Final-2008 - Econ 6202, Fall 2008 Dmitry Shapiro Final Exam...

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Unformatted text preview: Econ 6202, Fall 2008 Dmitry Shapiro Final Exam December 11, 2008 ATTENTION! THIS IS 150 MINUTE EXAM! There are FIVE questions in the final. You need to do ALL of them. There are THREE pages of the final exam including this one. 50%+1 is NOT the same as majority voting. 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 2008 Dmitry Shapiro 1. [General Equilibrium - I] Consider an economy with two goods, x and y , and three consumers 1,2 and 3. The consumers utility functions are u 1 ( x,y ) = x 2 y ; u 2 ( x,y ) = xy 2 u 3 ( x,y ) = xy respectively. The endowments are (3,1) for consumer 1, (3,6) for consumer 2 and (2,4) for consumer 3. (a) Find the aggregate excess demand for each good; (b) Show that your answer in part (a) satisfies Walras Law; (c) Find all of the Walrasian equilibria. 2. [General Equilibrium-II] An exchange economy has three consumers and three goods. Consumers utility functions and initial endowments are as follows: u 1 ( x 1 ,x 2 ,x 3 ) = min { x 1 ,x 2 } e 1 = (1 , , 0) , u 2 ( x 1 ,x 2 ,x 3 ) = min { x 2 ,x 3 } e 1 = (0 , 1 , 0) , u 3 ( x 1 ,x 2 ,x 3 ) = min { x 1 ,x 3 } e 1 = (0 , , 1) . Find the Walrasian equilibrium price and allocation. 3. [Choice Under Uncertainty] Consider an agent with von Neumann-Morgenstern utility u ( x ) = ln( x + 1) over levels of wealth x 0 (in dollars). The agent has 10 dollars initially, but faces a 10 percent chance of losing 4 dollars. An insurer offers him insurance at a price of p dollars per unit. If the agent purchases q units of insurance, then the insurer pays him q dollars if the loss occurs. (a) Is the agent risk-averse, risk-neutral or risk-loving? Justify your answer. (b) At what price, p * will the agent choose full insurance? How did we call this price in the class....
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This note was uploaded on 10/20/2010 for the course ECON 6202 taught by Professor Shapiro during the Fall '09 term at UNC Charlotte.

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Final-2008 - Econ 6202, Fall 2008 Dmitry Shapiro Final Exam...

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