ps4macro2sp08 - Econ 387L: Macro II Spring 2008, University...

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Econ 387L: Macro II Spring 2008, University of Texas Instructor: Dean Corbae Problem Set #4- Due 2/14/08 1. Consider the following static version of the Hansen (1985) indivisibility paper. There is a unit measure of ex-ante identical agents. There are only two possible number of hours per worker h { 0 , h } , h< 1 , which implies there are only two possible levels of leisure an agent can derive utility from given the normalization that 1= h + c. Let preferences be given by u ( C, c )=(1 α )ln C + α ln c. The production technology is given by y = zh θ with θ< 1 where z is the state of technology. a. Suppose that a planner has access to a randomization device which she can program such that π = prob ( h t = h ) . Assume further she can set this device to be i.i.d. across all households, can see the outcome of the realization of the device in each case, and can enforce that outcome. Given the state of technology z, state the planner’s problem using the notation that a realization of the lottery which entails the agent should work (should not
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