NotesECN741-page4

NotesECN741-page4 - -(1 + i ) p i for i = 1 ,...,n together...

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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 + i ) p i for i = 1 ,...,n together with the following budget constraint n X i =1 p i (1 + i ) c i = l. Replacing out for prices (and taxes) from FOC into budget constraint gives the imple-mentability constraint. The feasibility follows by denition 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 rm p i =-F i F l for i = 1 ,...,n set policy as 1 + i = U i U l F l F i for i = 1 ,...,n 4...
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This note was uploaded on 12/10/2011 for the course MAT 121 taught by Professor Wong during the Fall '10 term at SUNY Stony Brook.

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