中级微观济学课件尼科尔森ch21

柯孔林浙江工商大学金融学院1Chapter21POLITICALECONOMICS柯孔林浙江工商大学金融学院2SocialWelfareCriteriaAnalyzingthechoiceamongfeasibleallocationsofresourcesisdifficultitinvolvesmakingchoicesabouttheutilitylevelsofdifferentindividualsinchoosingbetweentwoallocations(AandB)theproblemarisesthatsomeindividualspreferAwhileotherspreferB柯孔林浙江工商大学金融学院3SocialWelfareCriteriaWecanusetheEdgeworthboxdiagramtoshowtheproblemsinvolvedinestablishingsocialwelfarecriteriaonlypointsonthecontractcurveareconsideredaspossiblecandidatesforasocialoptimumalongthecontractcurve,theutilitiesofthetwoindividualsvary,andtheseutilitiesaredirectlycompetitive柯孔林浙江工商大学金融学院4SocialWelfareCriteriaOJOSUJ4UJ3UJ2UJ1US4US3US2US1Contractcurve柯孔林浙江工商大学金融学院5SocialWelfareCriteriaIfwearewillingtoassumethatutilitycanbecomparedamongindividuals,wecanusethecontractcurvetoconstructtheutilitypossibilityfrontier柯孔林浙江工商大学金融学院6SocialWelfareCriteriaSmith’sutilityJones’sutilityOJOSTheutilitypossibilityfrontiershowsthoseutilitylevelsforSmithandJonesthatareobtainablefromthefixedquantityofgoodsavailableAnypointinsidethecurveisPareto-inefficient

C柯孔林浙江工商大学金融学院7EqualityCriterionSmith’sutilityJones’sutilityOJOSOnepossiblecriterioncouldrequirecompleteequitygivingSmithandJonesthesamelevelofwelfare45°Utilityisequalinthiscase,butthequantitiesofxandymaynotbeThisoccursatUJAandUSAUSAUJA

A柯孔林浙江工商大学金融学院8ContractcurveEqualityCriterionOJOSUJ2UJAUJ1US2USAUS1A

XSA

XJAYSAYSA柯孔林浙江工商大学金融学院9UtilitarianCriterionAsimilarcriterionwouldbetochoosetheallocationontheutilitypossibilityfrontiersothatthesumofSmith’sandJones’sutilitiesisthegreatestthispointwouldimplyacertainallocationofxandybetweenSmithandJones柯孔林浙江工商大学金融学院10TheRawlsCriterionThiswasfirstposedbyphilosopherJohnRawlsSupposethateachindividualbeginsinaninitialpositioninwhichnooneknowswhathisfinalpositionwillbeindividualsareriskaversesocietywillonlymoveawayfromperfectequalitywhentheworstoffpersonwouldbebetteroffunderinequalitythanequality柯孔林浙江工商大学金融学院11TheRawlsCriterionSmith’sutilityJones’sutilityOJOSUnequaldistributionssuchasBwouldbepermittedwhentheonlyattainableequaldistributionsarebelowD45°DBAEqualdistributionsthatliebetweenDandAaresuperiortoBbecausetheworse-offindividualisbetterofftherethanatB

柯孔林浙江工商大学金融学院12SocialWelfareFunctionsAsocialwelfarefunctionmaydependonSmith’sandJones’sutilitylevelssuchassocialwelfare=w(US,UJ)ThesocialproblemistoallocatexandybetweenSmithandJonesastomaximizew柯孔林浙江工商大学金融学院13Theoptimalpointofsocialwelfareiswherewismaximizedgiventheutilitypossibilityfrontierw1w2SocialWelfareFunctionsSmith’sutilityJones’sutilityOJOSEThisoccursatUJEandUSEUSEUJE

柯孔林浙江工商大学金融学院14w1w2SocialWelfareFunctionsSmith’sutilityJones’sutilityOJOSEventhoughpointFisPareto-inefficient,itisstillpreferredtopointDNotethetradeoffbetweenequityandefficiencyD

