NotesECN741-page12

NotesECN741-page12 - max c t,l t,x t,k t 1,b t 1 ∞ X t =0...

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ECN 741: Public Economics Fall 2008 2 Optimal Fiscal Policy-Dynamic Ramsey Taxation The main focus of this section is the derivation of Chamley-Judd result ( Chamley ( 1986 ) and Judd ( 1985 )). We are only going to consider deterministic environment. See Chari and Kehoe ( 1994 ) and Chari and Kehoe ( 1998 ) for stochastic environment and optimal policy over business cycle. The environment is the following. There are infinitely lived identical consumers. Government has to finance expenditure g t every period and levies distortionary taxes (or subsidies) on consumption, investment, labor and capital income. It can also issue debt. Consumer’s problem: consumers are endowed with k 0 unit of capital and b 0 unit of govern- ment debt
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Unformatted text preview: max c t ,l t ,x t ,k t +1 ,b t +1 ∞ X t =0 β t U ( c t ,l t ) subject to (1 + τ ct ) c t + (1 + τ xt ) x t + b t +1 ≤ (1-τ lt ) w t l t + (1-τ kt ) r t k t + R bt b t ; λ t k t +1 ≤ (1-δ ) k t + x t-b t +1 ≤ M k ,b given in which M is some large positive number. The FOC’s are β t U ct = λ t (1 + τ ct ) (9)-β t U lt = λ t w t (1-τ lt ) (10) (1 + τ xt ) λ t = λ t +1 [(1-τ xt +1 )(1-δ ) + (1-τ kt +1 ) r t +1 ] (11) λ t = λ t +1 R bt +1 (12) Government Budget: g t + R bt b t = b t +1 + τ xt x t + τ ct c t + τ lt w t l t + τ kt r t k t (13) Feasibility: c t + g t + k t +1 = F ( k t ,l t ) + (1-δ ) k t (14) 12...
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