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NotesECN741-page27 - < γ< 1 be government’s discount...

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ECN 741: Public Economics Fall 2008 Consumer’s problem is the following (for generation t > 0 ) max U ( c t, 0 , l t, 0 ) + βU ( c t, 1 , l t, 1 ) subject to (1 - τ c t, 0 ) c t, 0 + a t, 1 (1 - τ l t, 0 ) w t z 0 l t, 0 (1 - τ c t, 1 ) c t, 1 (1 - τ l t, 1 ) w t z 1 l t, 1 + (1 + (1 - τ k t, 1 )( r t - δ )) a t, 1 There is a constant return to scale technology and r t = f k ( k t , l t ) w t = f l ( k t , l t ) and feasibility requires that c t + k t +1 = f ( k t , l t ) + (1 - δ ) k t c t = c t, 0 + c t - 1 , 1 l t = l t, 0 + l t - 1 , 1 k t = a t - 1 , 1 Government budget constrain is X t =0 p t g t = X t =0 p t " X j =0 , 1 τ c t - j,j c t - j,j + X j =0 , 1 τ l t - j,j w t z j l t - j,j + τ k t - 1 , 1 ( r t - δ ) a t - 1 , 1 # Let U t = U ( c t, 0 , l t, 0 ) + βU ( c t, 1 , l t, 1 ) be the lifetime utility of generation t for a given se-
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Unformatted text preview: < γ < 1 be government’s discount factor across generations. Government objective is to maximize ∞ X t =0 γ t U t Exercise: Show that, in this environment, implementability constraint for generation t is the following U c t, c t, + U l t, l t, + β ( U c t, 1 c t, 1 + U l t, 1 l t, 1 ) = 0 (38) 27...
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