F柯孔林浙江工商大学金融学院15EquitableSharingAfatherarriveshomewithan8-piecepizzaandmustdecidehowtoshareitbetweenhistwosonsTeen1hasautilityfunctionoftheformTeen2hasautilityfunctionoftheform柯孔林浙江工商大学金融学院16EquitableSharingTheleastresistanceoptionwouldbetogiveeachteen4slicesU1=4,U2=2Thefathermaywanttomakesuretheteenshaveequalutilityx1=1.6,x2=6.4,U1=U2=2.53Thefathermaywanttomaximizethesumofhissonsutilityx1=6.4,x2=1.6,U1=5.06,U2=1.26柯孔林浙江工商大学金融学院17EquitableSharingSupposethefathersuggeststhathewillflipacointodeterminewhogetswhichportionlistedunderthethreeallocationsTheexpectedutilitiesofthetwoteensfromacoinflipthatyieldseither1.6or6.4slicesisE(U1)=0.5(2.53)+0.5(5.06)=3.80E(U2)=0.5(2.53)+0.5(1.26)=1.90柯孔林浙江工商大学金融学院18EquitableSharingGiventhischoice,theteenswilloptfortheequaldistributionbecauseeachgetshigherexpectedutilityfromitthanfromthecoinflip柯孔林浙江工商大学金融学院19EquitableSharingIfthefathercouldsubjecttheteenstoa“veilofignorance”sothatneitherwouldknowhisidentityuntilthepizzaisserved,thevotingmightstillbedifferentifeachteenfocusesonaworst-casescenario,hewilloptfortheequalutilityallocationinsuresthatutilitywillnotfallbelow2.53柯孔林浙江工商大学金融学院20EquitableSharingSupposethateachteenbelievesthathehasa50-50chanceofbeinglabeledas“teen1”or“teen2”Expectedutilitiesare

x1=x2=4E(U1)=0.5(4)+0.5(2)=3x1=1.6,x2=6.4E(U1)=0.5(2.53)+0.5(2.53)=2.53x1=6.4,x2=1.6E(U1)=0.5(5.06)+0.5(1.26)=3.16Theteenswilloptfortheutilitariansolution柯孔林浙江工商大学金融学院21TheArrowImpossibilityTheoremArrowviewsthegeneralsocialwelfareproblemasoneofchoosingamongseveralfeasible“socialstates”itisassumedthateachindividualcanrankthesestatesaccordingtotheirdesirabilityArrowraisesthefollowingquestion:doesthereexistarankingonasociety-widescalethatfairlyrecordsthesepreferences?柯孔林浙江工商大学金融学院22TheArrowImpossibilityTheoremAssumethatthereare3socialstates(A,B,andC)and2individuals(SmithandJones)SmithprefersAtoBandBtoCAPSBandBPSCandAPSCJonesprefersCtoAandAtoBCPJAandAPJBandCPJB柯孔林浙江工商大学金融学院23TheArrowImpossibilityTheoremArrow’simpossibilitytheoremconsistsofshowingthatareasonablesocialrankingofthesethreestatescannotexistArrowassumesthatanysocialrankingshouldobeysixseeminglyunobjectionableaxioms“P”shouldberead“issociallypreferredto”柯孔林浙江工商大学金融学院24TheArrowAxiomsItmustrankallsocialstateseitherAPB,BPA,orAandBareequallydesirable(AIB)foranytwostatesAandBTherankingmustbetransitiveifAPBandBPC(orBIC),thenAPCTherankingmustbepositivelyrelatedtoindividualpreferencesifAisunanimouslypreferredbySmithandJones,thenAPB柯孔林浙江工商大学金融学院25TheArrowAxiomsIfnewsocialstatesefeasible,thisfactshouldnotaffecttherankingoftheoriginalstatesIfAPB,thenthiswillremaintrueifsomenewstate(D)esfeasibleThesocialpreferencefunctionshouldnotbeimposedbycustomitshouldnotbethecasethatAPBregardlessofthetastesofindividualsinsociety柯孔林浙江工商大学金融学院26TheArrowAxiomsTherelationshipshouldbenondictatorialoneperson’spreferencesshouldnotdeterminesociety’spreferences柯孔林浙江工商大学金融学院27Arrow’sProofArrowwasabletoshowthatthesesixconditionsarenotcompatiblewithoneanotherbecauseBPSCandCPJB,itmustbethecasethatBIConeperson’spreferencescannotdominatebothAPSBandAPJB,soAPBtransitivityimpliesthatAPCthiscannotbetruebecauseAPSCbutCPJA柯孔林浙江工商大学金融学院28Significanceofthe

