NotesECN741-page15

NotesECN741-page15 - ECN 741: Public Economics Fall 2008...

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ECN 741: Public Economics Fall 2008 subject to X t =0 β t [ U ct c t + U lt l t ] = U 0 { [(1 + τ x 0 )(1 - δ ) + (1 - τ k 0 ) r 0 ] k 0 + R b 0 b 0 } ; λ c t + g t + k t +1 = F ( k t ,l t ) + (1 - δ ) k t ; φ t Define function W ( · , · , · ) as W ( c,l,λ ) = U ( c,l ) + λ [ U c c + U l l ] . Now we can rewrite the Ramsey problem as max c t ,k t +1 ,l t X t =0 β t W ( c t ,l t ) subject to c t + g t + k t +1 = F ( k t ,l t ) + (1 - δ ) k t ; φ t Take first order conditions W lt W ct = - F lt (21) W ct W ct +1 = β (1 - δ + F kt ) for t 1 (22) 2.2 Chamley-Judd result Proposition 5 If the solution to the Ramsey problem converges to a steady state, then at the steady state, the tax rate on capital income is zero.
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