Ch29Exchange微观范里安上海交通大学赵旭

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1、整理课件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 available AAA (,)12 BBB (,).12and A (,)6 4 B (,).2 2and 11628AB 22426AB units of good 1units of good 2.andare整理课件ExchangeuEdgeworth and Bowley devised a diagram,called

2、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=11628AB 整理课件Starting an Edgeworth BoxWidth=11628AB Height=22426AB 整理课件Starting an Edgeworth BoxWidth=11628AB Height

3、=22426AB 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 allocati

4、ons 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=11628AB Height=22426AB The endowmentallocation is A (,)

5、6 4 B (,).2 2andThe Endowment Allocation整理课件Width=11628AB Height=22426AB A (,)6 4 B (,)2 2The Endowment Allocation整理课件 A (,)6 4OAOB68 B (,)2 2The Endowment Allocation整理课件 A (,)6 4OAOB6846The Endowment Allocation整理课件 B (,)2 2OAOB684622The Endowment Allocation整理课件 A (,)6 4 B (,)2 2OAOB684622Theendowme

6、ntallocationThe Endowment Allocation整理课件More generally,The Endowment Allocation整理课件The Endowment AllocationOAOBTheendowmentallocation 11AB 2A 22AB 1A 1B 2B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

7、if(,)xxAA12(,)xxBB12xxABAB1111 xxABAB2222 .and整理课件Feasible ReallocationsOAOB 11AB xA2 22AB xA1xB1xB2整理课件Feasible ReallocationsOAOB 11AB xA2 22AB xA1xB1xB2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 Rea

8、llocationsuAll 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 Box 2A 1AxA2xA1OAFor consumer A.整理课件Adding Pre

9、ferences to the Box 2A 1AxA2xA1More preferredFor consumer A.OA整理课件Adding Preferences to the Box 2B 1BxB2xB1For consumer B.OB整理课件Adding Preferences to the BoxxB2xB1More preferredFor consumer B.OB 2B 1B整理课件Adding Preferences to the Box 2B 1BxB1xB2More preferredFor consumer B.OB整理课件Adding Preferences t

10、o the Box 2A 1AxA2xA1OAFor consumer A.整理课件Adding Preferences to the Box 2A 1AxA2xA1OA 2B 1BxB1xB2OB整理课件Edgeworths Box 2A 1AxA2xA1OA 2B 1BxB1xB2OB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

11、 allocation.uWhere are the Pareto-improving allocations?整理课件Edgeworths Box 2A 1AxA2xA1OA 2B 1BxB1xB2OB整理课件Pareto-Improvements 2A 1AxA2xA1OA 2B 1BxB1xB2OBThe set of Pareto-improving allocations整理课件Pareto-ImprovementsuSince each consumer can refuse to trade,the only possible outcomes from exchange are

12、 Pareto-improving allocations.uBut which particular Pareto-improving allocation will be the outcome of trade?整理课件Pareto-Improvements 2A 1AxA2xA1OA 2B 1BxB1xB2OBThe 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 we

13、lfares.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-ImprovementsFurt

14、her 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 strictlywors

15、e 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 off

16、Both 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 todecrea

17、se 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-Optimality 2A 1AxA2xA1OA 2B 1BxB1xB2OB整理课件Pareto-Optimality 2A 1AxA2xA1OA 2

18、B 1BxB1xB2OBAll 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-Optimality 2A 1AxA2xA1OA 2B 1BxB1xB2OBAll the allocations marked bya are Pareto-optimal.The contract curve整理课件Pareto-OptimalityuBut to which

19、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 Core 2A 1AxA2xA1OA 2B 1BxB1xB2OBThe set of Pareto-improving reallocations整理课件The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OB整理课件The Cor

20、e 2A 1AxA2xA1OA 2B 1BxB1xB2OBPareto-optimal trades blocked by BPareto-optimal trades blocked by A整理课件The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OBPareto-optimal trades not blocked by A or B整理课件The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OBPareto-optimal trades not blocked by A or B are the core.整理课件The CoreuThe core i

