NotesECN741-page5

NotesECN741-page5 - c x and l and price function p ...

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ECN 741: Public Economics Fall 2008 You can verify that the policy and prices (as constructed above) together with the allocation ( c,x,l ) is a competitive equilibrium. We are interested in the problem of choosing the best policy π to maximize the welfare of consumers. One restriction on such a problem is that the resulting allocation be a competitive equilibrium allocation for each given policy. The timing is the following: First, government chooses a policy, Second, private agents makes decision. We are interested in finding the equilibrium of this game. 1.1 Ramsey problem Suppose the set of feasible policy for government in Π . Definition 1 A Ramsey equilibrium is a policy π = ( τ 1 , ··· τ n ) Π , allocation rules
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Unformatted text preview: c ( · ) , x ( · ) and l ( · ) and price function p ( · ) such that π ∈ arg max π ∈ Π U ( c ( π ) ,l ( π )) subject to n X i =1 p i g i = n X i =1 p i τ i c i and ( c ( π ) ,x ( π ) ,l ( π )) together with p ( π ) is a competitive equilibrium for every π ∈ Π . Suppose π, ( c ( · ) ,x ( · ) ,l ( · ) ) and p ( · ) is a Ramsey equilibrium . Then we call ( c ( π ) ,x ( π ) ,l ( π )) a Ramsey allocation . Proposition 2 Suppose c * and l * are part of a Ramsey allocation. Then ( c * ,l * ) ∈ arg max c,l U ( c,l ) subject to ( 5 ) and ( 4 ) . Proof. Follows from the definition of Ramsey allocation. 5...
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