Public Economics

Econ-UA 353 Section003 HW #3

Due 5PM Monday May 13, to the box outside my office (Room 603,

Econ building), late homeworks will NOT be accepted

Question 1. Firm A is the sole supplier of a certain product. A’s marginal

cost equals average cost MC = AC = 30, and it faces market demand given by

inverse demand function P = 120 − 0.5Q. Suppose at the moment A produces quantity q = 120 units at price p = 60.

(a) Does firm A maximizes profit at current price and quantity? Explain.

(b) Is there any dead weight loss at current price and quantity? How much?

(c) What is the monopoly dead weight loss?

Question 2. The inverse market demand for mineral water is P = 200 − 10Q, where Q is total market output and P is the market price. Two firms have

complete control of the supply of mineral water and both have zero costs.

(a) Find the Cournot quantity, price, and each firm’s profit.

(b) Denote the Cournot quantity for each firm by qa, and denote half of the

monopoly quantity by qb. Suppose that the two firms interact with each other

for infinite periods, and in each period they choose quantities simultaneously.

Consider the following collusive strategy, the same as discussed in class: pro-

duce qb only if no one has cheated so far, and to produce qa forever if some

has cheated before. Assume each firm acts to maximize its sum of discounted

profits where the interest rate is r. Find the values for r such that this collusive

strategy is a Nash equilibrium, namely, for what values of r can the monopoly

profits be sustained through collusion?

(c) Find the Bertrand price, quantity, and each firm’s profit.

(d) Denote the Bertrand price by pa, and denote the monopoly price by pb.

Suppose that the two firms interact with each other for infinite periods, and

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in each period they set prices simultaneously. Consider the following collusive

strategy, the same as discussed in class: set price pb only if no one has cheated

so far, and to set price pa forever if some has cheated before. Assume each firm

acts to maximize its sum of discounted profits where the interest rate is r. Find

the values for r such that this collusive strategy is a Nash equilibrium, namely,

for what values of r can the monopoly profits be sustained through collusion?

Compare your answer to (b) and explain.

Question 3. Suppose that an industry has ten firms with market shares of the

following percentages: 25, 15, 12, 10, 10, 8, 7, 5, 5 and 3.

(i) Derive the four-firm concentration ratio.

(ii) Derive the HHI.

(iii) Derive the effect of a merger between the fifth and sixth largest firms on

the HHI.

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