lec11_with_answers

lec11_with_answers - Econ 138 Financial and Behavioral...

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Econ 138 Financial and Behavioral Economics Lecture 11: Diversi f cation and Micro f nance Ulrike Malmendier UC Berkeley Th, February 28, 2008
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Organization Lunches! Felipe and others remarked that many of you have class right after this one. Wed? (alternating) Midterm: Many impressive exams! Remember graded on a curve . .. As long as you got Q1 AND part (a)-(g) of Q2, you are on track. If you were struggling with the f rst 16 points . .. red F ag! Typically, this seemed to indicate some di culty with the basics (set up of the problem, general idea, . ..). Come and talk to me!
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1 Diversi f cation We have studied how debt capacity may be limited due to Moral Hazard. Diversi f cation : Might it help if the manager has more than one invest- ment project? Intuition : Since manager is risk neutral, compensate only when both projects succeed. Lenders lose less money in the case of failure, and man- ager will want to work hard on both projects if paid enough: R m, 2 > 0 , R m, 1 = R m, 0 =0 . Formally, we show (only) that there always exists one optimal incentive scheme with R m, 2 > 0 , R m, 1 = R m, 0 =0 :
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Given the above contract, when does the manager work? Works hard: p 2 H R m, 2 . Shirks: p 2 L R m, 2 +2 B . Hence, manager works hard on both projects rather than shirking (con- straint 1, or ‘IC1’) on both if and only if: p 2 H R m, 2 p 2 L R m, 2 +2 B ⇐⇒ ( p H + p L ) R m, 2 2 B p The manager works hard on both projects rather than shirking on one (constraint 2, or ‘IC2’) i f p H R m, 2 p B
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(by shirking on one project, the manager reduces the probability of full success by p H , i.e. the probability that that project succeeds, times p , i.e. the reduction in the second project’s probability of success.) IC2 says: loss from shriking on 1 outweighs gain ( B ). Since p H > 1 2 ( p H + p L ) , the IC2 is automatically satis f ed: ( p H + p L ) R m, 2 2 B p ⇐⇒ 1 2 ( p H + p L ) R m, 2 p B Hence the lowest R m, 2 = 2 B p ( p H + p L ) . Makes intuitive sense: the larger the bene f ts of shirking or the smaller the di f erence in probability the larger the reward needs to be to induce hard work.
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Back to the big question: How does this compare to the baseline case? Can we f nance the projects more often or less often? We derived R m, 2 = 2 B p ( p H + p L ) , and hence the expected payo f of the manager (if working hard) is p 2 H R m, 2 = p 2 H 2 B p ( p H + p L ) . To simplify the notation, denote d = p L p L + p H ,i .e . , 1 d = p H p L + p H . Hence, the expected payo f of the manager is 2 p H (1 d ) B p
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This note was uploaded on 04/02/2008 for the course ECON 138 taught by Professor Malmendier during the Spring '08 term at Berkeley.

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lec11_with_answers - Econ 138 Financial and Behavioral...

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