InformationAsymmetryBasicsSignaling,ScreeningandOtherTopicsBenjaminChiaoApr14,2011(afterclassversion)LectureNotesforUndergraduateLevelInformationEconomics,ShanghaiUniversityofFinanceandEconomicsTheProblemsofHiddenType:JobMarketSignalingIWhatiftheagent,withsomecost,cansendsignalsindicatingthehiddentypetothelessinformedperson?ILet’sconsiderajobmarketmodel(Spence[1973])whereworkersdecideonhowmuchtheywishtoinvestineducation.IOnecrucialassumptioninthismodelis:educationislesscostlyformoreproductiveworkers.IWorkersdecidethelevelofeducationtheywishtoreceive,andthecostsforthesamelevelofeducationisdi¤erentIWorkerswithhigherproductivityhavelowercostsforeducationIWorkerswithlowerproductivityhavehighercostsforeducationIEmployersobservethesignal.Theyformbeliefsontherelationshipbetweentheobservedsignalandunobservedproductivity.IEmployersandjobapplicantsareallriskneutral(i.e.maximizeexpectedvalues).ILabormarketisperfectlycompetitive(zeropro…timpliesthatwage=expectedmarginalproductivity)ITwotypesofjobapplicants:ITypeL:MarginalProduct(MP)=1ITypeH:MarginalProduct(MP)=2ITypeLandtypeHtakeupportionqand1qofthepopulation 1.FullInformationSolutionIWageequalstotheobservedmarginalproduct:wL=1;wH=2(1)2.NoSignalingSolutionITheemployerspayeveryonethesamewage,zero-pro…timpliesthatwageequalstoexpectedmarginalproduct:wns=1q+2(1q)=2q(2) 3.(SeparatingEquilibrium)SignalingSolutionsINowsupposethecrucialassumptionthatworkersofdi¤erentproductivitieshavedi¤erentcostsofobtainingeducation(y):yIcL(y)=y,cH(y)=2INowwageo¤erswillvarywitheducation:w=w(y)ISupposeemployersbelievethatapplicantswithyyareofhighproductivity.IWiththisbelief,thewagewillbew(y)=1ify<y,andw(y)=2ifyy.Withthiso¤er,eachworkerwillchooseeithery=0ory=y.IUnderwhatconditionswilltheemployer’sbeliefbecorrect?ITypeLwillchoosey=0i¤:w(0)c(0)w(y)c(y),i.e.y1(3) L LITypeHwillchoosey=yi¤Iw(0)c(0)w(y)c(y)i.e.y2(4) H HITherefore,aslongas1y2,theemployers’be
