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4721_MT_AK

# 4721_MT_AK - University of Minnesota Department of...

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University of Minnesota Department of Economics Econ 4721 Money and Banking Midterm Examination October 31, 2008 The rules of the test: You must choose one problem from Part 1 (problems 1.1 and 1.2), and one more problem from Part 2 (problems 2.1 and 2.2). Therefore, you must solve two problems in total. You may use the back of the page to continue your answer (but be sure to let me know where your answer continues). Please indicate clearly which of the problems you want to be graded. If you attempt to solve more than 2 problems, and do not provide any indication, problems 1.1 and 2.1 will be graded. Therefore, you will not get any extra credit for solving more than two problems. You have 50 minutes to answer the test. The maximum amount of points is 100. Calculators are allowed. Your test should have 9 (nine) pages including this one. Check to make sure! Good luck! 1

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Part 1. Stationary Equilibrium with Money (60 points) General Information, Problems Come on Next Pages Solve at most ONE problem from Part 1 The set-up of all these questions follows the one in the Overlapping Generations model (OLG) with fiat money. In each period t , N t consumers are born and they live for two periods. The number of people evolves according to N t +1 = nN t , where n 1 is a number, sometimes referred to as the gross rate of population growth. Each consumer is endowed with y 1 units of the consumption goods when young and y 2 units when old. The members of the initial old generation are also endowed with m 0 units of fiat money each. They only live for one period and have utility u ( c 2 , 1 ) = log [ c 2 , 1 ]. Members of the generations born in period 1 and later have the utility function: u ( c 1 ,t , c 2 ,t +1 ) = log [ c 1 ,t ] + β log [ c 2 ,t +1 ] The total supply of fiat money in period t is M t . The money stock evolves according to M t +1 = zM t , where z is a number which is called the gross rate of money stock growth. For some of the problems below, there is a government that must spend g units of consumption per each old person in every period, which may be financed either through money printing or taxes. Each question below gives you numbers for: n , y 1 , y 2 , β as well as the government policy parameters: z and g . Solve at most ONE problem from Part 1 2
Problem 1.1 (60 points) There are no government expenditures, g = 0. The government keeps the money supply constant, z = 1. The economy’s parameters are: n = 1, β = 1 3 , y 1 = 40, y 2 = 0 (a) (10 points) Write down the maximization problem that characterizes the Pareto optimal allocation. (b) (10 points) Consider a competitive equilibrium with money. Set up a problem that a person born at t 1 has to solve. (c) (15 points) Solve for the rate of return of money ( v t +1 /v t ) in a stationary competitive equilibrium. The answer should be a number . (d) (15 points) Solve for the consumption allocation ( c * 1 , c * 2 ) in a stationary competitive equilibrium. The answer should be two numbers .

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4721_MT_AK - University of Minnesota Department of...

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