Chapter Thirty-OneProduction生产生产Exchange Economies (revisited)uNo production, only endowments, so no description of how resources are converted to consumables.uGeneral equilibrium: all markets clear simultaneously.u1st and 2nd Fundamental Theorems of Welfare Economics.Now Add Production .uAdd input markets, output markets, describe firms technologies, the distributions of firms outputs and profits uThats not easy!ContentsuA one-person economyOptimal outcomeCompetitive equilibriumTwo welfare theoremsNon-convex technologiesuTwo-people economyProduction possibility frontierComparative advantagePareto efficient allocationCompetitive equilibriumRobinson Crusoes EconomyuOne agent, RC.uEndowed with a fixed quantity of one resource - 24 hours.uUse time for labor (production) or leisure (consumption).uLabor time = L. Leisure time = 24 - L.uWhat will RC choose?Robinson Crusoes TechnologyuTechnology: Labor produces output (coconuts) according to a concave production function.Robinson Crusoes TechnologyProduction functionLabor (hours)Coconuts240Robinson Crusoes TechnologyLabor (hours)CoconutsProduction function240Feasible productionplansRobinson Crusoes PreferencesuRCs preferences:coconut is a goodleisure is a goodRobinson Crusoes PreferencesLeisure (hours)CoconutsMore preferred240Robinson Crusoes PreferencesLeisure (hours)CoconutsMore preferred240Robinson Crusoes ChoiceLabor (hours)CoconutsFeasible productionplansProduction function240Robinson Crusoes ChoiceLabor (hours)CoconutsFeasible productionplansProduction function240Leisure (hours)240Robinson Crusoes ChoiceLabor (hours)CoconutsFeasible productionplansProduction function240Leisure (hours)240Robinson Crusoes ChoiceLabor (hours)CoconutsFeasible productionplansProduction function240Leisure (hours)240Robinson Crusoes ChoiceLabor (hours)CoconutsProduction function240Leisure (hours)240C*L*Robinson Crusoes ChoiceLabor (hours)CoconutsProduction function240Leisure (hours)240C*L*LaborRobinson Crusoes ChoiceLabor (hours)CoconutsProduction function240Leisure (hours)240C*L*LaborLeisureRobinson Crusoes ChoiceLabor (hours)CoconutsProduction function240Leisure (hours)240C*L*LaborLeisureOutputRobinson Crusoes ChoiceLabor (hours)CoconutsProduction function240Leisure (hours)240C*L*LaborLeisureMRS = MPLOutputCompetitive EquilibriumuA firmProduce coconutsDemand laboruA consumerDemand coconutsSupply laboruEquilibriumMarket clears for coconutsMarket clears for laborCompetitive EquilibriumuNow suppose RC is both a utility-maximizing consumer and a profit-maximizing firm.uUse coconuts as the numeraire good; i.e. price of a coconut = $1.uRCs wage rate is w.uCoconut output level is C.uLabor supply is L.Robinson Crusoe as a FirmuRCs firms profit is = C - wL.u = C - wL C = + wL, the equation of an isoprofit line.uSlope = + w .uIntercept = .Isoprofit LinesLabor (hours)Coconuts24Higher profit; Slopes = + w0Profit-MaximizationLabor (hours)CoconutsFeasible productionplansProduction function240Profit-MaximizationLabor (hours)CoconutsProduction function240Profit-MaximizationLabor (hours)CoconutsProduction function240Profit-MaximizationLabor (hours)CoconutsProduction function24C*L*Isoprofit slope = production function slope0Profit-MaximizationLabor (hours)CoconutsProduction function24C*L*Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL.0Profit-MaximizationLabor (hours)CoconutsProduction function24C*L*Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL.RC gets 0Profit-MaximizationLabor (hours)CoconutsProduction function24C*L*Isoprofit slope = production function slope i.e. w = MPL = 1 MPL = MRPL.Given w, RCs firms quantitydemanded of labor is L*LabordemandRC gets 0Profit-MaximizationLabor (hours)CoconutsProduction function24C*L*Isoprofit slope = production function slope i.e. w = MPL.Given w, RCs firms quantitydemanded of labor is L* andoutput quantity supplied is C*.LabordemandOutputsupplyRC gets 0Utility-MaximizationuNow consider RC as a consumer endowed with $ * who can work for $w per hour.uWhat is RCs most preferred consumption bundle?uBudget constraint isUtility-MaximizationLabor (hours)Coconuts240Budget constraint; slope = wUtility-MaximizationLabor (hours)CoconutsMore preferred240Utility-MaximizationLabor (hours)Coconuts240Budget constraint; slope = wUtility-MaximizationLabor (hours)CoconutsBudget constraint; slope = w240Utility-MaximizationLabor (hours)Coconuts240C*L*MRS = wBudget constraint; slope = wUtility-MaximizationLabor (hours)Coconuts240C*L*LaborsupplyBudget constraint; slope = wMRS = wGiven w, RCs quantitysupplied of labor is L*Utility-MaximizationLabor (hours)Coconuts240C*L*Given