ArrowTheoremIngeneral,Arrow’sresultappearstoberobusttoevenmodestchangesinthesetofbasicpostulatesThus,economistshavemovedawayfromthenormativequestionofhowchoicescanbemadeinasociallyoptimalwayandhavefocusedonthepositiveanalysisofhowsocialchoicesareactuallymade柯孔林浙江工商大学金融学院29DirectVotingVotingisusedasasocialdecisionprocessinmanyinstitutionsdirectvotingisusedinmanycasesfromstatewidereferendatosmallergroupsandclubsinothercases,societieshavefounditmoreconvenienttousearepresentativeformofgovernment柯孔林浙江工商大学金融学院30MajorityRuleThroughoutourdiscussionofvoting,wewillassumethatdecisionswillbemadebymajorityrulethereisnothingparticularlysacredaboutarulerequiringthatapolicyobtain50percentofthevotetobeadopted柯孔林浙江工商大学金融学院31TheParadoxofVotingInthe1780s,socialtheoristM.deCondorcetnotedthatmajorityrulevotingsystemsmaynotarriveatanequilibriuminstead,theymaycycleamongalternativeoptions柯孔林浙江工商大学金融学院32TheParadoxofVotingSupposetherearethreevoters(Smith,Jones,andFudd)choosingamongthreepolicyoptionswecanassumethatthesepolicyoptionsrepresentthreelevelsofspendingonaparticularpublicgood[(A)low,(B)medium,and(C)high]Condorcet’sparadoxwouldariseevenwithoutthisordering柯孔林浙江工商大学金融学院33TheParadoxofVotingPreferencesamongthethreepolicyoptionsforthethreevotersare:柯孔林浙江工商大学金融学院34TheParadoxofVotingConsideravotebetweenAandBAwouldwinInavotebetweenAandCCwouldwinInavotebetweenBandCBwouldwinNoequilibriumwilleverbereached柯孔林浙江工商大学金融学院35Single-PeakedPreferencesEquilibriumvotingesalwaysoccurincaseswheretheissuebeingvoteduponisone-dimensionalandwherevoterpreferencesare“single-peaked”柯孔林浙江工商大学金融学院36Single-PeakedPreferencesQuantityofpublicgoodUtilityABC

SmithWecanshoweachvoterspreferencesintermsofutilitylevels

Jones

FuddForSmithandJones,preferencesaresingle-peakedFudd’spreferenceshavetwolocalmaxima柯孔林浙江工商大学金融学院37Single-PeakedPreferencesQuantityofpublicgoodUtilityABC

Smith

JonesOptionBwillbechosenbecauseitwilldefeatbothAandCbyvotes2to1IfFuddhadalternativepreferenceswithasinglepeak,therewouldbenoparadox

Fudd柯孔林浙江工商大学金融学院38TheMedianVoterTheoremWiththealteredpreferencesofFudd,Bwillbechosenbecauseitisthepreferredchoiceofthemedianvoter(Jones)Jones’spreferencesarebetweenthepreferencesofSmithandtherevisedpreferencesofFudd柯孔林浙江工商大学金融学院39TheMedianVoterTheoremIfchoicesareunidimensionalandpreferencesaresingle-peaked,majorityrulewillresultintheselectionoftheprojectthatismostfavoredbythemedianvoterthatvoter’spreferenceswilldeterminewhatpublicchoicesaremade柯孔林浙江工商大学金融学院40ASimplePoliticalModelSupposeacommunityischaracterizedbyalargenumberofvoters(n)eachwitheofyiTheutilityofeachvoterdependsonhisconsumptionofaprivategood(ci)andofapublicgood(g)accordingtoutilityofpersoni=Ui=ci+f(g)wherefg>0andfgg<0柯孔林浙江工商大学金融学院41ASimplePoliticalModelEachvotermustpaytaxestofinancegTaxesareproportionaltoeandareimposedatarateoftEachperson’sbudgetconstraintisci=(1-t)yiThegovernmentalsofacesabudgetconstraint柯孔林浙江工商大学金融学院42ASimplePoliticalModelGiventheseconstraints,theutilityfunctionofindividualiisUi(g)=[yA-(g/n)]yi/yA+f(g)UtilitymaximizationoccurswhendUi/dg=-yi/(nyA)+fg(g)=0g=fg-1[yi/(nyA)]Desiredspendingongisinverselyrelatedtoe柯孔林浙江工商大学金融学院43ASimplePoliticalModelIfGisdeterminedthroughmajorityrule,itslevelwillbethatlevelfavoredbythemedianvotersincevoters’preferencesaredeterminedsolelybye,gwillbesetatthelevelpreferredbythevoterwiththemedianlevelofe(ym)g*=fg-1[ym/(nyA)]=fg-1[(1/n)(ym/yA)]柯孔林浙江工商大学金融学院44ASimplePoliticalModelUnderautilitariansocialwelfarecriterion,gwouldbechosensoastomaximizethesumofutilities:Theoptimalchoiceforgthenisg*=fg-1(1/n)=fg-1[(1/n)(yA/yA)]thelevelofgfavoredbythevoterwithaveragee柯孔林浙江工商大学金融学院45VotingforRedistributiveTaxationSupposevotersareconsideringalump-sumtransfertobepaidtoeverypersonandfinancedthroughproportionaltaxationIfwedenotetheper-persontransferb,eachindividual’sutilityisnowgivenbyUi=ci+b柯孔林浙江工商大学金融学院46VotingforRedistributiveTaxationThegovernment’sbudgetconstraintisnb=tnyAb=tyAForavoterwithyi>yA,utilityismaximizedbychoosingb=0Anyvoterwithyi<yAwillchooset=1andb=yAwouldfullyequalizees柯孔林浙江工商大学金融学院47VotingforRedistributiveTaxationNotethata100percenttaxratewouldloweraverageeAssumethateachindividual’sehastwocomponents,oneresponsivetotaxrates[yi(t)]andonenotresponsive(ni)alsoassumethattheaverageofniiszero,butitsdistributionisskewedrightsonm<0柯孔林浙江工商大学金融学院48VotingforRedistributiveTaxationNow,utilityisgivenbyUi=(1-t)[yi(t)+ni]+bTheindividual’sfirst-orderconditionforamaximuminhischoiceoftandgisnowdUi/dt=-ni+t(dyA/dt)=0ti=ni/(dyA/dt)Undermajorityrule,theequilibriumconditionwillbet*=nm/(dyA/dt)柯孔林浙江工商大学金融学院49RepresentativeGovernmentInrepresentativegovernments,peoplevoteforcandidates,notpoliciesPoliticians’policypreferencesareaffectedbyavarietyoffactorstheirperceptionsofwhattheirconstituentswanttheirviewofthe“publicgood”theforcefulnessof“specialinterests”theirdesireforreelection柯孔林浙江工商大学金融学院50ProbabilisticVotingAssumethereareonlytwocandidatesforapoliticalofficeeachcandidiateannounceshisplatform(

