NotesECN741-page60

NotesECN741-page60 - ECN 741: Public Economics Fall 2008 2...

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ECN 741: Public Economics Fall 2008 u ( c,l ) = log( c ) - l 2 2 , β = 1 . F ( K,Y ) = RK + wY , δ = 1 . There is endowment of K 1 in period 1 . The planner’s problem is max c 1 ,c 2 h ,c 2 l ,y 1 ,y 2 h ,K 2 log( c 1 ) - y 2 1 2 + 0 . 5 ± log( c 2 h ) - y 2 2 h 2 ² + 0 . 5[log( c 2 l )] sub. to c 1 + K 2 = RK 1 + wy 1 0 . 5 c 2 h + 0 . 5 c 2 l = RK 2 + 0 . 5 wy 2 h log( c 2 h ) - y 2 2 h 2 log( c 2 l ) c 1 ,c 2 h ,c 2 l ,y 1 ,y 2 h ,K 2 0 Let ( c * 1 ,c * 2 h ,c * 2 l ,y * 1 ,y * 2 h ,K * 2 ) be the solution. Then it should satisfy the following FOC c * 1 + K * 2 = RK 1 + wy * 1 0 . 5 c * 2 h + 0 . 5 c * 2 l = RK * 2 + 0 . 5 wy * 2 h log( c * 2 h ) - y * 2 2 h 2 = log( c * 2 l ) Rc
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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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