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Unformatted text preview: University of Minnesota Department of Economics Econ 3102: Intermediate Macroeconomics Problem Set 4 1 Problems (50 points) Exercise 1 (30 points) Consider a infinite horizon setup. The representative household enjoys consumption and leisure time in all periods t = 0, 1,..., ∞ . The household has no exogenous income, but it has fixed time endowments in each period, ¯ h , and an initial capital endowment, K . Assume that the household’s utility function is time-separable, and takes the form U ( C ,C 1 ,...,‘ ,‘ 1 ,... ) = ∞ X t =0 β t u ( C t ,‘ t ) where C t and ‘ t denote consumption and leisure in period t, u( · , · ) is a period utility function which is strictly increasing, strictly concave and satifies the Inada Conditions (lim C t → u C ( C t ,‘ t ) = ∞ , lim ‘ t → u ‘ ( C t ,‘ t ) = ∞ ; these help ensure that the solutions are interior). β ∈ (0 , 1) is the household’s discount factor. Note that N t = ¯ h- ‘ t ....
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This note was uploaded on 02/07/2011 for the course ECON 3102 taught by Professor Mingyi during the Spring '08 term at Minnesota.
- Spring '08