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Unformatted text preview: Econ 6202, Fall 2007 Dmitry Shapiro Final Exam December 10, 2007 • ATTENTION! THIS IS 150 MINUTE EXAM! • There are FIVE questions in the final. You need to do ALL of them. • The exam is 150 minutes long and has 150 points. Each question has 30 points assigned. Thus it would make sense for you to start with easier questions. • The exam is closedbook. • Please turn off your cellphones and other soundmaking devices. Good luck! 1 Econ 6202, Fall 2007 Dmitry Shapiro 1. [Partial Equilibrium  30 points] Let inverse market demand be the linear form p = 39 . 009 q . Technology for producing output, q , is identical for all firms, and all firms face identical input prices. The longrun profit function for a representative firm is given by π j ( p ) = p 2 2 p 399 . Find the longrun market equilibrium price, the output priduced by each firm in the equilib rium and the equilibrium number of firms. 2. [Choice Under Uncertainty  30 points] Consider the set outcome C = { c 1 ,c 2 ,c 3 } , and let L denote the set of simple lotteries over C . Suppose that the preference relation ” over L satisfies the independence axiom, and that c 1 ” c 2 ” c 3 . Show that c 1 ” L ” c 3 for every lottery L . 3. [GE and Monopoly  30 points] Consider an economy consisting of two goods, one agent of type a and ten agents of type b . The type a agent has utility given by U a ( x a 1 ,x a 2 ) = x a 1 x a 2 and an endowment e a = (20 , 10). Each type b agent has utility given by U b ( x b 1 ,x b 2 ) = x b 1 x b 2 and an endowment e b = (1 , 2). (a) Find the competitive equilibrium prices and allocations in this economy. Is this allocation Pareto Optimal? (b) Assume now that all type b agents are pricetakers, and that the type a agent acts as a monopolist. It means that he can set any price vector he likes and bagents would take it as given. What are the market prices and allocations in this noncompetitive equilibrium? Is the ratio p 1 p 2 greater than, less than, or the same as that in part (a)? What is the intuition for this? (even if you cannot compute p 1 p 2 for this market, argue qualitatively what you might expect it to be)....
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 Fall '09
 SHAPIRO
 Economics, Equilibrium, Supply And Demand, Economic equilibrium, Kenneth Arrow

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