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This 6 page Class Notes was uploaded by Ilene Heathcote on Wednesday October 21, 2015. The Class Notes belongs to ECN 611 at Syracuse University taught by Staff in Fall. Since its upload, it has received 34 views. For similar materials see /class/225651/ecn-611-syracuse-university in Economcs at Syracuse University.
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Date Created: 10/21/15
Ecowomics O11 Hamlout 3 THE ECONOMICS OFASYMMETRIC INFORMATION Chap 14 Cont d Asymmetric info after the time of contracting Moral Hazard Hidden Information vs hidden action Contracts WIIeII Wzve2Il uquot e Effort e 139re w VW 9eIe Assumptions Two values of 6 OH with prob A and BL 0ltAlt OH gt 6L e 2 0 150 0 Tr e gt 0 Tr e lt 0 Reservation utility u gt VO v gt 0 v lt 0 gm 6 0 Partial derivatives of disutility of effort gee 6 gt 0 ife gt 0 geee 6 gt 0 for all e gee 6 0 ife 0 geee 6 lt 0 ife gt 0 gee 6 lt 0 for all e geee 6 0 ife 0 Example we 61 vltw 23026 w mew ge6 eze 61109 l WW Profit First Treat related game where 6 is also observable after the contract by the owner Contract wH eH wL eL Owner With instruments wH eH wL eL maximize expected pro t A139ceH wH l ATreL wL subject to WH WL 6H 6L all 2 O and AVWH geH AVWL geL9 2 11 vw gee uquot rlu P rofit 61109 2 At the optimum contract the constraint will be satis ed with equality Lagrangian E9 MMGH W 1 A eL WL YAVWH g6H9H1 AVWL geL9L 11 KuhnTucker conditions 1 A YAV39WH geHaeHS0WH20 A YAV39WH g6H9HWH 0 2 1 A Y1 AV39WL gep9LSOWL20 1 A Y1 AV39WL g6L9LWL 0 3 611 YAV39WH geH9H geeH 911 S0 eHZO M396H YAV39WH g6H9H ge6H9HeH 0 4 1 MTE39EL Y1 AV39WL gep eL geep 9Q S0 BLZO 1 HEEL Y1 AV39WL geL9L ge6L9LeL 0 5 AVWH geH9H1 AVWL geL9L 11 0 Suppose eH 0 T 0 gt 0 and g0 6H 0 contrary to 3 Therefore eH gt 0 Similarly eL gt 0 Therefore WH gt 0 and WL gt 0 61109 3 So 139 A YAV39WH geH9H 0 239 1 A Y1 AV39WL geL3L 0 339 1711611 WWW geH9H geeH 910 0 439 1 A7T396L Y1 AV39WL geL9L geeL9L 0 539 W geH9H1 lVWL geL9L 11 0 From 1 and 2 Y AlV39WH geH 910 1 A1 AV39WL geL9L Hence V39WH geH9H V39WL geL9L Since V lt0thenVWH geH 9H VWL geL 9L Substituting into the constraint VWH geH 6H u and so also VWL geLa 6L 11 1T396Hquot geeH 9H 1T39eLquot geeL 9L VW 99191 U vw geeH uquot war 61109 4 VW 9109190 U vw geeH uquot 139re w I39ILquot 139re w I39IHquot Mm E 6 is NOT known by the owner not known by either at the time of the contract A Problem with previous contract Bi Possible new forms of contract The revelation principle Special case If optimal contracts exist one can be found having the following properties i revelation mechanism After nature selects 6 the manager announces a value 66 ii For each possible 6 the contract specifies a particular wage effort pair W9 69 iii Incentive compatibility 611l09 5 For every possible 6 the manager is induced to tell the truth 66 6 Special case in nite risk aversion for manager Manager announces 6H or 6L and With instruments wH eH wL eL the owner maximizes expected pro t MMBH WH1 MWBL WL subject to wH wL eH eL all 2 0 and V hi geH6H2 u V ampj geL6L2 u WH geH 9102 WL geL6H WL geL6L2 WH geH6L Proposition 14C3 i ii iii iV The solution wH eH wL eL to this problem has the properties 1 6H 611 2 6L lt cf 3 For the owner expected pro t is lower than for the case where 6 is observable 4 For the manager utility at 6H is greater than u but at 6L utility equals u so the payoff with in nite risk aversion is u just as in the case where 6 is 61109 6
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