clear whether this subsidy is total welfare enhancing
or reducing ? If yes, explain why. If no, explain why the welfare effects are ambiguous.
4. Imagine that instead of engaging in Cournot competition, firms A and B were Bertand
competing. In the absence of the subsidy, what quantity does each firm produce, and
what is the price of gasoline ?
5. Find firm quantities and the equilibrium price in a Bertrand scenario when a subsidy
of e 20/barrel is provided to firm A. (Assume that firms split the market 50 :50 if
they charge the same price.)
6. Finally, speculate on what would happen if firms A & B merge (and there is no
government subsidy). Why might this be a special case where a merger is total-surplus
Exercise 3 :
The market for widgets is a Cournot duopoly. The market demand for widgets is given by :
Q= 120 – 2P
where Q is total output (Q = Q1 + Q2 , the sum of firm 1’s output, Q1 , and firm 2’s output,
Q2 ). Each firm has a constant marginal cost of 0 of producing widgets.
1. Suppose that the two firms choose output cooperatively in order to maximize joint
profits. What is the resulting total output and price for widgets ? What are the resulting profits for each firm, if they choose the same output ?
2. Solve for the equilibrium choice of Qa , Qb , and the market price P.
3. Suppose that firm 1 decides to defect from the cooperative agreement. What quantity
Q1 would firm 1 choose to produce if firm 2 continues to produce the agreed output
from part (a) ? What are the resulting profits for firm 1 and firm 2 ? Given these
results is the cooperative agreement sustainable ?
4. What are the Cournot Equilibrium (simultaneous move game) output levels Q1 and
Q2 for each firm, and the resulting market price P and firm profits ?
5. Suppose now that firm 1 can choose its output level Q1 before firm 2 chooses Q2.
What are the equilibrium output levels Q1 and Q2 for each firm and the resulting
market price P and firm profits ?
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