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1、Chapter Twenty-NineExchange2024/7/31北大微观经济学英文版Ch29ExchangExchangeuTwo consumers, A and B.uTheir endowments of goods 1 and 2 are uE.g. uThe total quantities availableandandunits of good 1units of good 2.andare2024/7/31北大微观经济学英文版Ch29ExchangExchangeuEdgeworth and Bowley devised a diagram, called an Edg
2、eworth box, to show all possible allocations of the available quantities of goods 1 and 2 between the two consumers.2024/7/31北大微观经济学英文版Ch29ExchangStarting an Edgeworth Box2024/7/31北大微观经济学英文版Ch29ExchangStarting an Edgeworth BoxWidth = 2024/7/31北大微观经济学英文版Ch29ExchangStarting an Edgeworth BoxWidth = Hei
3、ght =2024/7/31北大微观经济学英文版Ch29ExchangStarting an Edgeworth BoxWidth = Height =The dimensions ofthe box are thequantities availableof the goods.2024/7/31北大微观经济学英文版Ch29ExchangFeasible AllocationsuWhat allocations of the 8 units of good 1 and the 6 units of good 2 are feasible?uHow can all of the feasibl
4、e allocations be depicted by the Edgeworth box diagram?2024/7/31北大微观经济学英文版Ch29ExchangFeasible 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
5、 before-trade allocation; i.e. the endowment allocation.2024/7/31北大微观经济学英文版Ch29ExchangWidth = Height =The endowmentallocation isandThe Endowment Allocation2024/7/31北大微观经济学英文版Ch29ExchangWidth = Height =The Endowment Allocation2024/7/31北大微观经济学英文版Ch29ExchangOAOB68The Endowment Allocation2024/7/31北大微观经济
6、学英文版Ch29ExchangOAOB6846The Endowment Allocation2024/7/31北大微观经济学英文版Ch29ExchangOAOB684622The Endowment Allocation2024/7/31北大微观经济学英文版Ch29ExchangOAOB684622TheendowmentallocationThe Endowment Allocation2024/7/31北大微观经济学英文版Ch29ExchangMore generally, The Endowment Allocation2024/7/31北大微观经济学英文版Ch29ExchangThe
7、 Endowment AllocationOAOBTheendowmentallocation2024/7/31北大微观经济学英文版Ch29ExchangOther Feasible Allocationsu denotes an allocation to consumer A.u denotes an allocation to consumer B.uAn allocation is feasible if and only ifand2024/7/31北大微观经济学英文版Ch29ExchangFeasible ReallocationsOAOB2024/7/31北大微观经济学英文版Ch
8、29ExchangFeasible ReallocationsOAOB2024/7/31北大微观经济学英文版Ch29ExchangFeasible ReallocationsuAll points in the box, including the boundary, represent feasible allocations of the combined endowments.2024/7/31北大微观经济学英文版Ch29ExchangFeasible ReallocationsuAll points in the box, including the boundary, represe
9、nt feasible allocations of the combined endowments.uWhich allocations will be blocked by one or both consumers?uWhich allocations make both consumers better off?2024/7/31北大微观经济学英文版Ch29ExchangAdding Preferences to the BoxOAFor consumer A.2024/7/31北大微观经济学英文版Ch29ExchangAdding Preferences to the BoxMore
10、 preferredFor consumer A.OA2024/7/31北大微观经济学英文版Ch29ExchangAdding Preferences to the BoxFor consumer B.OB2024/7/31北大微观经济学英文版Ch29ExchangAdding Preferences to the BoxMore preferredFor consumer B.OB2024/7/31北大微观经济学英文版Ch29ExchangAdding Preferences to the BoxMore preferredFor consumer B.OB2024/7/31北大微观经济学英
11、文版Ch29ExchangAdding Preferences to the BoxOAFor consumer A.2024/7/31北大微观经济学英文版Ch29ExchangAdding Preferences to the BoxOAOB2024/7/31北大微观经济学英文版Ch29ExchangEdgeworths BoxOAOB2024/7/31北大微观经济学英文版Ch29ExchangPareto-ImprovementuAn allocation of the endowment that improves the welfare of a consumer without re
12、ducing the welfare of another is a Pareto-improving allocation.uWhere are the Pareto-improving allocations?2024/7/31北大微观经济学英文版Ch29ExchangEdgeworths BoxOAOB2024/7/31北大微观经济学英文版Ch29ExchangPareto-ImprovementsOAOBThe set of Pareto-improving allocations2024/7/31北大微观经济学英文版Ch29ExchangPareto-ImprovementsuSin
13、ce 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?2024/7/31北大微观经济学英文版Ch29ExchangPareto-ImprovementsOAOBThe set of Pareto-improving reallocations2024/7/31北大微观经济
14、学英文版Ch29ExchangPareto-Improvements2024/7/31北大微观经济学英文版Ch29ExchangPareto-Improvements2024/7/31北大微观经济学英文版Ch29ExchangPareto-ImprovementsTradeimproves bothAs and Bs welfares.This is a Pareto-improvementover the endowment allocation.2024/7/31北大微观经济学英文版Ch29ExchangPareto-ImprovementsNew mutual gains-to-trad
15、e region is the set of all further Pareto- improving reallocations. Tradeimproves bothAs and Bs welfares.This is a Pareto-improvementover the endowment allocation.2024/7/31北大微观经济学英文版Ch29ExchangPareto-ImprovementsFurther trade cannot improve both A and Bs welfares.2024/7/31北大微观经济学英文版Ch29ExchangPareto
