Econ 6202, Fall 2009Dmitry ShapiroProblem Set 10Optional1. A monopolist faces a market demand curve given byq(p) = 70-p.(a) If the monopolist can produce at constant average and marginal costs ofAC=MC= 6, whatoutput level will the monopolist choose to maximize profits?What is the price at this outputlevel? What are the monopolist’s profits?(b) Assume instead that the monopolist has a cost structure where the total costs are described byTC(q) =14q2-5q+ 300.Find the price-quantity combination that maximize the monopolist’s profit. What will profits be?2.First-degree price discriminationConsider the following economy. There are two consumers, 1 and 2, who derive utility from a certaingood (x) and from money (m). The consumers’ utility functions areu1(x, m) = 40√x+m,u2(x, m) = 60√x+m.A monopolist produces the good at constant average and marginal costsc= 5.Suppose that themonopolist observes the consumers’ utility and makes take-it-or-leave-it offers (ri, xi)),i= 1,2 (ri
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