ChapterThirty-TwoProductionExchangeEconomies(revisited)Noproduction,onlyendowments,sonodescriptionofhowresourcesareconvertedtoconsumables.Generalequilibrium:allmarketsclearsimultaneously.1stand2ndFundamentalTheoremsofWelfareEconomics.NowAddProduction...Addinputmarkets,outputmarkets,describefirms’technologies,thedistributionsoffirms’outputsandprofits…NowAddProduction...Addinputmarkets,outputmarkets,describefirms’technologies,thedistributionsoffirms’outputsandprofits…That’snoteasy!RobinsonCrusoe’sEconomyOneagent,RC.Endowedwithafixedquantityofoneresource--24hours.Usetimeforlabor(production)orleisure(consumption).Labortime=L.Leisuretime=24-L.WhatwillRCchoose?RobinsonCrusoe’sTechnologyTechnology:Laborproducesoutput(coconuts)accordingtoaconcaveproductionfunction.RobinsonCrusoe’sTechnologyProductionfunctionLabor(hours)Coconuts240RobinsonCrusoe’sTechnologyLabor(hours)CoconutsProductionfunction240Feasibleproduction

plansRobinsonCrusoe’sPreferencesRC’spreferences:coconutisagoodleisureisagoodRobinsonCrusoe’sPreferencesLeisure(hours)CoconutsMorepreferred240RobinsonCrusoe’sPreferencesLeisure(hours)CoconutsMorepreferred240RobinsonCrusoe’sChoiceLabor(hours)CoconutsFeasibleproduction

plansProductionfunction240RobinsonCrusoe’sChoiceLabor(hours)CoconutsFeasibleproduction

plansProductionfunction240Leisure(hours)240RobinsonCrusoe’sChoiceLabor(hours)CoconutsFeasibleproduction

plansProductionfunction240Leisure(hours)240RobinsonCrusoe’sChoiceLabor(hours)CoconutsFeasibleproduction

plansProductionfunction240Leisure(hours)240RobinsonCrusoe’sChoiceLabor(hours)CoconutsProductionfunction240Leisure(hours)240C*L*RobinsonCrusoe’sChoiceLabor(hours)CoconutsProductionfunction240Leisure(hours)240C*L*LaborRobinsonCrusoe’sChoiceLabor(hours)CoconutsProductionfunction240Leisure(hours)240C*L*LaborLeisureRobinsonCrusoe’sChoiceLabor(hours)CoconutsProductionfunction240Leisure(hours)240C*L*LaborLeisureOutputRobinsonCrusoe’sChoiceLabor(hours)CoconutsProductionfunction240Leisure(hours)240C*L*LaborLeisureMRS=MPLOutputRobinsonCrusoeasaFirmNowsupposeRCisbothautility-maximizingconsumerandaprofit-maximizingfirm.Usecoconutsasthenumerairegood;i.e.priceofacoconut=$1.RC’swagerateisw.CoconutoutputlevelisC.RobinsonCrusoeasaFirmRC’sfirm’sprofitis=C-wL.=C-wLC=

+wL,theequationofanisoprofitline.Slope=+w.Intercept=

.IsoprofitLinesLabor(hours)Coconuts24Higherprofit;Slopes=+w0Profit-MaximizationLabor(hours)CoconutsFeasibleproduction

plansProductionfunction240Profit-MaximizationLabor(hours)CoconutsProductionfunction240Profit-MaximizationLabor(hours)CoconutsProductionfunction240Profit-MaximizationLabor(hours)CoconutsProductionfunction24C*L*0Profit-MaximizationLabor(hours)CoconutsProductionfunction24C*L*Isoprofitslope=productionfunctionslope0Profit-MaximizationLabor(hours)CoconutsProductionfunction24C*L*Isoprofitslope=productionfunctionslopei.e.w=MPL0Profit-MaximizationLabor(hours)CoconutsProductionfunction24C*L*Isoprofitslope=productionfunctionslopei.e.w=MPL=1MPL=MRPL.0Profit-MaximizationLabor(hours)CoconutsProductionfunction24C*L*Isoprofitslope=productionfunctionslopei.e.w=MPL=1MPL=MRPL.RCgets

0Profit-MaximizationLabor(hours)CoconutsProductionfunction24C*L*Isoprofitslope=productionfunctionslopei.e.w=MPL=1MPL=MRPL.Givenw,RC’sfirm’squantitydemandedoflaborisL*LabordemandRCgets

