Exercise 1. Suppose there are n identical firms in a market in long-run. Each firm's cost function is given by C = 32 + 0.5q2, where q is the amount that an individual firm produces. This means that an individual firm's marginal cost is given by MC = q. Also, the market demand is given by P = 96 - 2Q, where Q is the total amount of the good produced by all of the firms combined. Therefore, Q = n · q.
(a) How much output will each of them produce?
(b) What will be the market price?
(c) How many firms operate in long run? That is find n.
(d) What is the value of consumer surplus?
(e) What is the individual firm's supply curve? (f) What is the market supply curve?
Exercise 2. (Constant Marginal Cost) Suppose a monopolist faces the following demand curve: P = 100 - 2Q. The marginal cost of monopolist is constant and equals to 20 and fixed cost equals to 0.
(a) What is the monopolist's profit maximizing level of output?
(b) What price will the profit maximizing monopolist charge?
(c) What is the value of consumer surplus under monopoly?
(d) What is the value of producer surplus under monopoly?
(e) What is the value of deadweight loss?
(f) What is the value of consumer surplus if the market was perfectly competitive?
Exercise 3. Suppose that two players Ann and Bill are playing simultaneous move game. Ann is a row player who has two actions U and D. Bill is a column player who has two actions L and R. The payoffs are given in the following table (the first number corresponds to Ann's payoff and the second to Bill's payoff):
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L
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R
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U
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1, 1
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4, 2
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D
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2, 3
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2, 4
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(a) Does Ann have a dominant strategy, and if so what is it?
(b) Does Bill have a dominant strategy, and if so what is it?
(c) Find Nash equilibrium of the game (for this game is unique).
(d) Is Nash equilibrium found in part c) Pareto Efficient? Explain.
(e) Suppose the game changed: Ann chooses her action first and then Bill chooses his action. Using the backward induction method we discussed in class, what will be the outcome of the game?
(f) Suppose the game changed: Bill chooses his action first and then Ann chooses her action. Using the backward induction method we discussed in class, what will be the outcome of the game?