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387hw1anssp07

# 387hw1anssp07 - Economics 387L Dynamic Contracts Spring...

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Economics 387L. Dynamic Contracts. Spring 2007. Department of Economics, University of Texas Instructor: Dean Corbae, BRB 3.134A, (o) 512-475-8530 email: [email protected], web: www.eco.utexas.edu/˜corbae Homework #1 - Answers We take as given the programming problem (called PI.2’): min { u θ ,w θ } θ { H,L } X θ { H,L } π θ £ C ( u θ )+ βV ( w θ ) ¤ (1) s.t. X θ { H,L } π θ £ u θ + βw θ ¤ = ω (2) u H + βw H u ¡ C ( u L )+ ¢ + βw L (3) u L + βw L u ¡ C ( u H ) ¢ + βw H (4) where = y H y L > 0 . 1. Show (3) must bind. Suppose to the contrary that (3) is slack (i.e. u H + βw H >u ¡ C ( u L )+ ¢ + βw L ). Then w L w H .I fn o t ,t h a t is if w H >w L , then we can decrease w H and increase w L in such a

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387hw1anssp07 - Economics 387L Dynamic Contracts Spring...

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