0Profit-MaximizationLabor(hours)CoconutsProductionfunction24C*L*Isoprofitslope=productionfunctionslopei.e.w=MPL=1MPL=MRPL.Givenw,RC’sfirm’squantitydemandedoflaborisL*andoutputquantitysuppliedisC*.LabordemandOutputsupplyRCgets

0Utility-MaximizationNowconsiderRCasaconsumerendowedwith$*whocanworkfor$wperhour.WhatisRC’smostpreferredconsumptionbundle?BudgetconstraintisUtility-MaximizationLabor(hours)Coconuts240BudgetconstraintUtility-MaximizationLabor(hours)Coconuts240Budgetconstraint;slope=wUtility-MaximizationLabor(hours)CoconutsMorepreferred240Utility-MaximizationLabor(hours)Coconuts240Budgetconstraint;slope=wUtility-MaximizationLabor(hours)CoconutsBudgetconstraint;slope=w240Utility-MaximizationLabor(hours)Coconuts240C*L*Budgetconstraint;slope=wUtility-MaximizationLabor(hours)Coconuts240C*L*MRS=wBudgetconstraint;slope=wUtility-MaximizationLabor(hours)Coconuts240C*L*LaborsupplyBudgetconstraint;slope=wMRS=wGivenw,RC’squantitysuppliedoflaborisL*Utility-MaximizationLabor(hours)Coconuts240C*L*Givenw,RC’squantitysuppliedoflaborisL*andoutputquantitydemandedisC*.LaborsupplyOutputdemandBudgetconstraint;slope=wMRS=wUtility-Maximization&Profit-MaximizationProfit-maximization:w=MPLquantityofoutputsupplied=C*quantityoflabordemanded=L*Utility-Maximization&Profit-MaximizationProfit-maximization:w=MPLquantityofoutputsupplied=C*quantityoflabordemanded=L*Utility-maximization:w=MRSquantityofoutputdemanded=C*quantityoflaborsupplied=L*Utility-Maximization&Profit-MaximizationProfit-maximization:w=MPLquantityofoutputsupplied=C*quantityoflabordemanded=L*Utility-maximization:w=MRSquantityofoutputdemanded=C*quantityoflaborsupplied=L*Coconutandlabormarketsbothclear.Utility-Maximization&Profit-MaximizationLabor(hours)Coconuts24C*L*0MRS=w

=MPLGivenw,RC’squantitysuppliedoflabor=quantitydemandedoflabor=L*andoutputquantitydemanded=outputquantitysupplied=C*.ParetoEfficiencyMusthaveMRS=MPL.ParetoEfficiencyLabor(hours)Coconuts240MRSMPLParetoEfficiencyLabor(hours)Coconuts240MRSMPLPreferredconsumptionbundles.ParetoEfficiencyLabor(hours)Coconuts240MRS=MPLParetoEfficiencyLabor(hours)Coconuts240MRS=MPL.Thecommonsloperelativewageratewthatimplements

theParetoefficientplanbydecentralizedpricing.FirstFundamentalTheoremofWelfareEconomicsAcompetitivemarketequilibriumisParetoefficientifconsumers’preferencesareconvextherearenoexternalitiesinconsumptionorproduction.SecondFundamentalTheoremofWelfareEconomicsAnyParetoefficienteconomicstatecanbeachievedasacompetitivemarketequilibriumifconsumers’preferencesareconvexfirms’technologiesareconvextherearenoexternalitiesinconsumptionorproduction.Non-ConvexTechnologiesDotheWelfareTheoremsholdiffirmshavenon-convextechnologies?Non-ConvexTechnologiesDotheWelfareTheoremsholdiffirmshavenon-convextechnologies?The1stTheoremdoesnotrelyuponfirms’technologiesbeingconvex.Non-ConvexTechnologiesLabor(hours)Coconuts240MRS=MPL

ThecommonsloperelativewageratewthatimplementstheParetoefficientplanbydecentralizedpricing.Non-ConvexTechnologiesDotheWelfareTheoremsholdiffirmshavenon-convextechnologies?The2ndTheoremdoesrequirethatfirms’technologiesbeconvex.Non-ConvexTechnologiesLabor(hours)Coconuts240MRS=MPL.TheParetooptimalallocation

