NotesECN741-page14

# NotesECN741-page14 - c t,l t and k t 1 uniquely identiﬁes...

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ECN 741: Public Economics Fall 2008 Now replace ( 9 )-( 10 ) and we arrive at the implementability constraint 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 } (18) Proposition 4 A feasible allocation x = { c t ,l t ,b t +1 ,k t +1 ,x t } t =0 is a competitive equilibrium allocation if and only it satisﬁes the implementability constraint ( 18 ) (for some period zero policies). Proof. Suppose x is the competitive equilibrium allocation, then following the steps outlines above we can show that it should satisfy the implementability constraint ( 18 ). Now suppose an allocation x * is feasible and satisfy ( 18 ) for some proof zero policies. Note that in any competitive equilibrium, the bond holding must satisfy b t +1 = X s = t +1 β t - s [ U cs c s + U ls l s ] U ct - k t +1 (19) in other words, any sequence of
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Unformatted text preview: c * t ,l * t and k * t +1 uniquely identiﬁes a sequence of b t that is a part of competitive equilibrium. Candidate wage and rate of return on capital is given by ( 15 ). Therefore, from the FOC ( 9 )-( 12 ) we have 1-τ lt 1 + τ ct =-U * lt F * lt U * ct (1 + τ xt ) U * ct 1 + τ ct = β U * ct +1 1 + τ ct +1 ± (1-τ xt +1 )(1-δ ) + (1-τ kt +1 ) F * kt +1 ² (20) U * ct 1 + τ ct = β U * ct +1 1 + τ ct +1 R bt +1 any two of the four taxes can be chosen such that the above conditions hold. 2.1 Ramsey problem The Ramsey problem is the following max c t ,k t +1 ,l t ∞ X t =0 β t U ( c t ,l t ) 14...
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