1and2)alsoassumethatthecandidate,onceelected,willactuallyseektoimplementtheplatformhehasstatedEachofthenvotersobservethetwoplatformsandchoosehowtovote柯孔林浙江工商大学金融学院51ProbabilisticVotingTheprobabilitythatvoteriwillvoteforcandidate1is

i=fi[Ui(1)-Ui(2)]wheref’>0andUi(j)istheutilitythatvoteriexpectstoreceivefromplatformjTheprobabilitythatvoteriwillvoteforcandidate1is1-

i柯孔林浙江工商大学金融学院52TheCandidateGameCandidate1chooses

1tomaximizetheprobabilityofhiselectionCandidate2chooses

2tomaximizehisexpectedvotes柯孔林浙江工商大学金融学院53TheCandidateGameOurvotinggameisazero-sumgamewithcontinuousstrategies(

1and2)Thus,thisgamewillhaveaNashequilibriumsetofstrategiesforwhichEV1(1,2*)EV1(1*,2*)EV1(1*,2)

Candidate1doesbestagainst2*bychoosing1*Candidate2doesbestagainst1*bychoosing2*柯孔林浙江工商大学金融学院54NetValuePlatformsA“netvalue”platformisoneunderwhichacandidatepromisesauniquedollarbenefittoeachvoterSupposecandidate1promisesanetdollarbenefitof

1itoeachvoterThecandidateisboundbyagovernmentbudgetconstraint:柯孔林浙江工商大学金融学院55NetValuePlatformsThecandidates’goalistochoose

1ithatmaximizesEV1against2*SettinguptheLagrangianyields柯孔林浙江工商大学金融学院56NetValuePlatformsThefirst-orderconditionforthenetbenefitpromisedtovoteriisgivenbyL/1i=fi’Ui’+=0Ifthefunctionfiisthesameforallvoters,thismeansthatthecandidateshouldchoose1isothatUi’isthesameforallvotersautilitariane柯孔林浙江工商大学金融学院57Rent-SeekingBehaviorElectedpoliticiansperformtheroleofagentschoosepoliciesfavoredbyprincipals(voters)Aperfectagentwouldchoosepoliciesthatthefullyinformedmedianvoterwouldchoosearepoliticianssoselfless?柯孔林浙江工商大学金融学院58Rent-SeekingBehaviorPoliticiansmightengageinrent-seekingactivitiesactivitiest