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Lecture 26

# Lecture 26 - Economics 101A(Lecture 26 and Last Stefano...

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Economics 101A (Lecture 26, and Last) Stefano DellaVigna December 2, 2009

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Outline 1. Hidden Action (Moral Hazard) II 2. The Takeover Game 3. Hidden Type (Adverse Selection) 4. Evidence of Hidden Type and Hidden Action 5. Some Advice 6. Course Evaluation
1 Hidden Action (Moral Hazard) II Back to Principal-Agent problem Solve problem in three Steps, starting from last stage (backward induction) —S tep1 (E f ort Decision) . Given contract w ( y ) , what e f ort e is agent going to put in? tep2 . (Individual Rationality) Given contract w ( y ) and anticipating to put in e f e , does agent accept the contract? tep3 . (Pro f t Maximization) Anticipating that the e f ort of the agent e (and the acceptance of the contract) will depend on the contract, what contract w ( y ) does principal choose to maximize pro f ts?

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Step 1. Solve e f ort maximization of agent: Max e a + be γ 2 b 2 σ 2 c ( e ) Solution: c 0 ( e )= b If assume c ( e ce 2 / 2 >e = b/c Check comparative statics With respect to b > What happens with more pay-for-performance? With respect to c > What happens with higher cost of e f ort?
Step 2. Agent needs to be willing to work for prin- cipal Individual rationality condition: EU ( w ( e )) c ( e ) 0 Substitute in the solution for e and obtain a + be γ 2 b 2 σ 2 c ( e ) 0 Will be satis f ed with equality: a = be + γ 2 b 2 σ 2 + c ( e )

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Step 3 : Owner maximizes expected pro f ts max a,b E [ π ]= e E [ w ( y )] = e a be Substitute in the two constraints: c 0 ( e )= b (Step 1) and a = be + γ 2 b 2 σ 2 + c ( e ) (Step 2) Obtain E [ π e μ be + γ 2 b 2 σ 2 + c ( e ) c 0 ( e ) e = e + be γ 2 b 2 σ 2 c ( e ) c 0 ( e ) e = e + c 0 ( e ) e γ 2 ³ c 0 ( e ) ´ 2 σ 2 c ( e ) c 0 ( e ) e = e γ 2 ³ c 0 ( e ) ´ 2 σ 2 c ( e ) Pro f t maximization yields f.o.c. 1 γc 0 ( e ) σ 2 c 00 ( e ) c 0 ( e )=0
and hence c 0 ( e )= 1 1+ γσ 2 c 00 ( e ) Notice: This implies c 0 ( e ) < 1 Substitute c ( e ce 2 / 2 to get e = 1 c 1 2 c Comparative Statics: Higher risk aversion γ > ...

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Lecture 26 - Economics 101A(Lecture 26 and Last Stefano...

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