从化各科课件微观第30章

1、Chapter ThirtyExchange交换ContentsThe Edgeworth (艾奇沃斯) BoxPareto improving tradePareto Efficient AllocationThe Core (核心)Trade in a competitive marketWalras Law of general equilibrium (一般均衡)First Fundamental Theorem of Welfare Economics (福利经济学第一定理)Second Fundamental Theorem of Welfare Economics (福利经济学第

2、二定理)ExchangeTwo consumers, A and B.Their endowments of goods 1 and 2 are E.g. The total quantities availableandandunits of good 1units of good 2.andareExchangeEdgeworth and Bowley devised a diagram, called an Edgeworth box, to show all possible allocations of the available quantities of goods 1 and

3、2 between the two consumers.Starting an Edgeworth BoxStarting an Edgeworth BoxWidth = Starting an Edgeworth BoxWidth = Height =Starting an Edgeworth BoxWidth = Height =The dimensions ofthe box are thequantities availableof the goods.Feasible AllocationsWhat allocations of the 8 units of good 1 and t

4、he 6 units of good 2 are feasible?How can all of the feasible allocations be depicted by the Edgeworth box diagram?One feasible allocation is the before-trade allocation; i.e. the endowment allocation.Width = Height =The endowmentallocation isandThe Endowment AllocationWidth = Height =The Endowment

5、AllocationOAOB68The Endowment AllocationOAOB6846The Endowment AllocationOAOB684622The Endowment AllocationOAOB684622TheendowmentallocationThe Endowment AllocationMore generally, The Endowment AllocationThe Endowment AllocationOAOBTheendowmentallocationOther Feasible Allocations denotes an allocation

6、 to consumer A. denotes an allocation to consumer B.An allocation is feasible if and only ifandFeasible ReallocationsOAOBFeasible ReallocationsOAOBFeasible ReallocationsAll points in the box, including the boundary, represent feasible allocations of the combined endowments.Which allocations will be

7、blocked by one or both consumers?Which allocations make both consumers better off?Adding Preferences to the BoxOAFor consumer A.Adding Preferences to the BoxMore preferredFor consumer A.OAAdding Preferences to the BoxFor consumer B.OBAdding Preferences to the BoxMore preferredFor consumer B.OBAdding

8、 Preferences to the BoxMore preferredFor consumer B.OBAdding Preferences to the BoxOAFor consumer A.Adding Preferences to the BoxOAOBEdgeworths BoxOAOBPareto-ImprovementAn allocation of the endowment that improves the welfare of a consumer without reducing the welfare of another is a Pareto-improvin

9、g allocation.Where are the Pareto-improving allocations?Edgeworths BoxOAOBPareto-ImprovementsOAOBThe set of Pareto-improving allocationsPareto-ImprovementsSince each consumer can refuse to trade, the only possible es from exchange are Pareto-improving allocations.But which particular Pareto-improvin

10、g allocation will be the e of trade?Pareto-ImprovementsOAOBThe set of Pareto-improving reallocationsPareto-ImprovementsPareto-ImprovementsPareto-ImprovementsTradeimproves bothAs and Bs welfares.This is a Pareto-improvementover the endowment allocation.Pareto-ImprovementsNew mutual gains-to-trade reg

11、ion is the set of all further Pareto- improving reallocations. Tradeimproves bothAs and Bs welfares.This is a Pareto-improvement(帕累托改进)over the endowment allocation.Pareto-ImprovementsFurther trade cannot improve both A and Bs welfares.Pareto-Optimality (帕累托最优)Better forconsumer BBetter forconsumer

12、APareto-OptimalityA is strictly better off but B is strictly worse offB is strictly betteroff but A is strictlyworse offPareto-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 worseoffPareto-Optim

13、alityThe allocation isPareto-optimal since theonly way one consumerswelfare can be increased is todecrease the welfare of the otherconsumer.Pareto-OptimalityThe allocation isPareto-optimal since theonly way one consumerswelfare can be increased is todecrease the welfare of the otherconsumer.The Marg

14、inal Rates of Substitution Are Equal.Pareto-OptimalityWhere are all of the Pareto-optimal allocations of the endowment?Pareto-OptimalityOAOBPareto-OptimalityOAOBAll the allocations marked bya are Pareto-optimal.Pareto-OptimalityThe contract curve (契约线) is the set of all Pareto-optimal allocations.Pa

15、reto-OptimalityOAOBAll the allocations marked bya are Pareto-optimal.The contract curvePareto-OptimalityBut to which of the many allocations on the contract curve will consumers trade?That depends upon how trade is conducted.In perfectly competitive markets? By one-on-one bargaining?The Core (核心)OAO

16、BThe set of Pareto-improving reallocationsThe CoreOAOBThe CoreOAOBPareto-optimal trades blocked by BPareto-optimal trades blocked by AThe CoreOAOBPareto-optimal trades not blocked by A or B are the core.The CoreThe core is the set of all Pareto-optimal allocations that are welfare-improving for both

