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Unformatted text preview: Econ 387L: Macro II Spring 2008, University of Texas Instructor: Dean Corbae Problem Set #4 Answers Consider the following static version of the Hansen (1985) indivisibility pa per. There is a unit measure of exante identical agents. There are only two pos sible number of hours per worker h ∈ { , h } , h < 1 , which implies there are only two possible levels of leisure an agent can derive utility from given the normal ization 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 work) is denoted C e ( C u ). Answer . max π ∈ [0 , 1] ,C e ,C u π £ (1 − α ) ln( C e ) + α ln(1 − h ) ¤ + (1 − π )(1 − α ) ln( C u ) s.t. πC e + (1 − π ) C u = z ( π h ) θ b. Show that it is optimal to provide full insurance with respect to theb....
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 Spring '07
 CORBAE
 Economics, Game Theory, The Higher, Natural logarithm

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