PS5 - 3[35 points Consider the following variation of...

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ECN 713 Spring 2010 Natalia Kovrijnykh Problem Set 5: Due on Tuesday, March 23, in class (100 points total) 1. [20 points] Consider the version of Thomas and Worrall (1988) with one-sided commit- ment that we studied in class. Show that there exists ° ° 2 (0 ; 1) such that the full-insurance allocation is self-enforcing and yields non-negative (expected discounted present value) prof- its to the lender if and only if ° ° ° ° . 2. [20 points] Consider the following variation of the version of Thomas and Worrall (1988) with one-sided commitment that we studied in class. Assume that the household in each period can save part of its income. Set up the optimal contracting problem in a recursive form assuming that savings are observable by the principal. Without solving, do you think that having savings in the problem will be bene°cial for both parties? Explain.
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Unformatted text preview: 3. [35 points] Consider the following variation of Thomas and Worrall (1990). Instead of private information of the household±s endowment, assume the household has a constant income y but he is subjected to ²taste shocks± . Formally, his per-period utility from con-sumption is ±u ( c ) , where u is strictly increasing and strictly concave and ± 2 f ± ‘ ; ± h g , where Pr f ± = ± ‘ g = ² 2 (0 ; 1) . (a) Set up the Bellman equation for the optimal contract problem with in&nite horizon. Derive the &rst-order conditions. (b) Suppose there are two periods only and u ( c ) = ln c . Characterize the optimal contract in this case as fully as possible. 4. [25 points] Solve exercise 21.5 in Ljungqvist and Sargent (2nd edition). 1...
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