17、 consumers relative to their own endowments.Rational trade should achieve a core allocation.The CoreBut which core allocation?Again, that depends upon the manner in which trade is conducted.Trade in Competitive MarketsConsider trade in perfectly competitive markets.Each consumer is a price-taker try

18、ing to maximize her own utility given p1, p2 and her own endowment. That is, .Trade in Competitive MarketsOAFor consumer A.Trade in Competitive MarketsSo given p1 and p2, consumer As net demands for commodities 1 and 2 areandTrade in Competitive MarketsAnd, similarly, for consumer B Trade in Competi

19、tive MarketsFor consumer B.OBTrade in Competitive MarketsSo given p1 and p2, consumer Bs net demands for commodities 1 and 2 areandTrade in Competitive MarketsA general equilibrium occurs when prices p1 and p2 cause both the markets for commodities 1 and 2 to clear; i.e.andTrade in Competitive Marke

20、tsOAOBTrade in Competitive MarketsOAOBCan this PO allocation beachieved?Trade in Competitive MarketsOAOBBudget constraint for consumer ATrade in Competitive MarketsOAOBBudget constraint for consumer ATrade in Competitive MarketsOAOBBudget constraint for consumer BTrade in Competitive MarketsOAOBBudg

21、et constraint for consumer BTrade in Competitive MarketsOAOBButTrade in Competitive MarketsOAOBandTrade in Competitive MarketsSo at the given prices p1 and p2 there is an excess supply of commodity 1 excess demand for commodity 2.Neither market clears so the prices p1 and p2 do not cause a general e

22、quilibrium.Trade in Competitive MarketsOAOBSo this PO allocation cannot beachieved by competitive trading.Trade in Competitive MarketsOAOBWhich PO allocations can beachieved by competitive trading?Trade in Competitive MarketsSince there is an excess demand for commodity 2, p2 will rise.Since there i

23、s an excess supply of commodity 1, p1 will fall.The slope of the budget constraints is - p1/p2 so the budget constraints will pivot about the endowment point and e less steep.Trade in Competitive MarketsOAOBWhich PO allocations can beachieved by competitive trading?Trade in Competitive MarketsOAOBWh

24、ich PO allocations can beachieved by competitive trading?Trade in Competitive MarketsOAOBWhich PO allocations can beachieved by competitive trading?Trade in Competitive MarketsOAOBBudget constraint for consumer ATrade in Competitive MarketsOAOBBudget constraint for consumer ATrade in Competitive Mar

25、ketsOAOBBudget constraint for consumer BTrade in Competitive MarketsOAOBBudget constraint for consumer BTrade in Competitive MarketsOAOBSoTrade in Competitive MarketsOAOBandTrade in Competitive MarketsAt the new prices p1 and p2 both markets clear; there is a general equilibrium.Question 1: Are pric

26、es p1 and p2 determined independently at equilibrium?Question 2: Does the equilibrium exist?Walras Law (瓦尔拉斯法则)Walras Law is an identity; i.e. a statement that is true for any positive prices (p1,p2), whether these are equilibrium prices or not.Walras LawEvery consumers preferences are well-behaved

27、so, for any positive prices (p1,p2), each consumer spends all of his budget.For consumer A:For consumer B:Walras LawSumming givesWalras LawRearranged,That is, .Walras LawThis says that the summed marketvalue of excess demands is zero forany positive prices p1 and p2 - this is Walras Law.Implications

28、 of Walras LawSuppose the market for commodity Ais in equilibrium; that is,ThenimpliesSo one implication of Walras Law for a modity exchange economy is that if one market is in equilibrium then the other market must also be in equilibrium.In general, if there are k markets, then only k-1 prices are

29、determined at equilibrium.I.e., the general equilibrium determines only relative prices.Implications of Walras LawImplications of Walras LawWhat if, for some positive prices p1 andp2, there is an excess quantity suppliedof commodity 1? That is,ThenimpliesImplications of Walras LawSo a second implica

30、tion of Walras Lawfor a modity exchange economyis that an excess supply in one marketimplies an excess demand in the othermarket.Existence of EquilibriumRequire that the aggregate excess demand functions be a continuous function, which in turn require thatEach individuals demand function be continuo

31、us, orEach consumer is small relative to the market.Trade in Competitive MarketsTrading in competitive markets achieves a particular Pareto-optimal allocation of the endowments.This is an example of the First Fundamental Theorem of Welfare Economics.First Fundamental Theorem of Welfare EconomicsGive

32、n that consumers preferences are well-behaved, trading in perfectly competitive markets implements a Pareto-optimal allocation of the economys endowment.The Equilibrium with MonopolySee Fig. 30.5 in textbook.The Equilibrium with MonopolyFigure 30.6 in book.Implicit AssumptionsNo consumption external

33、ity (外部效应)Agents behave competitivelyEquilibrium existsMarket Socialism: The DebateLange vs. HayekSocialism with economic planningState-ownershipGovernment chooses prices to clear marketsAdvantage of competitive marketsInformationSecond Fundamental Theorem of Welfare EconomicsThe First Theorem is followed by a second that states that any Pareto-optimal allocation (i.e. any