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NotesECN741-page13

# NotesECN741-page13 - Weitzman 1973 are satisﬁed then the...

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ECN 741: Public Economics Fall 2008 Competitive pricing implies that r t = F k ( k t , l t ) (15) w t = F l ( k t , l t ) A competitive equilibrium is: the sequence of allocations x = { c t , l t , b t +1 , k t +1 , x t } t =0 , prices { r t , w t , R bt } t =0 , policy π = { τ ct , τ lt , τ xt , τ kt +1 } t =0 such that, the allocations solve consumer problem, given prices and policy, prices are competitive, government budget holds and allo- cations are feasible. A Ramsey Equilibrium is a policy π , an allocation rule x ( · ) and price rules r ( · ) , w ( · ) and R b ( · ) such that: π arg max X t =0 β t U ( c t , l t ) subject to 12 and x ( π ) be a competitive equilibrium, and for any policy π 0 , allocation x ( π 0 ) and prices ( r ( π 0 ) , w ( π 0 ) , R b ( π 0 )) be a competitive equilib- rium. We next derive the implementability condition. Note that if conditions of Ekeland and Scheinkman
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Unformatted text preview: Weitzman ( 1973 ) are satisﬁed, then the equilibrium allocations should also satisfy the following Transversality conditions lim t →∞ λ t b t +1 = 0 (16) lim t →∞ λ t k t +1 = 0 (17) Now multiply consumer’s budget constraint by λ t and sum over t and use ( 16 )-( 17 ) ∞ X t =0 λ t [(1 + τ ct ) c t + (1 + τ xt )( k t +1-(1-δ ) k t ) + b t +1 ] = ∞ X t =0 λ t [(1-τ lt ) w t l t + (1-τ kt ) r t k t + R bt b t ] . Now use ( 9 )-( 12 ) and we get ∞ X t =0 λ t [(1 + τ ct ) c t-(1-τ lt ) w t l t ] = λ { [(1 + τ x )(1-δ ) + (1-τ k ) r ] k + R b b } . 13...
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