微观经济学课件：第31章 生产

1、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

2、markets, output markets, describe firms technologies, the distributions of firms outputs and profits uThats not easy!ContentsuA one-person economy Optimal outcome Competitive equilibrium Two welfare theorems Non-convex technologiesuTwo-people economy Production possibility frontier Comparative advan

3、tage Pareto efficient allocation Competitive 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 TechnologyuT

4、echnology: 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:coco

5、nut 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)Coconuts

6、Feasible productionplansProduction function240Leisure (hours)240Robinson Crusoes ChoiceLabor (hours)CoconutsFeasible productionplansProduction function240Leisure (hours)240Robinson Crusoes ChoiceLabor (hours)CoconutsFeasible productionplansProduction function240Leisure (hours)240Robinson Crusoes Cho

7、iceLabor (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)Coc

8、onutsProduction function240Leisure (hours)240C*L*LaborLeisureOutputRobinson Crusoes ChoiceLabor (hours)CoconutsProduction function240Leisure (hours)240C*L*LaborLeisureMRS = MPLOutputCompetitive EquilibriumuA firm Produce coconuts Demand laboruA consumer Demand coconuts Supply laboruEquilibrium Marke

9、t clears for coconuts Market 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 a

10、s a FirmuRCs firms profit is = C - wL.u = C - wL C = + wL, the equation of an isoprofit line.uSlope = + w .uIntercept = .Isoprofit LinesLabor (hours)Coconuts24CwLHigher profit; 1 12 23 3Slopes = + w3 32 21 10Profit-MaximizationLabor (hours)CoconutsFeasible productionplansProduction function240Profit

11、-MaximizationLabor (hours)CoconutsProduction function240Profit-MaximizationLabor (hours)CoconutsProduction function240Profit-MaximizationLabor (hours)CoconutsProduction function24C*L*Isoprofit slope = production function slope0Profit-MaximizationLabor (hours)CoconutsProduction function24C*L*Isoprofi

12、t 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.*CwLRC gets 0Profit-MaximizationLabor (hours)CoconutsProduction function24C*L*Isoprofit slope = pr

13、oduction function slope i.e. w = MPL = 1 MPL = MRPL.*CwL*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*

14、 andoutput quantity supplied is C*.LabordemandOutputsupply*CwLRC 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 isCwL*.Utility-MaximizationLabor (hours)Coconuts*240CwL*.Budget co

15、nstraint; slope = wUtility-MaximizationLabor (hours)CoconutsMore preferred240Utility-MaximizationLabor (hours)Coconuts*240CwL*.Budget constraint; slope = wUtility-MaximizationLabor (hours)Coconuts*Budget constraint; slope = w240CwL*.Utility-MaximizationLabor (hours)Coconuts*240CwL*.C*L*MRS = wBudget

16、 constraint; slope = wUtility-MaximizationLabor (hours)Coconuts*240CwL*.C*L*LaborsupplyBudget constraint; slope = wMRS = wGiven w, RCs quantitysupplied of labor is L*Utility-MaximizationLabor (hours)Coconuts*240CwL*.C*L*Given w, RCs quantitysupplied of labor is L* andoutput quantity demanded is C*.L

17、aborsupplyOutputdemandBudget constraint; slope = wMRS = wUtility-Maximization & Profit-MaximizationuProfit-maximization: w = MPL quantity of output supplied = C* quantity of labor demanded = L*uUtility-maximization: w = MRS quantity of output demanded = C* quantity of labor supplied = L*uCoconut

18、 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

19、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 Fundame

20、ntal 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 prefere

21、nces 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 th

22、at 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 all

23、ocation 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

24、 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 PossibilitiesFishCoc

25、onutsFeasible 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).

