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# Final-2007 - Econ 6202 Fall 2007 Dmitry Shapiro Final Exam...

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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 closed-book. • Please turn off your cellphones and other sound-making 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 long-run profit function for a representative firm is given by π j ( p ) = p 2- 2 p- 399 . Find the long-run 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 price-takers, and that the type a agent acts as a monopolist. It means that he can set any price vector he likes and b-agents would take it as given. What are the market prices and allocations in this non-competitive 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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Final-2007 - Econ 6202 Fall 2007 Dmitry Shapiro Final Exam...

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