MidPracProbs_ProblemSet

# MidPracProbs_ProblemSet - AEM 331 Practice Problems 1...

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AEM 331 Practice Problems 1. Consider a market with demand: Q = 100 – P. Let marginal costs be 20 if there is perfect competition. However, if there is a monopolist, assume it must pay an additional \$10 per unit of output to reimburse lobbyists for their efforts in persuading legislators to keep the monopoly insulated from competition. a. Calculate the prices and quantities under monopoly and competition. b. Calculate total economic surplus under monopoly and competition. The difference is the social cost of monopoly. c. The social cost of monopoly can be disaggregated into two distinct types of cost: the resources cost of rent seeking and the usual deadweight loss of output restriction. What are their respective magnitudes? 2. The inverse market demand for mineral water is P = 200 – 10*Q, where Q is total market output and P is the market price. Two firms, A and B, have complete control of the supply of mineral water and both have zero costs. a. Find the Cournot solution. b. Find an identical output for each firm that maximizes joint profits. 3. Continuing with problem 2, assume that each firm can choose only two outputs – the ones from parts a and b in question 2. Denote those outputs a q and b q . a. Compute the payoff/profit matrix showing the four possible outcomes (this is just a table similar to the ones we’ve used to solve for equilibria of games). b. Show that each firm’s optimal output is independent of what the other firm produces. Now consider firms playing an infinitely repeated version of this game and consider the following strategy for each firm: (i) produce b q in period 1, (ii) produce b q in period t if both firms produced b q in all preceding periods, and (iii) produce a q in period t if one or more firms did not produce b q in some past period. Assume each firm acts to maximize its sum of discounted profits where the discount rate is r.

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MidPracProbs_ProblemSet - AEM 331 Practice Problems 1...

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