26、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

27、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 =

28、 -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 AdvantageFCFCRCMF2050

29、3025MRPT = -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 on

30、emore 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. c

31、ost 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 s

32、pecializes 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 AdvantageFCEcon

33、omyFCFCRCMF2050302570555030Use 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 withdiffere

34、nt opp. costs“smooth out” the ppf.Coordinating Production & ConsumptionuThe ppf contains many technically efficient output bundles.uWhich are Pareto efficient?Coordinating Production & ConsumptionFishCoconuts C FOutput bundle is(,) F CCoordinating Production & ConsumptionFishCoconuts C F

35、Output bundle isand is the aggregateendowment for distribution to consumers RC and MF.(,) F CCoordinating Production & ConsumptionFishCoconutsORCOMF C FOutput bundle isand is the aggregateendowment for distribution to consumers RC and MF.(,) F CCoordinating Production & ConsumptionFishCoconu

36、tsORCOMF C FAllocate efficiently;say to RC(,) F C CRC FRC(,) FCRCRCCoordinating Production & ConsumptionFishCoconutsORCOMF C FAllocate efficiently;say to RC and to MF.(,) F C CRC CMF FMF FRC(,) FCRCRC(,) FCMFMFCoordinating Production & ConsumptionFishCoconutsORCOMF C F CRC CMF FMF FRCCoordin

37、ating Production & ConsumptionFishCoconutsORCOMF C F CRC CMF FMF FRCCoordinating Production & ConsumptionFishCoconutsORCOMF C F CRC CMF FMF FRCCoordinating Production & ConsumptionFishCoconutsORCOMF C F CRC CMF FMF FRCMRS MRPTCoordinating Production & ConsumptionFishCoconutsORCOMF C

38、F CRC CMF FMF FRCOMF C F(,). FCInstead produceCoordinating Production & ConsumptionFishCoconutsORCOMF C F CRC CMF FMF FRCOMF C F(,). FCInstead produceCoordinating Production & ConsumptionFishCoconutsORCOMF C F CRC CMF FMF FRC C F(,). FCOMF CMFInstead produceGive MF same allocation as before.

39、 FMFCoordinating Production & ConsumptionFishCoconutsORCOMF C F CRC CMF FMF FRC C F(,). FCOMF CMFInstead produceGive MF same allocation as before. MFs utility is unchanged. FMFCoordinating Production & ConsumptionFishCoconutsORCOMF C F(,). FCOMF FMFInstead produceGive MF same allocation as b

40、efore. MFs utility is unchanged CMFCoordinating Production & ConsumptionFishCoconutsORCOMF FRC C F(,). FCOMF CRC FMF CMFInstead produceGive MF same allocation as before. MFs utility is unchangedCoordinating Production & ConsumptionFishCoconutsORCOMF FRC C F(,). FCOMF CRC FMF CMFInstead produ

41、ceGive MF same allocation as before. MFs utility is unchanged, RCs utility is higherCoordinating Production & ConsumptionFishCoconutsORCOMF FRC C F(,). FCOMF CRC FMF CMFInstead produceGive MF same allocation as before. MFs utility is unchanged, RCs utility is higher; Pareto improvement.Coordinat

42、ing Production & ConsumptionuMRS MRPT inefficient coordination of production and consumption.uHence, MRS = MRPT is necessary for a Pareto optimal economic state.Coordinating Production & ConsumptionFishCoconutsORCOMFFRCCFCRCFMFCMFDecentralized Coordination of Production & Consumption uRC

43、 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.u

44、Firms profit-maximization problem is choose C, F, LRC and LMF tom axm ax. . p p C Cp p F Fw wL Lw wL LC CF FRCRCRCRCM FM FM FM FA SimplificationuSuppose labor market equilibrium is already achieved.uAllows us to focus on the product market.uTechnically, can simultaneously look at all the markets Fir

45、m: 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 & Consumptionm axm ax. . p p C Cp p F Fw wL Lw wL LC CF FRCRCRCRCM FM FM FM FIsoprofit line equation isconstantconstant p p C Cp p F Fw wL Lw wL LC CF FRCRCRCRCM FM FM FM FDecentralized Coordination of Production & Consumptionm