02-Lecture-2-Tools-of-Public-Economics

Lecture2WelfareEconomicesandToolsofPublicEconomics–AreviewBinzhenWuSchoolofEconomicsandManagementOutlineWelfareEconomics–ConditionsforParetoEfficiency–TheFirstandSecondWelfareTheorem–Efficiencyvs.EquityCompetitiveMarketEquilibrium–Consumers’ConstrainedUtilityMaximization–Firms’ProfitMaximization–MarketclearDemandcurveandSupplycurve–Elasticity;aggregation–Socialsurplus,consumersurplus,producersurplusWelfareEconomicsWelfareeconomics:theframeworkusedbymostpubliceconomiststoevaluatethesocialdesirabilityofdifferenteconomicstates.AcentralconceptinwelfareeconomicsisParetoEfficiencyandCompetitiveEquilibrium.ParetoEfficiency-DefinitionAnallocationisParetoOptimalifthereisnootherfeasibleallocationthatmakesatleastonepersonbetteroffandnooneelseworseoff.AParetoimprovementisareallocationofresourcesthatmakesatleastonepersonbetteroffwithoutmakinganyoneelseworseoff.–ItiswelljustifiedforgovernmenttointerveneifitcanmakeParetoimprovement.ConditionsforParetoEfficiency-PureExchangeEconomyPureExchangeEconomy–2people(Adam&Eve)–2commodities(apple&figleaves)–Fixedsupplyofgoods–Assume:AdamandEveeachhaveconventionallyshapedindifferencecurves.TheEdgeworthBoxFigure3.2Graphically,ParetooptimalallocationrequiresAdam’sindifferencecurvetangenttoEve’sindifferencecurve.ParetoEfficiency-GraphicanalysisParetoEfficiency-PureExchangeEconomyMathematically,theslopesofAdam’sandEve’sindifferencecurvesareequal.The|slope|oftheindifferencecurveisknowasthemarginalrateofsubstitutionofaforf(MRSa,f).Itindicatestherateatwhichtheindividualiswillingtotradeaforf;higherMRSafmeanstheindividuallovestheapplemore.Diminishingwitha.fafaMUMUMRS,ParetoEfficiency-PureExchangeEconomyTherefore,paretoefficiencyrequires:MRSMRSafAdamafEveParetoEfficiency–MathParetooptimalallocationsarethesolutionsfortheproblem:•Here,xandyaregoods,Misthetotalamountofgoodsavailable.DifferentucorrespondstodifferentParetooptimalallocation.Thesolutionssatisfy:yxyxyxMyyMxxuyxUtsyxUMax2121222111,,,),(.),(22112,1,yxyxMRSMRSParetoEfficiency-GraphicanalysisManyallocationsareP.O.P.O.isnotrelatetofairness.–ThelocusofallP.O.pointsiscalledthecontractcurve.Contractcurve→UtilityPossibilityCurve.ParetoEfficiency-InputAllocationTwoinputs,laborLandcapitalK,withfixedsupplies.Twofirms:AppleandFigleavesFirm’stechnologyisrepresentedbyitsisoquantcurve:allcombinationsofLandKthatproduceagivenamountofoutput.•LaborConsideranexamplethattwofirmsAandEusingtheinputs.•Capital•Apple•FigLeaveParetoEfficiency-InputAllocationGraph:theParetoefficientallocationsrequirestheisoquantcurveoffirmAandthatofFistangenttoeachotherMath:theslopesoftwofirms’isoquantcurvesareequal.ParetoEfficiency-InputAllocationThe|slope|ofisoquantcurvesismarginalrateoftechnologysubstitution(MRTS).MRTSL,KshowstherateatwhichthefirmcansubstituteLforKwithoutchangingtheamountofoutput;HigherMRTL,Kmeansthefirmismoreefficientinlabor.KLKLMPMPMRTS,ParetoEfficiency-InputAllocationParetoOptimalrequires:FKFLAKALMPMPMPMPi.e.FKLAKLMRTSMRTS,,ParetoEfficiency-Graphicanalysis•Apple•labor•Capital•FigleavesAlotP.Oallocations.TheP.Oallocationset→ProductionPossibilityCurve.ParetoEfficiency-EconomywithProductionConsideraeconomywithproductionforappleandfigleave.Theavailableinputtoisfixed.Theproductionpossibilitiescurveshowsthemaximumquantityoffigsthatcanproducedwithanygivenquantityofapples.ProductionPossibilitiesCurveThe|slope|isthemarginalrateoftransformationofapplesforfigs(MRTaf),showingtherateatwhichtheeconomycantransformapplestofigleavesfafaMCMCMRT,ParetoEfficiency-EconomywithProductionParetoefficiencyrequires:therateatwhichapplescanbetransformedintofigsisequaltotherateatwhichconsumersarewillingtotradeapplesforfigs.:MRTMRSMRSafafAdamafEveEvefEveaAdamfAdamafaMUMUMUMUMCMCorParetoEfficiencyConditions-SummaryInsummary,thenecessaryconditionsforparetoefficiencyare:Anotherformtowriteis:EvefEveaAdamfAdamafaMUMUMUMUMCMCEKELAKALMPMPMPMPEvefaAdamfaafEKLAKLEvefaAdamfaMRSMRSMRTMRTSMRTSMRSMRS,,,,,,FirstFundamentalTheoremofWelfareEconomicsHowcanweattainParetoEfficientoutcomes?FirstWelfareTheorem:aParetoefficientallocationwillemergeinacompetitivemarketif–Allproducersandconsumersactasperfectcompetitors(e.g.,nomarketpower)–AmarketexistsforeverycommodityImplication:Competitiveeconomyautomaticallyallocatesresourcesefficiently,withoutcentralplanning.CompetitiveMarketEquilibriumThreeconditionsforCompetitiveMarketEquilibrium(WalrasEquilibrium):–Givenprices,consumerschooseconsumptionstomaximizeutilitysubjecttothebudgetconstraint–Givenpricesandtechnology,firmschooseinputsandoutputstomaximizeprofit–MarketsclearFeature:–price-takingconsumersandfirms.–Pricesaredeterminedbymarketclearing.Individual’sConstrainedUtilityMaximizationEx.Adamchoosetwogoods:MovieandCDs–Giventheprices,Adammakechoicestomaximizehisutilitygivenhisbudgeconstraint.Graphically:findthehighestindifferencecurvegiventhebudgetconstraint–Theoptimalchoiceoccurswheretheindifferencecurveistangenttothebudgetconstraint.Figure1UtilityMaximizationQM(quantityofmovies)QCD(quantityofCDs)012