1、Chapter Twenty-NineExchange1ppt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.andare2ppt课件ExchangeuEdgeworth and Bowley devised a diagram,
2、called an Edgeworth box, to show all possible allocations of the available quantities of goods 1 and 2 between the two consumers.3ppt课件Starting an Edgeworth Box4ppt课件Starting an Edgeworth BoxWidth = 11628AB 5ppt课件Starting an Edgeworth BoxWidth = 11628AB Height = 22426AB 6ppt课件Starting an Edgeworth B
3、oxWidth = 11628AB Height = 22426AB The dimensions ofthe box are thequantities availableof the goods.7ppt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?8ppt课件Feas
4、ible 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.9ppt课件Width = 11628AB Height = 22
5、426AB The endowmentallocation is A ( , )6 4 B ( , ).2 2andThe Endowment Allocation10ppt课件Width = 11628AB Height = 22426AB A ( , )6 4 B ( , )2 2The Endowment Allocation11ppt课件 A ( , )6 4OAOB68 B ( , )2 2The Endowment Allocation12ppt课件 A ( , )6 4OAOB6846The Endowment Allocation13ppt课件 B ( , )2 2OAOB68
6、4622The Endowment Allocation14ppt课件 A ( , )6 4 B ( , )2 2OAOB684622TheendowmentallocationThe Endowment Allocation15ppt课件More generally, The Endowment Allocation16ppt课件The Endowment AllocationOAOBTheendowmentallocation 11AB 2A 22AB 1A 1B 2B17ppt课件Other Feasible Allocationsu denotes an allocation to c
7、onsumer A.u denotes an allocation to consumer B.uAn allocation is feasible if and only if(,)xxAA12(,)xxBB12xxABAB1111 xxABAB2222 .and18ppt课件Feasible ReallocationsOAOB 11AB xA2 22AB xA1xB1xB219ppt课件Feasible ReallocationsOAOB 11AB xA2 22AB xA1xB1xB220ppt课件Feasible ReallocationsuAll points in the box,
8、including the boundary, represent feasible allocations of the combined endowments.21ppt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
9、 both consumers better off?22ppt课件Adding Preferences to the Box 2A 1AxA2xA1OAFor consumer A.23ppt课件Adding Preferences to the Box 2A 1AxA2xA1More preferredFor consumer A.OA24ppt课件Adding Preferences to the Box 2B 1BxB2xB1For consumer B.OB25ppt课件Adding Preferences to the BoxxB2xB1More preferredFor cons
10、umer B.OB 2B 1B26ppt课件Adding Preferences to the Box 2B 1BxB1xB2More preferredFor consumer B.OB27ppt课件Adding Preferences to the Box 2A 1AxA2xA1OAFor consumer A.28ppt课件Adding Preferences to the Box 2A 1AxA2xA1OA 2B 1BxB1xB2OB29ppt课件Edgeworths Box 2A 1AxA2xA1OA 2B 1BxB1xB2OB30ppt课件Pareto-ImprovementuAn
11、 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?31ppt课件Edgeworths Box 2A 1AxA2xA1OA 2B 1BxB1xB2OB32ppt课件Pareto-Improvements 2A 1AxA2xA1OA 2B 1BxB1xB2OBThe set of
12、Pareto-improving allocations33ppt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?34ppt课件Pareto-Improvements 2A 1AxA2xA1OA 2B 1BxB1xB
13、2OBThe set of Pareto-improving reallocations35ppt课件Pareto-Improvements36ppt课件Pareto-Improvements37ppt课件Pareto-ImprovementsTradeimproves bothAs and Bs welfares.This is a Pareto-improvementover the endowment allocation.38ppt课件Pareto-ImprovementsNew mutual gains-to-trade region is the set of all furthe
14、r Pareto- improving reallocations. Tradeimproves bothAs and Bs welfares.This is a Pareto-improvementover the endowment allocation.39ppt课件Pareto-ImprovementsFurther trade cannot improve both A and Bs welfares.40ppt课件Pareto-OptimalityBetter forconsumer BBetter forconsumer A41ppt课件Pareto-OptimalityA is
15、 strictly better off but B is strictly worse off42ppt课件Pareto-OptimalityA is strictly better off but B is strictly worse offB is strictly betteroff but A is strictlyworse off43ppt课件Pareto-OptimalityA is strictly better off but B is strictly worse offB is strictly betteroff but A is strictlyworse off
16、Both A andB are worseoff44ppt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 worseoff45ppt课件Pareto-OptimalityThe allocation isPareto-optimal since theonly way one consumerswelfare can be
17、 increased is todecrease the welfare of the otherconsumer.46ppt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 Paret
18、o-optimal.47ppt课件Pareto-OptimalityuWhere are all of the Pareto-optimal allocations of the endowment?48ppt课件Pareto-Optimality 2A 1AxA2xA1OA 2B 1BxB1xB2OB49ppt课件Pareto-Optimality 2A 1AxA2xA1OA 2B 1BxB1xB2OBAll the allocations marked bya are Pareto-optimal.50ppt课件Pareto-OptimalityuThe contract curve is
19、 the set of all Pareto-optimal allocations.51ppt课件Pareto-Optimality 2A 1AxA2xA1OA 2B 1BxB1xB2OBAll the allocations marked bya are Pareto-optimal.The contract curve52ppt课件Pareto-OptimalityuBut to which of the many allocations on the contract curve will consumers trade?uThat depends upon how trade is
20、conducted.uIn perfectly competitive markets? By one-on-one bargaining?53ppt课件The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OBThe set of Pareto-improving reallocations54ppt课件The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OB55ppt课件The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OBPareto-optimal trades blocked by BPareto-optimal trades bloc
21、ked by A56ppt课件The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OBPareto-optimal trades not blocked by A or B57ppt课件The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OBPareto-optimal trades not blocked by A or B are the core.58ppt课件The CoreuThe core is the set of all Pareto-optimal allocations that are welfare-improving for both