cannotbeimplementedbyacompetitiveequilibrium.ProductionPossibilitiesResourceandtechnologicallimitationsrestrictwhataneconomycanproduce.Thesetofallfeasibleoutputbundlesistheeconomy’sproductionpossibilityset.Theset’souterboundaryistheproductionpossibilityfrontier.ProductionPossibilitiesFishCoconutsProductionpossibilityfrontier(ppf)ProductionPossibilitiesFishCoconutsProductionpossibilityfrontier(ppf)ProductionpossibilitysetProductionPossibilitiesFishCoconutsFeasiblebutinefficientProductionPossibilitiesFishCoconutsFeasiblebutinefficientFeasibleandefficientProductionPossibilitiesFishCoconutsFeasiblebutinefficientFeasibleandefficientInfeasibleProductionPossibilitiesFishCoconutsPpf’sslopeisthemarginalrateofproducttransformation.ProductionPossibilitiesFishCoconutsPpf’sslopeisthemarginalrateofproducttransformation.IncreasinglynegativeMRPTincreasingopportunitycosttospecialization.ProductionPossibilitiesIftherearenoproductionexternalitiesthenappfwillbeconcavew.r.t.theorigin.Why?ProductionPossibilitiesIftherearenoproductionexternalitiesthenappfwillbeconcavew.r.t.theorigin.Why?Becauseefficientproductionrequiresexploitationofcomparativeadvantages.Imagineaneconomicsystemwithonlytwogoods,

potatoesandmeatandonlytwopeople,

apotatofarmerandacattlerancherWhatshouldeachpersonproduce?Whyshouldthesepeopletrade?APARABLEFORTHEMODERNECONOMYProductionPossibilitiesSupposethefarmerandrancherdecidenottoengageintrade:Eachconsumesonlywhatheorshecanproducealone.Theproductionpossibilitiesfrontierisalsotheconsumptionpossibilitiesfrontier.Withouttrade,economicgainsarediminished.Figure1TheProductionPossibilitiesFrontierPotatoes(ounces)416832A0Meat(ounces)(a)TheFarmer’sProductionPossibilitiesFrontierIfthereisnotrade,thefarmerchoosesthisproductionandconsumption.Copyright?2003Southwestern/ThomsonLearningFigure1TheProductionPossibilitiesCurveCopyright?2003Southwestern/ThomsonLearningPotatoes(ounces)1224B0Meat(ounces)(b)TheRancher’sProductionPossibilitiesFrontier4824Ifthereisnotrade,therancherchoosesthisproductionandconsumption.ProductionandConsumptionWithoutTradeThefarmershouldproducepotatoes.Theranchershouldproducemeat.SpecializationandTradeSupposeinsteadthefarmerandtherancherdecidetospecializeandtrade…Bothwouldbebetteroffiftheyspecializeinproducingtheproducttheyaremoresuitedtoproduce,andthentradewitheachother.Figure2HowTradeExpandstheSetofConsumptionOpportunitiesCopyright?2003Southwestern/ThomsonLearningPotatoes(ounces)416517832AA*0Meat(ounces)(a)TheFarmer’sProductionandConsumptionFarmer'sproductionandconsumptionwithouttradeFarmer'sconsumptionwithtradeFarmer'sproductionwithtradeFigure2HowTradeExpandstheSetofConsumptionOpportunitiesCopyright?2004South-WesternPotatoes(ounces)12241327B0Meat(ounces)(b)TheRancher’sProductionandConsumption48241218B*Rancher'sconsumptionwithtradeRancher'sproductionwithtradeRancher'sproductionandconsumptionwithouttradeCOMPARATIVEADVANTAGEDifferencesinthecostsofproductiondeterminethefollowing:Whoshouldproducewhat?Howmuchshouldbetradedforeachproduct?COMPARATIVEADVANTAGETwowaystomeasuredifferencesincostsofproduction:Thenumberofhoursrequiredtoproduceaunitofoutput(forexample,onepoundofpotatoes).Theopportunitycostofsacrificingonegoodforanother.ComparativeAdvantageandTradePotatocosts…TheRancher’sopportunitycostofanounceofpotatoesis1/2anounceofmeat.TheFarmer’sopportunitycostofanounceofpotatoesis1/4anounceofmeat.Meatcosts…TheRancher’sopportunitycostofapoundofmeatisonly2ouncesofpotatoes.TheFarmer’sopportunitycostofanounceofmeatisonly4ouncesofpotatoes...ComparativeAdvantageandTrade…so,theRancherhasacomparativeadvantageintheproductionofmeatbuttheFarmerhasacomparativeadvantageintheproductionofpotatoes.ComparativeAdvantageandTradeComparativeadvantageanddifferencesinopportunitycostsarethebasisforspecializedproductionandtrade.Wheneverpotentialtradingpartieshavedifferencesinopportunitycosts,theycaneachbenefitfromtrade.GainsfromTradeComparativeAdvantageandTradeBenefitsofTrade

