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1、14.03Fall2000ProblemSet#7:AsymmetricInformation,Signaling,andGameTheoryDueinClass#24Theory:1.Itisknownthatsomefractiondofallnewcarsisdefective.Defectivecarscannotbeidentifiedassuchexceptbythepeoplewhoownthem.Eachconsumerisriskneutralandvaluesanon-defectivecarat$6,000.Newcarssellfor$4
2、,000each,usedonesfor$1,000.Ifcarsdonotdepreciatephysicallywithuse,whatisd?2.TheMassachusettsInstituteofTiddlywinks(thepremierinstitutionofitskind)hiresTiddlywinksAssistants(TAs)fromamongapoolofavailableapplicants.Applicantsvaryinquality.Somearegood(G);someareexcellent(E);andsomearest
3、upendous(S).Unfortunately,anapplicant’stypescannotbedetermineduntilapproximately1A.M.onthemorningthefirstproblemsetisdue,bywhichtimeitistoolatetochangeassistants.ApplicantswhoarenotchosenspendthesemesterplayinginTiddlywinkstournamentsprofessionally.Goodplayersearn$50persemester;Excel
4、lentplayersearn$200persemesterandStupendousplayersearn$400.Theapplicantpoolissplitevenlyamongthethreetypes(eachofwhomknowsherquality),andtheInstitutechoosesrandomlyamongthosecandidateswhoapplyatthestatedwage.Regardlessofquality,noTAeveragreestodoitmorethanonce.EachTiddlywinksclasshas
5、100students,whoseV-N-MutilitydependsontheirwealthandtheirTA’squalityandisgivenby:U=WiftheytakeaclassandgetagoodTA;U=W+5iftheytakeaclassandgetanexcellentTA;U=W+7iftheytakeaclassandgetastupendousTA.Eachstudenttakesonly1class.TherearenocostsofofferingcoursesotherthanhiringTAs.(TheProfes
6、sors,ofcourse,workforLoveofLearning.)A.AssumethattheInstitutemaximizesexpectedstudentutilitysubjecttotheconstraintthatitnotlosemoney.WhatwageshoulditoffertopayTAs,andwhatpriceshoulditchargeforclasses?WhatisthequalitycompositionoftheTAapplicantpool(intermsofG,E,andS)?B.ThenewDeanhasde
7、cidedtodosomethingaboutthequalityofteachingatMIT.Shehasdecreedthatfromnowon,theaveragequalityofTAsmustbeatleastExcellent.Whatwagemustbeoffered,andwhatpricechargedtostudentstobringthisabout?C.AProfessoratCalTiddly(arivalinstitutionontheWestcoast)hasdevelopedatestthatcandistinguishGood
8、TAsfromtheot