16、-OptimalityBetter forconsumer BBetter forconsumer A2024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityA is strictly better off but B is strictly worse off2024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityA is strictly better off but B is strictly worse offB is strictly betteroff but A is strictlyworse off2
17、024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityA is strictly better off but B is strictly worse offB is strictly betteroff but A is strictlyworse offBoth A andB are worseoff2024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityA is strictly better off but B is strictly worse offB is strictly betteroff but A
18、 is strictlyworse offBoth Aand B are worse offBoth A andB are worseoff2024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityThe allocation isPareto-optimal since theonly way one consumerswelfare can be increased is todecrease the welfare of the otherconsumer.2024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityT
19、he 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.2024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityuWhere are all of the Pare
20、to-optimal allocations of the endowment?2024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityOAOB2024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityOAOBAll the allocations marked bya are Pareto-optimal.2024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityuThe contract curve is the set of all Pareto-optimal allocati
21、ons.2024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityOAOBAll the allocations marked bya are Pareto-optimal.The contract curve2024/7/31北大微观经济学英文版Ch29ExchangPareto-OptimalityuBut to which of the many allocations on the contract curve will consumers trade?uThat depends upon how trade is conducted.uIn per
22、fectly competitive markets? By one-on-one bargaining?2024/7/31北大微观经济学英文版Ch29ExchangThe CoreOAOBThe set of Pareto-improving reallocations2024/7/31北大微观经济学英文版Ch29ExchangThe CoreOAOB2024/7/31北大微观经济学英文版Ch29ExchangThe CoreOAOBPareto-optimal trades blocked by BPareto-optimal trades blocked by A2024/7/31北大微
23、观经济学英文版Ch29ExchangThe CoreOAOBPareto-optimal trades not blocked by A or B2024/7/31北大微观经济学英文版Ch29ExchangThe CoreOAOBPareto-optimal trades not blocked by A or B are the core.2024/7/31北大微观经济学英文版Ch29ExchangThe CoreuThe core is the set of all Pareto-optimal allocations that are welfare-improving for both
24、 consumers relative to their own endowments.uRational trade should achieve a core allocation.2024/7/31北大微观经济学英文版Ch29ExchangThe CoreuBut which core allocation?uAgain, that depends upon the manner in which trade is conducted.2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsuConsider trade in
25、perfectly competitive markets.uEach consumer is a price-taker trying to maximize her own utility given p1, p2 and her own endowment. That is, .2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAFor consumer A.2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsuSo given p1 and p2, con
26、sumer As net demands for commodities 1 and 2 areand2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsuAnd, similarly, for consumer B 2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsFor consumer B.OB2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsuSo given p1 and p2, consu
27、mer Bs net demands for commodities 1 and 2 areand2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsuA general equilibrium occurs when prices p1 and p2 cause both the markets for commodities 1 and 2 to clear; i.e.and2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOB2024/7/31北大微观经济
28、学英文版Ch29ExchangTrade in Competitive MarketsOAOBCan this PO allocation beachieved?2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBBudget constraint for consumer A2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBBudget constraint for consumer A2024/7/31北大微观经济学英文版Ch29ExchangT
29、rade in Competitive MarketsOAOBBudget constraint for consumer B2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBBudget constraint for consumer B2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBBut2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBand2024/7/31北大微观
