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##### Econ-UA 353 HW #3

**Description**

solution.

**Question**

Econ-UA 353 HW #3

Due at the beginning of class on Monday Dec 8

Late homeworks will NOT be accepted

Question 1. Firm A is the sole producer of a sport drink. A’s marginal cost

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

inverse demand function P = 120 ? 0.5Q.

(a) Suppose A produces quantity q = 120 units at price p = 60. Is there any

dead weight loss at current price and quantity? If yes, how much is the DWL?

(b) What is the monopoly price? What is the monopoly DWL?

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: produce

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

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.

1Question 3. Two firms produce candies that are imperfect substitutes. This

is reflected in the demand curves of the two firms’ candies, D1(p1, p2) = 100 ?

p1 + 0.5p2 and D2(p1, p2) = 100 ? p2 + 0.5p1. Suppose each firm has constant

marginal cost of 20.

(a) Interpret the demand curves, in particular, explain from the demand curves

why the candies produced by the two firms are imperfect substitutes.

(b) Suppose the two firms compete by making simultaneous price decisions.

Calculate the equilibrium price, quantity and profit for each firm.

(c) Suppose the two firms compete by making sequential price decisions, where

firm 1 is the leader. Calculate the equilibrium price, quantity and profit for

each firm. Compare the profits of the leader vs. the follower and explain.

Question 4. Suppose an industry has ten firms. The market shares of each

firm are: 25%, 15%, 10%, 10%, 8%, 8%, 7%, 7%, 5% and 5%.

(a) What is the four-firm concentration ratio?

(b) What is the Herfindahl-Hirschman Index?

(c) According to the merger guidelines, if the HHI is in the range of 1000-1800

after a merger, you will not allow the merger if it increased the HHI by 100

points or more. Would you allow a merger between the 2 firms that had 5%

market share each? Would you allow a merger between the 2 firms that had 8%

market share each?

(d) Suppose the ten firms compete in a Cournot oligopoly in this industry, and

the current price elasticity of demand is -0.8. What are the profit margins for

each of the four biggest firms? What is the average profit margin (weighted by

each firm’s market share) of this industry?

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