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# 387hw5a - ﬃ cient Allocations with Hidden Income and...

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Economics 387. Banking and Financial Intermediation. Spring 2002. Department of Economics, University of Texas Instructor: Dean Corbae, BRB 3.118, (o) 512-475-8530 email: [email protected], web: www.eco.utexas.edu/°corbae Homework #5 - Due 3/27/02 Consider the two period hidden information problem studied in class and problem sets 1 and 3 based on R. Townsend (1982). Now suppose that agents are able to privately store goods in period t = 0 (denoted s θ 0 since their savings can potentially di ff er across states). They enter period 0 with no storage and there is constant returns to scale, so 1 unit of storage at date t = 0 yields R > 0 units of goods at t = 1 . Show how the possibility of private storage a ff ects incentive feasible allocations vis-a-vis the framework you al- ready studied in Problem set 1. Can we interpret the allocation as one that arises out of a decentralized bond market? For background information on this problem, see Cole, H. and N. Kocherlakota (2001) ±E
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Unformatted text preview: ﬃ cient Allocations with Hidden Income and Hidden Storage², Review of Economic Studies, 68, p. 523-42. To proceed, given that the problem is only two periods, there will be no storage in period t = 1 since preferences are strictly increasing in con-sumption. Also, as before, incentive compatibility at t = 1 implies that the transfer cannot be contingent on the t = 1 report. Thus, the constraint set for the problem is given by the following promise keeping and incentive compatibility constraint at t = 0 : s.t. X θ ∈ { H,L } π θ u ¡ y θ + T θ − s θ ¢ + β X θ ∈ { H,L } π θ u ‡ y θ + T θ 1 + Rs θ · = ω u ¡ y θ + T θ − s θ ¢ + β X θ ∈ { H,L } π θ u ‡ y θ + T θ 1 + Rs θ · ≥ u ‡ y θ + T e θ − s θ · + β X θ ∈ { H,L } π θ u ‡ y θ + T e θ 1 + Rs θ · , ∀ θ, e θ 1...
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