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handoutramsey

# handoutramsey - Optimal Taxation with Commitment in...

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Optimal Taxation with Commitment in In f nite Horizon Models Draws on Atkeson, Chari, and Kehoe (1999, FRBMinn QR). See also p.478— 88 of L-S. 1 First Best Planner solves max { c t ,C t ,k t +1 } t =0 X t =0 β t U ( c t ,C t ) subject to c t + g + k t +1 = F ( k t t )+(1 δ ) k t (1) First order conditions C t : U C,t = U c,t F C,t (2) k t +1 : U c,t = βU c,t +1 [ F k,t +1 +1 δ ]( 3 ) First best has no distortion to the MB of working F C,t or saving F k,t +1 + 1 δ . 2 Statement of the Competitive Equilibrium Prob- lem Govt expenditure g is f nanced through proportional taxes on income from capital (rate θ t )andlabor(rate τ t ). The government’s intertemporal budget constraint is X t =0 p t g = X t =0 p t ( τ t w t C t + θ t ( r t δ ) k t )( 4 ) HH problem max { c t ,C t ,k t +1 } t =0 X t =0 β t U ( c t t ) subject to X t =0 p t ( c t + k t +1 )= X t =0 p t ((1 τ t ) w t C t + R kt k t 5 ) where R kt =1+(1 θ t )( r t δ )and p 0 =1 . 1

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The f rst order conditions for a HH are c t : β t U c,t = λp t (6) C t : β t U C,t = λp t (1 τ t ) w t (7) k t +1 : p t = R k,t +1 p t +1 (8) where λ is the multiplier on (5). The f rm’s problem is max k t ,C t F ( k t ,C t ) r t k t w t C t The f rst order conditions for the f rm are: r t = F k,t (9) w t = F C,t (10) Let π t =( τ t t
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handoutramsey - Optimal Taxation with Commitment in...

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