market equilibrium under uncertainty

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1、4MarketEquilibriumunderUncertaintyWehavesofarconsideredonlythedecisionsoftheindividual.Inthischapterthelevelofanalysisshiftstomarketinteractionsandtheconditionsofequilibrium.Thefirmwillbeintroducedasanagencyofindividualsengagedintheprocessofproduction.Wecontinuetodealonlywitheventuncertaintyunderper

2、fectmarketsrulingoutmarketuncertaintywithitscharacteristicattendantphenomenaofsearchandoftradingatnon-clearingprices.Butaccountwillbetakenofpossiblyincompleteregimesofmarkets;i.e.,wewillnotalwaysassumethateachdistinctstateclaimis,directlyorindirectly,tradable.InSection4.3,webuildonSection2.2toflesho

3、utthecapitalassetpricingmodel,whichisthecornerstoneofassetpricinginfinancialeconomics.4.1MarketEquilibriuminPureExchangeIntheregimeofCompleteContingentMarkets(CCM),whereclaimstoageneralizedconsumptiongoodCundereachandeverystatecontingencyareseparatelytradable,asshowninChapter2,Equation(2.1.6),theind

4、ividualsoptimumpositioncanbeexpressedastheFundamentalTheoremofRiskBearing:πv(c)πv(c)πv(c)1122ss==···=(4.1.1)P1P2Ps(Thisformofthetheoremisvalidonlyforinteriorsolutions.1)Atthispoint,wecallattentiontothefactthat,inprincipleatleast,allofthefollowingelementsmaydifferamongthevariousindividualsj=1,...

5、,J:1Unlessotherwiseindicated,itwillbeassumedthroughoutthatinterior(andnotcorner)solutionsapplyforalleconomicagents.123124MarketEquilibriumunderUncertaintyjjtheprobabilitybeliefsπs,theconsumptionquantitiescs,andtheutilityfunctionsv(cj).However,thepricesPwillbethesameforallmarketjsparticipants.Inmovi

6、ngfromindividualoptimizationtomarketequilibriumunderCCM,Equation(4.1.1)mustholdforeachandeverymarketparticipant.Itfollowsimmediatelythat,foranytwoindividualsjandk,andcomparingstate1withanyotherstates:jjkkπsvjcsPsπsvkcs==(4.1.2)πjvcjPπkvck1j111k1Thus,foreachandeveryindividual(ataninterio

7、rsolution),thepriceratiobetweenanytwostateclaimswillequaltheratioofexpectedmarginalutilityofincomesinthetwostates.Asanevidentcorollary,ifinadditionindividualsjandkhavethesamebeliefs,thenforalls:vcjjs=ξ