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ps13macro2sp06 - Econ 387L Macro II Spring 2006 University...

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Econ 387L: Macro II Spring 2006, University of Texas Instructor: Dean Corbae Problem Set #13- Part 1 due 5/2/06, Part 2 due 5/5/06 1. Consider the following search model of money. Time is discrete and there is a continuum of agents with population normalized to 1 . Any particular agent specializes in the production of one service (a nonstorable good) but likes other services in an interval of size x (0 , 1) . She derives utility u ( q ) = q 1 / 2 from consuming q R + units of the service provided it falls in her desired interval. An agent discounts the future at rate (1 + r ) 1 . There is a constant disutility q to producing q units of a service. Production and consumption occur at the end of the period (and hence should be appropriately discounted). At the beginning of time, a fraction of agents M (0 , 1) are randomly given one unit of currency. Currency is indivisible and can be stored only one unit at a time. Agents are exogenously matched in the following way. Agents with money (we will term them buyers) are randomly matched in pairs with agents without money. Thus, the probability that a buyer
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