waiver-14-451-spring2005

waiver-14-451-spring2005 - 14.451 Waiver George-Marios...

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14.451 Waiver George-Marios Angeletos Spring 2005 You have 1.5 hours. You must answer all questions. No books or notes are allowed. Question 1 (60%) Consider the neoclassical growth model, in discrete time. There is no exogenous technological change and no population growth; the size of population and labor is 1 . The technology is Cobb-Douglas: y t = f ( k t )= k α t g γ t where k t denotes the capital stock, g t denotes productive services provided by the government, and y t denotes output or income, and where 0 <α< 1 , 0 <γ< 1 + γ< 1 . The government f nances the productive services g t with income taxation: g t = τy t , where τ [0 , 1) . The representative household’s budget is c t + i t =(1 τ ) y t , where c t denotes consumption and i t denotes investment. The capital stock accumulates according to k t +1 =(1 δ ) k t + i t , where δ (0 , 1) . The household maximizes his lifetime utility, U = X t =0 β t u ( c t ) ,u ( c )= c 1 θ 1 θ ,
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waiver-14-451-spring2005 - 14.451 Waiver George-Marios...

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