Tradecanbenefiteveryoneinasocietybecauseitallowspeopletospecializeinactivitiesinwhichtheyhaveacomparativeadvantage.ComparativeAdvantageTwoagents,RCandManFriday(MF).RCcanproduceatmost20coconutsor30fish.MFcanproduceatmost50coconutsor25fish.ComparativeAdvantageFCFCRCMF20503025ComparativeAdvantageFCFCRCMF20503025MRPT=-2/3coconuts/fishsoopp.costofonemorefishis2/3foregonecoconuts.ComparativeAdvantageFCFCRCMF20503025MRPT=-2/3coconuts/fishsoopp.costofonemorefishis2/3foregonecoconuts.MRPT=-2coconuts/fishsoopp.costofonemorefishis2foregonecoconuts.ComparativeAdvantageFCFCRCMF20503025MRPT=-2/3coconuts/fishsoopp.costofonemorefishis2/3foregonecoconuts.MRPT=-2coconuts/fishsoopp.costofonemorefishis2foregonecoconuts.RChasthecomparativeopp.costadvantageinproducingfish.ComparativeAdvantageFCFCRCMF20503025MRPT=-2/3coconuts/fishsoopp.costofonemorecoconutis3/2foregonefish.ComparativeAdvantageFCFCRCMF20503025MRPT=-2/3coconuts/fishsoopp.costofonemorecoconutis3/2foregonefish.MRPT=-2coconuts/fishsoopp.costofonemorecoconutis1/2foregonefish.ComparativeAdvantageFCFCRCMF20503025MRPT=-2/3coconuts/fishsoopp.costofonemorecoconutis3/2foregonefish.MRPT=-2coconuts/fishsoopp.costofonemorecoconutis1/2foregonefish.MFhasthecomparativeopp.costadvantageinproducingcoconuts.ComparativeAdvantageFCEconomyFCFCRCMF2050302570555030UseRCtoproducefishbeforeusingMF.UseMFtoproducecoconutsbeforeusingRC.ComparativeAdvantageFCEconomyFCFCRCMF2050302570555030Usinglowopp.costproducersfirstresultsinappfthatisconcavew.r.ttheorigin.ComparativeAdvantageFCEconomyMoreproducerswithdifferentopp.costs“smoothout〞theppf.CoordinatingProduction&ConsumptionTheppfcontainsmanytechnicallyefficientoutputbundles.WhichareParetoefficientforconsumers?CoordinatingProduction&ConsumptionFishCoconutsOutputbundleisCoordinatingProduction&ConsumptionFishCoconutsOutputbundleisandistheaggregateendowmentfordistributiontoconsumersRCandMF.CoordinatingProduction&ConsumptionFishCoconutsORCOMFOutputbundleisandistheaggregateendowmentfordistributiontoconsumersRCandMF.CoordinatingProduction&ConsumptionFishCoconutsORCOMFAllocateefficiently;saytoRCCoordinatingProduction&ConsumptionFishCoconutsORCOMFAllocateefficiently;saytoRCandtoMF.CoordinatingProduction&ConsumptionFishCoconutsORCOMFCoordinatingProduction&ConsumptionFishCoconutsORCOMFCoordinatingProduction&ConsumptionFishCoconutsORCOMFCoordinatingProduction&ConsumptionFishCoconutsORCOMFMRSMRPTCoordinatingProduction&ConsumptionFishCoconutsORCOMFO’MFInsteadproduceCoordinatingProduction&ConsumptionFishCoconutsORCOMFO’MFInsteadproduceCoordinatingProduction&ConsumptionFishCoconutsORCOMFO’MFInsteadproduceGiveMFsameallocationasbefore.CoordinatingProduction&ConsumptionFishCoconutsORCOMFO’MFInsteadproduceGiveMFsameallocationasbefore.MF’sutilityisunchanged.CoordinatingProduction&ConsumptionFishCoconutsORCOMFO’MFInsteadproduceGiveMFsameallocationasbefore.MF’sutilityisunchangedCoordinatingProduction&ConsumptionFishCoconutsORCOMFO’MFInsteadproduceGiveMFsameallocationasbefore.MF’sutilityisunchangedCoordinatingProduction&ConsumptionFishCoconutsORCOMFO’MFInsteadproduceGiveMFsameallocationasbefore.MF’sutilityisunchanged,RC’sutilityishigherCoordinatingProduction&ConsumptionFishCoconutsORCOMFO’MFInsteadproduceGiveMFsameallocationasbefore.MF’sutilityisunchanged,RC’sutilityishigher;

Paretoimprovement.CoordinatingProduction&ConsumptionMRSMRPTinefficientcoordinationofproductionandconsumption.Hence,MRS=MRPTisnecessaryforaParetooptimaleconomicstate