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387hw1sp07 - Economics 387 Dynamic Contracts Spring 2007...

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Economics 387. 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 - Due 2/6/07 Consider the two period hidden information problem studied in class based on R. Townsend (1982). It was shown to generate the following pro- gramming problem (called PI.2’) where the principal minimizes the cost of providing the agent with a “utility” allocation © u θ , w θ ª θ { H,L } that respects incentive feasibility: 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 . Equation (2) is known as the promise keeping constraint and inequalities (3) and (4) are incentive compatibility constraints in the H and L states, respectively.
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