Chapter Twenty-NineExchange整理课件ExchangeuTwo consumers, A and B.uTheir endowments of goods 1 and 2 are uE.g. uThe total quantities availableandandunits of good 1units of good 2.andare整理课件ExchangeuEdgeworth and Bowley devised a diagram, called an Edgeworth box, to show all possible allocations of the available quantities of goods 1 and 2 between the two consumers.整理课件Starting an Edgeworth Box整理课件Starting an Edgeworth BoxWidth = 整理课件Starting an Edgeworth BoxWidth = Height =整理课件Starting an Edgeworth BoxWidth = Height =The dimensions ofthe box are thequantities availableof the goods.整理课件Feasible AllocationsuWhat allocations of the 8 units of good 1 and the 6 units of good 2 are feasible?uHow can all of the feasible allocations be depicted by the Edgeworth box diagram?整理课件Feasible AllocationsuWhat allocations of the 8 units of good 1 and the 6 units of good 2 are feasible?uHow can all of the feasible allocations be depicted by the Edgeworth box diagram?uOne feasible allocation is the before-trade allocation; i.e. the endowment allocation.整理课件Width = Height =The endowmentallocation isandThe Endowment Allocation整理课件Width = Height =The Endowment Allocation整理课件OAOB68The Endowment Allocation整理课件OAOB6846The Endowment Allocation整理课件OAOB684622The Endowment Allocation整理课件OAOB684622TheendowmentallocationThe Endowment Allocation整理课件More generally, The Endowment Allocation整理课件The Endowment AllocationOAOBTheendowmentallocation整理课件Other Feasible Allocationsu denotes an allocation to consumer A.u denotes an allocation to consumer B.uAn allocation is feasible if and only ifand整理课件Feasible ReallocationsOAOB整理课件Feasible ReallocationsOAOB整理课件Feasible ReallocationsuAll points in the box, including the boundary, represent feasible allocations of the combined endowments.整理课件Feasible ReallocationsuAll points in the box, including the boundary, represent feasible allocations of the combined endowments.uWhich allocations will be blocked by one or both consumers?uWhich allocations make both consumers better off?整理课件Adding Preferences to the BoxOAFor consumer A.整理课件Adding Preferences to the BoxMore preferredFor consumer A.OA整理课件Adding Preferences to the BoxFor consumer B.OB整理课件Adding Preferences to the BoxMore preferredFor consumer B.OB整理课件Adding Preferences to the BoxMore preferredFor consumer B.OB整理课件Adding Preferences to the BoxOAFor consumer A.整理课件Adding Preferences to the BoxOAOB整理课件Edgeworths BoxOAOB整理课件Pareto-ImprovementuAn allocation of the endowment that improves the welfare of a consumer without reducing the welfare of another is a Pareto-improving allocation.uWhere are the Pareto-improving allocations?整理课件Edgeworths BoxOAOB整理课件Pareto-ImprovementsOAOBThe set of Pareto-improving allocations整理课件Pareto-ImprovementsuSince each consumer can refuse to trade, the only possible outcomes from exchange are Pareto-improving allocations.uBut which particular Pareto-improving allocation will be the outcome of trade?整理课件Pareto-ImprovementsOAOBThe set of Pareto-improving reallocations整理课件Pareto-Improvements整理课件Pareto-Improvements整理课件Pareto-ImprovementsTradeimproves bothAs and Bs welfares.This is a Pareto-improvementover the endowment allocation.整理课件Pareto-ImprovementsNew mutual gains-to-trade region is the set of all further Pareto- improving reallocations. Tradeimproves bothAs and Bs welfares.This is a Pareto-improvementover the endowment allocation.整理课件Pareto-ImprovementsFurther trade cannot improve both A and Bs welfares.整理课件Pareto-OptimalityBetter forconsumer BBetter forconsumer A整理课件Pareto-OptimalityA is strictly better off but B is strictly worse off整理课件Pareto-OptimalityA is strictly better off but B is strictly worse offB is strictly betteroff but A is strictlyworse off整理课件Pareto-OptimalityA is strictly better off but B is strictly worse offB is strictly betteroff but A is strictlyworse offBoth A andB are worseoff整理课件Pareto-OptimalityA is strictly better off but B is strictly worse offB is strictly betteroff but A is strictlyworse offBoth Aand B are worse offBoth A andB are worseoff整理课件Pareto-OptimalityThe allocation isPareto-optimal since theonly way one consumerswelfare can be increased is todecrease the welfare of the otherconsumer.整理课件Pareto-OptimalityThe allocation isPareto-optimal since theonly way one consumerswelfare can be increased is todecrease the welfare of the otherconsumer.An allocation where convexindifference curves are “only just back-to-back” is Pareto-optimal.整理课件Pareto-OptimalityuWhere are all of the Pareto-optimal allocations of the endowment?整理课件Pareto-OptimalityOAOB整理课件Pareto-OptimalityOAOBAll the allocations marked bya are Pareto-optimal.整理课件Pareto-OptimalityuThe contract curve is the set of all Pareto-optimal allocations.整理课件Pareto-OptimalityOAOBAll the allocations marked bya are Pareto-optimal.The contract curve整理课件Pareto-OptimalityuBut to which of the many allocations on the contract curve will consumers trade?uThat depends upon how trade is conducted.uIn perfectly competitive markets? By one-on-one bargaining?整理课件The CoreOAOBThe set of Pareto-improving reallocations整理课件The CoreOAOB整理课件The CoreOAOBPareto-optimal trades blocked by BPareto-optimal trades blocked by A整理课件The CoreOAOBPareto-optimal trades not blocked by A or B整理课件The CoreOAOBPareto-optimal trades not blocked by A or B are the core.整理课件The CoreuThe core is the set of all Pareto-optimal allocations that are welfare-improving for both consumers relative to their own endowments.uRational trade should achieve a core allocation.