30、经济学英文版Ch29ExchangTrade 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.2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBSo thi
31、s PO allocation cannot beachieved by competitive trading.2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBWhich PO allocations can beachieved by competitive trading?2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsuSince there is an excess demand for commodity 2, p2 will rise.u
32、Since 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.2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBWhich PO allocations can beachieved by compe
33、titive trading?2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBWhich PO allocations can beachieved by competitive trading?2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBWhich PO allocations can beachieved by competitive trading?2024/7/31北大微观经济学英文版Ch29ExchangTrade in Comp
34、etitive MarketsOAOBBudget constraint for consumer A2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBBudget constraint for consumer A2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBBudget constraint for consumer B2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAO
35、BBudget constraint for consumer B2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBSo2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsOAOBand2024/7/31北大微观经济学英文版Ch29ExchangTrade in Competitive MarketsuAt the new prices p1 and p2 both markets clear; there is a general equilibrium.
36、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.2024/7/31北大微观经济学英文版Ch29ExchangFirst Fundamental Theorem of Welfare EconomicsuGiven that consumers preferences are well-behaved,
37、trading in perfectly competitive markets implements a Pareto-optimal allocation of the economys endowment.2024/7/31北大微观经济学英文版Ch29ExchangSecond 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 cont
38、ract curve) can be achieved by trading in competitive markets provided that endowments are first appropriately rearranged amongst the consumers.2024/7/31北大微观经济学英文版Ch29ExchanguGiven that consumers preferences are well-behaved, for any Pareto-optimal allocation there are prices and an allocation of th
39、e total endowment that makes the Pareto-optimal allocation implementable by trading in competitive markets.Second Fundamental Theorem of Welfare Economics2024/7/31北大微观经济学英文版Ch29ExchangSecond Fundamental TheoremOAOBThe contract curve2024/7/31北大微观经济学英文版Ch29ExchangSecond Fundamental TheoremOAOB2024/7/3
40、1北大微观经济学英文版Ch29ExchangSecond Fundamental TheoremOAOBImplemented by competitivetrading from the endowment w w.2024/7/31北大微观经济学英文版Ch29ExchangSecond Fundamental TheoremOAOBCan this allocation be implementedby competitive trading from w w?2024/7/31北大微观经济学英文版Ch29ExchangSecond Fundamental TheoremOAOBCan t
41、his allocation be implementedby competitive trading from w w? No.2024/7/31北大微观经济学英文版Ch29ExchangSecond Fundamental TheoremOAOBBut this allocation is implementedby competitive trading from q q.2024/7/31北大微观经济学英文版Ch29ExchangWalras LawuWalras Law is an identity; i.e. a statement that is true for any pos
42、itive prices (p1,p2), whether these are equilibrium prices or not.2024/7/31北大微观经济学英文版Ch29ExchangWalras 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:2024/7/31北大微观经济学英文版Ch29ExchangWalras LawS
43、umming gives2024/7/31北大微观经济学英文版Ch29ExchangWalras LawRearranged,That is, .2024/7/31北大微观经济学英文版Ch29ExchangWalras LawThis says that the summed marketvalue of excess demands is zero forany positive prices p1 and p2 - this is Walras Law.2024/7/31北大微观经济学英文版Ch29ExchangImplications of Walras LawSuppose the m
44、arket for commodity Ais in equilibrium; that is,Thenimplies2024/7/31北大微观经济学英文版Ch29ExchangImplications 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.2024/7/31北大微观经济学英文版Ch29Exchan
45、gImplications of Walras LawWhat if, for some positive prices p1 andp2, there is an excess quantity suppliedof commodity 1? That is,Thenimplies2024/7/31北大微观经济学英文版Ch29ExchangImplications 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.2024/7/31北大微观经济学英文版Ch29Exchang
