Chapter 16Perfectly Competitive Price SystemLaw of One PriceAssumptions of Perfect CompetitionGeneral EquilibriumEdgeworth Box DiagramSlide 7Slide 8Slide 9Slide 10Slide 11Slide 12Production Possibility FrontierSlide 14Rate of Product TransformationSlide 16Shape of the Production Possibility FrontierSlide 18Slide 19Opportunity CostSlide 21Production PossibilitiesSlide 23Determining Equilibrium PricesSlide 25Slide 26Slide 27General Equilibrium PricingSlide 29Slide 30Slide 31Comparative Statics AnalysisSlide 33Technical Progress in the Production of XThe Corn Laws DebateSlide 36Slide 37Slide 38Slide 39Slide 40Slide 41Political Support for Trade PoliciesExistence of General Equilibrium PricesSlide 44Slide 45Excess Demand FunctionsSlide 47Walras’ LawSlide 49Walras’ Proof of the Existence of Equilibrium PricesSlide 51Slide 52Slide 53Brouwer’s Fixed-Point TheoremSlide 55Slide 56Slide 57Proof that Equilibrium Prices ExistSlide 59Slide 60Free GoodsSlide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68A General Equilibrium with Three GoodsSlide 70Slide 71Slide 72Money in General Equilibrium ModelsSlide 74Slide 75Slide 76Slide 77Slide 78Slide 79Slide 80Slide 81Slide 82Slide 83Important Points to Note:Slide 85Slide 86Slide 87Slide 88Chapter 16GENERAL COMPETITIVE EQUILIBRIUMCopyright ©2002 by South-Western, a division of Thomson Learning. All rights reserved.MICROECONOMIC THEORYBASIC PRINCIPLES AND EXTENSIONSEIGHTH EDITIONWALTER NICHOLSONPerfectly CompetitivePrice System•We will assume that all markets are perfectly competitive–There is some number of homogeneous goods in the economy•both consumption goods and factors of production–Each good has an equilibrium price–There are no transaction or transportation costs–Everyone has perfect informationLaw of One Price•A homogeneous good trades at the same price no matter who buys it or who sells it–if one good traded at two different prices, demanders would rush to buy the good where it was cheaper and firms would try to sell their output where the price was higher•these actions would tend to equalize the price of the goodAssumptions of Perfect Competition•There are a large number of people buying any one good–each person takes all prices as given–each person seeks to maximize utility given his budget constraint•There are a large number of firms producing each good–each firm attempts to maximize profits–each firm takes all prices as givenGeneral Equilibrium•Assume that there are only two goods, X and Y•All individuals have identical preferences–can be represented by an indifference map•The production possibility curve can be used to show how outputs and inputs are relatedEdgeworth Box Diagram•Construction of the production possibility curve for X and Y starts with the assumption that the amounts of K and L are fixed•An Edgeworth box shows every possible way the existing K and L might be used to produce X and Y–Any point in the box represents a fully employed allocation of the available resources to X and YEdgeworth Box DiagramOXOYTotal LaborTotal CapitalA-Capital for XCapital for YLabor for YLabor for XCapitalin YproductionCapitalin XproductionLabor in Y productionLabor in X productionEdgeworth Box Diagram•Many of the allocations in the Edgeworth box are inefficient–it is possible to produce more X and more Y by shifting capital and labor around•We will assume that competitive markets will not exhibit inefficient input choices•We want to find the efficient allocations–they illustrate the actual production outcomesEdgeworth Box Diagram•We will use isoquant maps for the two goods–the isoquant map for good X uses OX as the origin–the isoquant map for good Y uses OY as the origin•The efficient allocations will occur where the isoquants are tangent to one anotherEdgeworth Box DiagramOXOYTotal LaborTotal CapitalX2X1Y1Y2A-Point A is inefficient because, by moving along Y1, we can increaseX from X1 to X2 while holding Y constantEdgeworth Box DiagramOXOYTotal LaborTotal CapitalX2X1Y1Y2A-We could also increase Y from Y1 to Y2 while holding X constantby moving along X1Edgeworth Box DiagramOXOYTotal LaborTotal CapitalAt each efficient point, the RTS (of K for L) is equal in bothX and Y productionX2X1X4X3Y1Y2Y3Y4P4P3P2P1Production Possibility Frontier•The locus of efficient points shows the maximum output of Y that can be produced for any level of X–we can use this information to construct a production possibility frontier•shows the alternative outputs of X and Y that can be produced with the fixed capital and labor inputsProduction Possibility FrontierQuantity of XQuantity of YP4P3P2P1Y1Y2Y3Y4X1X2X3X4OXOYEach efficient point of productionbecomes a point on the productionpossibility frontierThe negative of the slope ofthe production possibilityfrontier is the rate of producttransformation (RPT)Rate of Product Transformation•The rate of product transformation (RPT) between two outputs is the negative of the slope of the production possibility frontierfrontiery possibilit production of slope ) for (of YXRPT) (along ) for (of YXOOdXdYYXRPT Rate of Product Transformation•The rate of product transformation shows how X can be technically traded for Y while continuing to keep the available productive inputs efficiently employedShape of the Production Possibility Frontier•The production possibility frontier shown earlier exhibited an increasing RPT–this concave shape will characterize most production situations•RPT is equal to the ratio of MCX to MCYShape of the Production Possibility Frontier•As production of X rises and production of Y falls, the ratio of MCX to MCY rises–this occurs if both goods are produced under diminishing returns•increasing the production of X raises MCX, while reducing the production of Y lowers MCY–this could also occur if some inputs were more suited for X production than for Y productionShape of the Production Possibility Frontier•But we have assumed that inputs are homogeneous•We need an explanation that allows homogeneous inputs and constant returns to scale•The production possibility frontier will be concave if goods X and Y use inputs in different proportionsOpportunity Cost•The production possibility frontier demonstrates that there are many possible efficient combinations of two goods•Producing more of one good necessitates lowering the production of the other good–this is what economists mean by