handouttwexample

# handouttwexample - 1 A s i m p l e e x a m p l e Consider...

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Unformatted text preview: 1 A s i m p l e e x a m p l e Consider the following 2 state case (i.e. S = 2) where y L < y H and consider an exponential utility function u ( c ) = e c . In that case the problem is written as P ( V ) = max { b H ,w H ,b L ,w L } H [ b H + P ( w H )] + L [ b L + P ( w L )] . (1) st. H h e ( y H + b H ) + w H i + L h e ( y L + b L ) + w L i V aut = V (2) e ( y H + b H ) + w H e ( y H + b L ) + w L (3) e ( y L + b L ) + w L e ( y L + b H ) + w H (4) where V aut = n H h e y H i + L h e y L io / (1 ) . Conjecture the value function P ( ) takes the following form P ( V ) = 1 1 { log( V A ) + K } (5) where A and K are constants to be determined and that the upward incen- tive compatibility constraint does not bind. Then verify these conjectures. The lagrangian is = n H b H + 1 { log( w H A ) + K } + L b L + 1 { log( w L A ) + K } o + n H h e ( y H + b H ) + w H i + L h e ( y L + b L )...
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## This note was uploaded on 08/06/2008 for the course ECON 387 taught by Professor Corbae during the Spring '07 term at University of Texas at Austin.

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handouttwexample - 1 A s i m p l e e x a m p l e Consider...

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