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NotesECN741-page4

# NotesECN741-page4 - (1 τ i p i for i = 1,n together with...

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ECN 741: Public Economics Fall 2008 3. Government budget (equation ( 2 )) holds 4. Allocations are feasible (or market clearing if you like!) c i + g i = x i for i = 1 , . . . , n (3) Proposition 1 Any competitive equilibrium allocations must satisfy the resource feasibility constraint F ( c 1 + g 1 , . . . , c n + g n , l ) = 0 (4) and an implementability constraint n X i =1 U i c i + U l l = 0 . (5) Furthermore, any allocations that satisfy ( 4 ) and ( 6 ) can be supported as a competitive equilibrium for appropriately constructed polices and prices. Proof. Suppose ( c, x, l ) is a competitive equilibrium allocation. Then the following FOC must hold U i U l
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Unformatted text preview: -(1 + τ i ) p i for i = 1 ,...,n together with the following budget constraint n X i =1 p i (1 + τ i ) c i = l. Replacing out for prices (and taxes) from FOC into budget constraint gives the imple-mentability constraint. The feasibility follows by deﬁnition of equilibrium. Now consider allocations ( c,x,l ) that are feasible (given vector of g ) and satisfy ( 5 ). Con-struct prices from the FOC of the ﬁrm p i =-F i F l for i = 1 ,...,n set policy as 1 + τ i = U i U l F l F i for i = 1 ,...,n 4...
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