w, RCs quantitysupplied of labor is L* andoutput quantity demanded is C*.LaborsupplyOutputdemandBudget constraint; slope = wMRS = wUtility-Maximization & Profit-MaximizationuProfit-maximization: w = MPLquantity of output supplied = C*quantity of labor demanded = L*uUtility-maximization: w = MRSquantity of output demanded = C*quantity of labor supplied = L*uCoconut and labor markets both clear.At Equilibrium Labor (hours)Coconuts24C*L*0MRS = w = MPLGiven w, RCs quantitysupplied of labor = quantitydemanded of labor = L* andoutput quantity demanded =output quantity supplied = C*.Pareto EfficiencyuMust have MRS = MPL.Pareto EfficiencyLabor (hours)Coconuts240MRS MPLPareto EfficiencyLabor (hours)Coconuts240MRS MPLPreferred consumptionbundles.Pareto EfficiencyLabor (hours)Coconuts240MRS = MPLPareto EfficiencyLabor (hours)Coconuts240MRS = MPL. The common slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing.First Fundamental Theorem of Welfare EconomicsuA competitive market equilibrium is Pareto efficient ifthere are no externalities in consumption or production.Second Fundamental Theorem of Welfare EconomicsuAny Pareto efficient economic state can be achieved as a competitive market equilibrium ifconsumers preferences are convexfirms technologies are convexNon-Convex TechnologiesuDo the Welfare Theorems hold if firms have non-convex technologies?uThe 1st Theorem does not rely upon firms technologies being convex.Non-Convex TechnologiesLabor (hours)Coconuts240MRS = MPL The common slope relative wage rate w that implements the Pareto efficient plan by decentralized pricing.Non-Convex TechnologiesuDo the Welfare Theorems hold if firms have non-convex technologies?uThe 2nd Theorem does require that firms technologies be convex.Non-Convex TechnologiesLabor (hours)Coconuts240MRS = MPL. The Pareto optimal allocation cannot be implemented by a competitive equilibrium.Production PossibilitiesuResource and technological limitations restrict what an economy can produce.uThe set of all feasible output bundles is the economys production possibility set (生产可能性集生产可能性集).uThe sets outer boundary is the production possibility frontier（生产可能性边界生产可能性边界）.Production PossibilitiesFishCoconutsProduction possibility frontier (ppf)Production PossibilitiesFishCoconutsProduction possibility frontier (ppf)Production possibility setProduction PossibilitiesFishCoconutsFeasible butinefficientProduction PossibilitiesFishCoconutsFeasible butinefficientFeasible and efficientProduction PossibilitiesFishCoconutsFeasible butinefficientFeasible and efficientInfeasibleProduction PossibilitiesFishCoconutsPpfs slope is the marginal rateof product transformation (边际生产转换率边际生产转换率), or marginal rate of transformation (边际转换率边际转换率).Production PossibilitiesFishCoconutsPpfs slope is the marginal rateof product transformation.Increasingly negative MRPT increasing opportunitycost to specialization.Production PossibilitiesuIf there are no production externalities then a ppf will be concave w.r.t. the origin.uWhy?uBecause efficient production requires exploitation of comparative advantages(比较优势比较优势).Comparative AdvantageuTwo agents, RC and Man Friday (MF).uRC can produce at most 20 coconuts or 30 fish.uMF can produce at most 50 coconuts or 25 fish.Comparative AdvantageFCFCRCMF20503025Comparative AdvantageFCFCRCMF20503025MRPT = -2/3 coconuts/fish so opp. cost of onemore fish is 2/3 foregone coconuts.Comparative AdvantageFCFCRCMF20503025MRPT = -2/3 coconuts/fish so opp. cost of onemore fish is 2/3 foregone coconuts.MRPT = -2 coconuts/fish so opp. cost of onemore fish is 2 foregone coconuts.Comparative AdvantageFCFCRCMF20503025MRPT = -2/3 coconuts/fish so opp. cost of onemore fish is 2/3 foregone coconuts.MRPT = -2 coconuts/fish so opp. cost of onemore fish is 2 foregone coconuts.RC has the comparativeopp. cost advantage inproducing fish.Comparative AdvantageFCFCRCMF20503025MRPT = -2/3 coconuts/fish so opp. cost of onemore coconut is 3/2 foregone fish.Comparative AdvantageFCFCRCMF20503025MRPT = -2/3 coconuts/fish so opp. cost of onemore coconut is 3/2 foregone fish.MRPT = -2 coconuts/fish so opp. cost of onemore coconut is 1/2 foregone fish.Comparative AdvantageFCFCRCMF20503025MRPT = -2/3 coconuts/fish so opp. cost of onemore coconut is 3/2 foregone fish.MRPT = -2 coconuts/fish so opp. cost of onemore coconut is 1/2 foregone fish.MF has the comparativeopp. cost advantage inproducing coconuts.Supplement: TradeFCFCRCMF20503025Autarky: Produce and consume at A.Trade: Both countries completely specialize. RC specializes on Fish; MF specializes on coconuts.Produce at B and consume