325_PS2 - Department of Economics University of Maryland...

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Department of Economics University of Maryland Economics 325 Intermediate Macroeconomic Analysis Problem Set 2 Professor Sanjay Chugh Spring 2011 Due: Monday, May 9, 2011 Instructions : Written (typed is strongly preferred, but not required) solutions must be submitted no later than 11:00am on the date listed above. You must submit your own independently-written solutions. You are permitted (in fact, encouraged) to work in groups to think through issues and ideas, but you must submit your own independently-written solutions. Groups may be no larger than four students total, and all group members’ names must be listed on the first page. Under no circumstances will multiple verbatim identical solutions be considered acceptable. Failure to adhere to these guidelines may result in your problem set not being accepted, and a grade of zero being assigned. Your solutions, which likely require some combination of mathematical derivations, economic reasoning, graphical analysis, and pure logic, should be clearly, logically, and thoroughly presented; they should not leave the reader (i.e., your TAs and I) guessing about what you actually meant. Your method of argument(s) and approach to problems is as important as, if not more important than, your “final answer.” Throughout, your analysis should be based on the frameworks, concepts, and methods we have developed in class. There are three problems in total, each with multiple subparts.
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2 Problem 1: The Money-in-the-Utility-Function (MIU) Framework (20 points). Consider an extension of the MIU framework studied in Chapter 14. Specifically, suppose the instantaneous (i.e., period-t) utility function of the representative consumer is ,, t t t t M ucn P §· ¨¸ ©¹ , in which P t denotes the nominal price during period t of the consumption good, t M denotes the nominal money holdings of the consumer at the end of period t (thus, the consumer’s holdings of nominal money at the start of period t is 1 t M ± ), and t n is the individual’s labor during period t. (As in Chapter 2, suppose that total hours available in any given time period is 168, and the only possible uses of time are labor or leisure.) The consumer’s period-t budget constraint is a slight modification of the one presented in Chapter 14, 11 tt t t t t b t t Pc M P B Pwn M B ± ± ²² ² ² . Income is earned from labor supply (with t w denoting the market determined real wage in period t, which is taken as given by the individual), and, for simplicity, suppose there are no stock markets (hence one-period riskless bonds and money markets are the only two asset markets). Besides these slight changes, the notation and timing of events is identical to that in Chapter 14. The individual’s budget constraints for period t+1, t+2, … are identical to the above, with the time subscripts appropriately updated. As always, suppose the representative consumer’s subjective discount factor between any pair of time periods is (0,1) E ³ .
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325_PS2 - Department of Economics University of Maryland...

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