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ps3macro2sp06 - 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 #3- Due 2/7/06 Consider a stochastic growth model with the following speci fi cation. Preferences: U ( C t , H t , λ t ) = ³ C t + λ t h (1 H t ) 1 η 1 1 η 1 ψ 1 1 ψ where λ t = (1 γ ) 1 λ t 1 ε t , λ 1 = 1 . (1) and log ε t is i.i.d. N (0 , σ ε ) . Agents discount the future at rate β < 1 . Technology: Y t = K θ t ¡ (1 + g ) t H t ¢ 1 θ (2) where K 0 is given, 1 H t 0 . Information: Households must choose H t before knowing the shock to preferences λ t but choose K t +1 after its realization. 1) Derive the stochastic Euler equation for the savings choice. 2) Derive the equation describing the labor/leisure choice. 3) Along a possible balanced growth path, assume that ε t is constant and equal to its expected value of 1. Under what conditions on parameters might a balanced growth path where K t , C t , Y t all grow at rate κ while H t remains constant exist? Is the set empty?
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