Question 1.
The inverse market demand for mineral water is P = 200 10Q, where Q is total market output and P is the market price. Two rms have complete control of the supply of mineral water and both have zero costs.
(a) Find the Cournot quantity, price, and each rm's pro t.
(b) Denote the Cournot quantity for each rm by qa, and denote half of the monopoly quantity by qb. Suppose that the two rms interact with each other for in nite 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 rm acts to maximize its sum of discounted pro ts 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 pro ts be sustained through collusion?
(c) Find the Bertrand price, quantity, and each rm's pro t.
(d) Denote the Bertrand price by pa, and denote the monopoly price by pb. Suppose that the two rms interact with each other for in nite 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 rm acts to maximize its sum of discounted pro ts 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 pro ts be sustained through collusion?
Compare your answer to (b) and explain.
Question 2.
Suppose that an industry has ten rms with market shares of the following percentages: 25, 15, 12, 10, 10, 8, 7, 5, 5 and 3.
(i) Derive the four- rm concentration ratio.
(ii) Derive the HHI.
(iii) Derive the e ect of a merger between the fth and sixth largest rms on the HHI.