22、consumers relative to their own endowments.uRational trade should achieve a core allocation.59ppt课件The CoreuBut which core allocation?uAgain, that depends upon the manner in which trade is conducted.60ppt课件Trade in Competitive MarketsuConsider trade in perfectly competitive markets.uEach consumer is
23、 a price-taker trying to maximize her own utility given p1, p2 and her own endowment. That is, .61ppt课件Trade in Competitive Markets 2A 1AxA2xA1OAFor consumer A.p xp xppAAAA1 12 21122 xA2*xA1*62ppt课件Trade in Competitive MarketsuSo given p1 and p2, consumer As net demands for commodities 1 and 2 arexA
24、A11* xAA22*. and63ppt课件Trade in Competitive MarketsuAnd, similarly, for consumer B 64ppt课件Trade in Competitive Markets 2B 1BxB2xB1For consumer B.OBxB1*xB2*p xp xppBBBB1 12 21122 65ppt课件Trade in Competitive MarketsuSo given p1 and p2, consumer Bs net demands for commodities 1 and 2 arexBB11* xBB22*.
25、and66ppt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*. and67ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OB68ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1
26、xB2OBCan this PO allocation beachieved?69ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer A70ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer AxA2*xA1*71ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OB
27、Budget constraint for consumer BxA2*xA1*72ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer BxA2*xA1*xB1*xB2*73ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBxA2*xA1*xB1*xB2*ButxxABAB1111* 74ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1B
28、xB1xB2OBxA2*xA1*xB1*xB2*andxxABAB2222* 75ppt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.76ppt课件Trade in Competitive Markets 2A
29、1AxA2xA1OA 2B 1BxB1xB2OBSo this PO allocation cannot beachieved by competitive trading.77ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved by competitive trading?78ppt课件Trade in Competitive MarketsuSince there is an excess demand for commodity 2, p2 wil
30、l 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.79ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved
31、 by competitive trading?80ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved by competitive trading?81ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved by competitive trading?82ppt课件Trade in Competitive Mark
32、ets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer A83ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer AxA2*xA1*84ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer BxA2*xA1*85ppt课件Trade in Competitive Mar
33、kets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer BxA2*xA1*xB1*xB2*86ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBxA2*xA1*xB1*xB2*SoxxABAB1111* 87ppt课件Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBxA2*xA1*xB1*xB2*andxxABAB2222* 88ppt课件Trade in Competitive Marke
34、tsuAt 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.89ppt课件First Fundamental Theorem of Welfare Ec
35、onomicsuGiven that consumers preferences are well-behaved, trading in perfectly competitive markets implements a Pareto-optimal allocation of the economys endowment.90ppt课件Second Fundamental Theorem of Welfare EconomicsuThe First Theorem is followed by a second that states that any Pareto-optimal al
36、location (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.91ppt课件uGiven that consumers preferences are well-behaved, for any Pareto-optimal allocation there are prices and an all
37、ocation of the total endowment that makes the Pareto-optimal allocation implementable by trading in competitive markets.Second Fundamental Theorem of Welfare Economics92ppt课件Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OBThe contract curve93ppt课件Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1Bx
38、B1xB2OBA*2xB*2xA*1xB*1x94ppt课件Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OBA*2xB*2xA*1xB*1xImplemented by competitivetrading from the endowment .95ppt课件Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OBCan this allocation be implementedby competitive trading from ?96ppt课件Second Fundamen
39、tal Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OBCan this allocation be implementedby competitive trading from ? No.97ppt课件Second Fundamental TheoremxA2xA1OAxB1xB2OBBut this allocation is implementedby competitive trading from q q.A1q qB2q qB1q qA2q q98ppt课件Walras LawuWalras Law is an identity; i.e. a stateme
40、nt that is true for any positive prices (p1,p2), whether these are equilibrium prices or not.99ppt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
41、 12 21122* 100ppt课件Walras Lawp xp xppAAAA1 12 21122* p xp xppBBBB1 12 21122* pxxpxxppABABABBB111222111222()()()().* Summing gives101ppt课件Walras LawpxxpxxppABABABBB111222111222()()()().* Rearranged,pxxpxxABABABAB11111222220()().* That is, .102ppt课件Walras Law. 0)xx(p)xx(pB2A2B*2A*22B1A1B*1A*11 This sa
42、ys that the summed marketvalue of excess demands is zero forany positive prices p1 and p2 - this is Walras Law.103ppt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 104ppt课件Implica
43、tions 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.105ppt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 106ppt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.107ppt课件