整理课件The CoreuBut which core allocation?uAgain, that depends upon the manner in which trade is conducted.整理课件Trade in Competitive MarketsuConsider trade in perfectly competitive markets.uEach consumer is a price-taker trying to maximize her own utility given p1, p2 and her own endowment. That is, .整理课件Trade in Competitive MarketsOAFor consumer A.整理课件Trade in Competitive MarketsuSo given p1 and p2, consumer As net demands for commodities 1 and 2 areand整理课件Trade in Competitive MarketsuAnd, similarly, for consumer B 整理课件Trade in Competitive MarketsFor consumer B.OB整理课件Trade in Competitive MarketsuSo given p1 and p2, consumer Bs net demands for commodities 1 and 2 areand整理课件Trade in Competitive MarketsuA general equilibrium occurs when prices p1 and p2 cause both the markets for commodities 1 and 2 to clear; i.e.and整理课件Trade in Competitive MarketsOAOB整理课件Trade in Competitive MarketsOAOBCan this PO allocation beachieved?整理课件Trade in Competitive MarketsOAOBBudget constraint for consumer A整理课件Trade in Competitive MarketsOAOBBudget constraint for consumer A整理课件Trade in Competitive MarketsOAOBBudget constraint for consumer B整理课件Trade in Competitive MarketsOAOBBudget constraint for consumer B整理课件Trade in Competitive MarketsOAOBBut整理课件Trade in Competitive MarketsOAOBand整理课件Trade in Competitive MarketsuSo at the given prices p1 and p2 there is an excess supply of commodity 1 excess demand for commodity 2.uNeither market clears so the prices p1 and p2 do not cause a general equilibrium.整理课件Trade in Competitive MarketsOAOBSo this PO allocation cannot beachieved by competitive trading.整理课件Trade in Competitive MarketsOAOBWhich PO allocations can beachieved by competitive trading?整理课件Trade in Competitive MarketsuSince there is an excess demand for commodity 2, p2 will rise.uSince there is an excess supply of commodity 1, p1 will fall.uThe slope of the budget constraints is - p1/p2 so the budget constraints will pivot about the endowment point and become less steep.整理课件Trade in Competitive MarketsOAOBWhich PO allocations can beachieved by competitive trading?整理课件Trade in Competitive MarketsOAOBWhich PO allocations can beachieved by competitive trading?整理课件Trade in Competitive MarketsOAOBWhich PO allocations can beachieved by competitive trading?整理课件Trade in Competitive MarketsOAOBBudget constraint for consumer A整理课件Trade in Competitive MarketsOAOBBudget constraint for consumer A整理课件Trade in Competitive MarketsOAOBBudget constraint for consumer B整理课件Trade in Competitive MarketsOAOBBudget constraint for consumer B整理课件Trade in Competitive MarketsOAOBSo整理课件Trade in Competitive MarketsOAOBand整理课件Trade in Competitive MarketsuAt the new prices p1 and p2 both markets clear; there is a general equilibrium.uTrading in competitive markets achieves a particular Pareto-optimal allocation of the endowments.uThis is an example of the First Fundamental Theorem of Welfare Economics.整理课件First Fundamental Theorem of Welfare EconomicsuGiven that consumers preferences are well-behaved, trading in perfectly competitive markets implements a Pareto-optimal allocation of the economys endowment.整理课件Second Fundamental Theorem of Welfare EconomicsuThe First Theorem is followed by a second that states that any Pareto-optimal allocation (i.e. any point on the contract curve) can be achieved by trading in competitive markets provided that endowments are first appropriately rearranged amongst the consumers.整理课件uGiven that consumers preferences are well-behaved, for any Pareto-optimal allocation there are prices and an allocation of the total endowment that makes the Pareto-optimal allocation implementable by trading in competitive markets.Second Fundamental Theorem of Welfare Economics整理课件Second Fundamental TheoremOAOBThe contract curve整理课件Second Fundamental TheoremOAOB整理课件Second Fundamental TheoremOAOBImplemented by competitivetrading from the endowment w w.整理课件Second Fundamental TheoremOAOBCan this allocation be implementedby competitive trading from w w?整理课件Second Fundamental TheoremOAOBCan this allocation be implementedby competitive trading from w w? No.整理课件Second Fundamental TheoremOAOBBut this allocation is implementedby competitive trading from q q.整理课件Walras LawuWalras Law is an identity; i.e. a statement that is true for any positive prices (p1,p2), whether these are equilibrium prices or not.整理课件Walras LawuEvery consumers preferences are well-behaved so, for any positive prices (p1,p2), each consumer spends all of his budget.uFor consumer A:For consumer B:整理课件Walras LawSumming gives整理课件Walras LawRearranged,That is, .整理课件Walras LawThis says that the summed marketvalue of excess demands is zero forany positive prices p1 and p2 - this is Walras Law.整理课件Implications of Walras LawSuppose the market for commodity Ais in equilibrium; that is,Thenimplies整理课件Implications of Walras LawSo one implication of Walras Law fora two-commodity exchange economyis that if one market is in equilibriumthen the other market must also be inequilibrium.整理课件Implications of Walras LawWhat if, for some positive prices p1 andp2, there is an excess quantity suppliedof commodity 1? That is,Thenimplies整理课件Implications of Walras LawSo a second implication of Walras Lawfor a two-commodity exchange economyis that an excess supply in one marketimplies an excess demand in the othermarket.整理课件