387hw2sp07 - an optimal debt contract where in exchange for...

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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: corbae@eco.utexas.edu, web: www.eco.utexas.edu/˜corbae Homework #2 - Due 2/13/07 Consider the following variant of the costly state veri f cation problem by R. Townsend (1979) studied in class. The main di f erence between homework and class is that both the principal and agent are risk neutral. Suppose there is a risk neutral entrepreneur who has a project that yields a random return x [0 , x ] drawn from distribution function F ( x )a ttheendo fthepe r iod if an investment is made at the beginning of the period and yields zero otherwise. There is a risk neutral lender who has one unit of an investment good, access to a storage technology which yields r at the end of the period, and access to a veri f cation technology which takes κ
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Unformatted text preview: an optimal debt contract where in exchange for 1 unit of investment good lent to the entrepreneur at the beginning of the period, the lender receives return B ( x ) [0 , x ] if the entrepreneur reports e x S [0 , x ] and the lender veri f es the report while the lender receives R ( e x ) if the entrepreneur reports e x S c and the lender does not verify. 1. Prove that R ( e x ) must be a constant (say R ) on e x S c . 2. State the programming problem which maximizes the entrepreneurs utility subject to participation by the lender. 3. Prove that the veri f cation region S = { e x : e x [0 , x ] } (i.e. a lower interval). 4. Prove that B ( x ) = x < R. Note that (1)-(4) implies that the optimal contract has all the essential features of a debt contract where veri f cation can be interpreted as bankruptcy. 1...
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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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