21、s 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

22、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 Markets 2A 1AxA2xA1OAFor consumer A.p xp xppAAAA1 12 21122 xA2*xA1*整理课件Trade in Competitive MarketsuSo given

23、p1 and p2,consumer As net demands for commodities 1 and 2 arexAA11*xAA22*.and整理课件Trade in Competitive MarketsuAnd,similarly,for consumer B 整理课件Trade in Competitive Markets 2B 1BxB2xB1For consumer B.OBxB1*xB2*p xp xppBBBB1 12 21122 整理课件Trade in Competitive MarketsuSo given p1 and p2,consumer Bs net d

24、emands for commodities 1 and 2 arexBB11*xBB22*.and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.xxABAB1111*xxABAB2222*.and整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OB整理课件Trade in Competi

25、tive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBCan this PO allocation beachieved?整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer A整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer AxA2*xA1*整理课件Trade in Competitive Markets 2

26、A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer BxA2*xA1*整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer BxA2*xA1*xB1*xB2*整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBxA2*xA1*xB1*xB2*ButxxABAB1111*整理课件Trade in Competitive Markets 2A

27、1AxA2xA1OA 2B 1BxB1xB2OBxA2*xA1*xB1*xB2*andxxABAB2222*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 Ma

28、rkets 2A 1AxA2xA1OA 2B 1BxB1xB2OBSo this PO allocation cannot beachieved by competitive trading.整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved by competitive trading?整理课件Trade in Competitive MarketsuSince there is an excess demand for commodity 2,p2 w

29、ill 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 Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved by

30、competitive trading?整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved by competitive trading?整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved by competitive trading?整理课件Trade in Competitive Markets 2A 1AxA2x

31、A1OA 2B 1BxB1xB2OBBudget constraint for consumer A整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer AxA2*xA1*整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer BxA2*xA1*整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B

32、1BxB1xB2OBBudget constraint for consumer BxA2*xA1*xB1*xB2*整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBxA2*xA1*xB1*xB2*SoxxABAB1111*整理课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBxA2*xA1*xB1*xB2*andxxABAB2222*整理课件Trade in Competitive MarketsuAt the new prices p1 and p2 bo

33、th 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 preferen

34、ces 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 cu

35、rve)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 Pa

36、reto-optimal allocation implementable by trading in competitive markets.Second Fundamental Theorem of Welfare Economics整理课件Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OBThe contract curve整理课件Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OBA*2xB*2xA*1xB*1x整理课件Second Fundamental Theorem

37、2A 1AxA2xA1OA 2B 1BxB1xB2OBA*2xB*2xA*1xB*1xImplemented by competitivetrading from the endowment .整理课件Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OBCan this allocation be implementedby competitive trading from?整理课件Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OBCan this allocation be im

38、plementedby competitive trading from?No.整理课件Second Fundamental TheoremxA2xA1OAxB1xB2OBBut this allocation is implementedby competitive trading from q q.A1q qB2q qB1q qA2q 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 equilibri

39、um 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:p xp xppAAAA1 12 21122*p xp xppBBBB1 12 21 122*整理课件Walras Lawp xp xppAAAA1 12 21122*p xp xppBBBB1 12 21 122*pxxpxxppABA

40、BABBB111222111222()()()().*Summing gives整理课件Walras LawpxxpxxppABABABBB111222111222()()()().*Rearranged,pxxpxxABABABAB11111222220()().*That is,.整理课件Walras Law.0)xx(p)xx(pB2A2B*2A*22B1A1B*1A*11 This says that the summed marketvalue of excess demands is zero forany positive prices p1 and p2-this is Wal

41、ras Law.整理课件Implications of Walras Law0)xx(p)xx(pB2A2B*2A*22B1A1B*1A*11 Suppose the market for commodity Ais in equilibrium;that is,.0 xxB1A1B*1A*1 Thenimplies.0 xxB2A2B*2A*2 整理课件Implications of Walras LawSo one implication of Walras Law fora two-commodity exchange economyis that if one market is in

42、 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,.0 xxB1A1B*1A*1 0)xx(p)xx(pB2A2B*2A*22B1A1B*1A*11 Thenimplies.0 xxB2A2B*2A*2 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.