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387hw4anssp07

# 387hw4anssp07 - ECO 387 Dynamic Contracts Spring 2007...

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ECO 387: Dynamic Contracts, Spring 2007. Department of Economics, University of Texas. Instructor: Dean Corbae Solution Problem Set #4- Due 3/20/07 The principal solves P ( V ) = max { b s ,w s } S s =1 S X s =1 π s [ - b s + βP ( w s )] (1) s.t. S X s =1 π s [ u ( y s + b s ) + βw s ] = V (2) C s,k [ u ( y s + b s ) + βw s ] - [ u ( y s + b k ) + βw k ] 0 , s,k (3) y s + b s [0 , ] (4) w s [ V min ,V max ] (5) where V max = sup u ( c ) = 0 , and V min = S s =1 π s [ u ( y s - y L )] (1 - β ) . The value of V max is the highest that the agent can get as b s → ∞ . The value of V min is derived from the minimum value of transfers that the principal could give to the agent permanently in every state such that it is still incentive compatible, that is b s = - y L for s = L,H . We prove here that there is no solution to the problem stated above when the set of promised utilities is extended to V [ ˆ V ,V max ] with ˆ V < V min .

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387hw4anssp07 - ECO 387 Dynamic Contracts Spring 2007...

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