at C. Better off with trade.ABCABCSupplement: Trade EquilibriumFCFCRCMF20503025Prices adjust to clear the markets.At equilibrium, export of one country = import of the other country for each product.ooComparative AdvantageFCEconomyFCFCRCMF2050302570555030Use RC to producefish before using MF.Use MF toproducecoconuts before using RC.Comparative AdvantageFCEconomyFCFCRCMF2050302570555030Using low opp. costproducers first resultsin a ppf that is concave w.r.t the origin.Comparative AdvantageFCEconomyMore producers withdifferent opp. costs“smooth out” the ppf.Coordinating Production & ConsumptionuThe ppf contains many technically efficient output bundles.uWhich are Pareto efficient?Coordinating Production & ConsumptionFishCoconutsOutput bundle isCoordinating Production & ConsumptionFishCoconutsOutput bundle isand is the aggregateendowment for distribution to consumers RC and MF.Coordinating Production & ConsumptionFishCoconutsORCOMFOutput bundle isand is the aggregateendowment for distribution to consumers RC and MF.Coordinating Production & ConsumptionFishCoconutsORCOMFAllocate efficiently;say to RCCoordinating Production & ConsumptionFishCoconutsORCOMFAllocate efficiently;say to RC and to MF.Coordinating Production & ConsumptionFishCoconutsORCOMFCoordinating Production & ConsumptionFishCoconutsORCOMFCoordinating Production & ConsumptionFishCoconutsORCOMFCoordinating Production & ConsumptionFishCoconutsORCOMFMRS MRPTCoordinating Production & ConsumptionFishCoconutsORCOMFOMFInstead produceCoordinating Production & ConsumptionFishCoconutsORCOMFOMFInstead produceCoordinating Production & ConsumptionFishCoconutsORCOMFOMFInstead produceGive MF same allocation as before.Coordinating Production & ConsumptionFishCoconutsORCOMFOMFInstead produceGive MF same allocation as before. MFs utility is unchanged.Coordinating Production & ConsumptionFishCoconutsORCOMFOMFInstead produceGive MF same allocation as before. MFs utility is unchangedCoordinating Production & ConsumptionFishCoconutsORCOMFOMFInstead produceGive MF same allocation as before. MFs utility is unchangedCoordinating Production & ConsumptionFishCoconutsORCOMFOMFInstead produceGive MF same allocation as before. MFs utility is unchanged, RCs utility is higherCoordinating Production & ConsumptionFishCoconutsORCOMFOMFInstead produceGive MF same allocation as before. MFs utility is unchanged, RCs utility is higher; Pareto improvement.Coordinating Production & ConsumptionuMRS MRPT inefficient coordination of production and consumption.uHence, MRS = MRPT is necessary for a Pareto optimal economic state.Coordinating Production & ConsumptionFishCoconutsORCOMFDecentralized Coordination of Production & Consumption uRC and MF jointly run a firm producing coconuts and fish.uRC and MF are also consumers who can sell labor.uPrice of coconut = pCuPrice of fish = pFuRCs wage rate = wRCuMFs wage rate = wMFDecentralized Coordination of Production & ConsumptionuLRC, LMF are amounts of labor purchased from RC and MF.uFirms profit-maximization problem is choose C, F, LRC and LMF toA SimplificationuSuppose labor market equilibrium is already achieved.uAllows us to focus on the product market.uTechnically, can simultaneously look at all the marketsFirm: two outputs, two inputs.Crusoe or Friday: two consumer goods, one leisure good.4 markets clear simultaneously.vFish; coconuts; Crusoes labor; Fridays laborDecentralized Coordination of Production & ConsumptionIsoprofit line equation isDecentralized Coordination of Production & ConsumptionIsoprofit line equation iswhich rearranges toDecentralized Coordination of Production & ConsumptionFishCoconutsHigher profitSlopes =Decentralized Coordination of Production & ConsumptionFishCoconutsThe firms productionpossibility set.Decentralized Coordination of Production & ConsumptionFishCoconutsSlopes =Decentralized Coordination of Production & ConsumptionFishCoconutsProfit-max. planSlopes =Decentralized Coordination of Production & ConsumptionFishCoconutsProfit-max. planSlope =Decentralized Coordination of Production & ConsumptionFishCoconutsProfit-max. planSlope =Competitive marketsand profit-maximizationDecentralized Coordination of Production & ConsumptionFishCoconutsORCOMFCompetitive marketsand utility-maximization Decentralized Coordination of Production & ConsumptionFishCoconutsORCOMFCompetitive markets, utility-maximization and profit- maximization Decentralized Coordination of Production & ConsumptionuSo competitive markets, profit-maximization, and utility maximization all together causethe condition necessary for a Pareto optimal economic state.