1、2023-1-9中级微观经济学Chapter Twenty-NineExchange2023-1-9中级微观经济学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.andare2023-1-9中级微观经济学ExchangeuEdgeworth and
2、 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.2023-1-9中级微观经济学Starting an Edgeworth Box2023-1-9中级微观经济学Starting an Edgeworth BoxWidth=11628AB 2023-1-9中级微观经济学Starting an Edgeworth BoxWidth=11628A
3、B Height=22426AB 2023-1-9中级微观经济学Starting an Edgeworth BoxWidth=11628AB Height=22426AB The dimensions ofthe box are thequantities availableof the goods.2023-1-9中级微观经济学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 all
4、ocations be depicted by the Edgeworth box diagram?2023-1-9中级微观经济学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 alloca
5、tion;i.e.the endowment allocation.2023-1-9中级微观经济学Width=11628AB Height=22426AB The endowmentallocation is A (,)6 4 B (,).2 2andThe Endowment Allocation2023-1-9中级微观经济学Width=11628AB Height=22426AB A (,)6 4 B (,)2 2The Endowment Allocation2023-1-9中级微观经济学 A (,)6 4OAOB68 B (,)2 2The Endowment Allocation20
6、23-1-9中级微观经济学 A (,)6 4OAOB6846The Endowment Allocation2023-1-9中级微观经济学 B (,)2 2OAOB684622The Endowment Allocation2023-1-9中级微观经济学 A (,)6 4 B (,)2 2OAOB684622TheendowmentallocationThe Endowment Allocation2023-1-9中级微观经济学More generally,The Endowment Allocation2023-1-9中级微观经济学The Endowment AllocationOAOBTh
7、eendowmentallocation 11AB 2A 22AB 1A 1B 2B2023-1-9中级微观经济学Other Feasible Allocationsu denotes an allocation to consumer A.u denotes an allocation to consumer B.uAn allocation is feasible if and only if(,)xxAA12(,)xxBB12xxABAB1111 xxABAB2222 .and2023-1-9中级微观经济学Feasible ReallocationsOAOB 11AB xA2 22AB
8、xA1xB1xB22023-1-9中级微观经济学Feasible ReallocationsOAOB 11AB xA2 22AB xA1xB1xB22023-1-9中级微观经济学Feasible ReallocationsuAll points in the box,including the boundary,represent feasible allocations of the combined endowments.2023-1-9中级微观经济学Feasible ReallocationsuAll points in the box,including the boundary,re
9、present feasible allocations of the combined endowments.uWhich allocations will be blocked by one or both consumers?uWhich allocations make both consumers better off?2023-1-9中级微观经济学Adding Preferences to the Box 2A 1AxA2xA1OAFor consumer A.2023-1-9中级微观经济学Adding Preferences to the Box 2A 1AxA2xA1More
10、preferredFor consumer A.OA2023-1-9中级微观经济学Adding Preferences to the Box 2B 1BxB2xB1For consumer B.OB2023-1-9中级微观经济学Adding Preferences to the BoxxB2xB1More preferredFor consumer B.OB 2B 1B2023-1-9中级微观经济学Adding Preferences to the Box 2B 1BxB1xB2More preferredFor consumer B.OB2023-1-9中级微观经济学Adding Prefe
11、rences to the Box 2A 1AxA2xA1OAFor consumer A.2023-1-9中级微观经济学Adding Preferences to the Box 2A 1AxA2xA1OA 2B 1BxB1xB2OB2023-1-9中级微观经济学Edgeworths Box 2A 1AxA2xA1OA 2B 1BxB1xB2OB2023-1-9中级微观经济学Pareto-ImprovementuAn allocation of the endowment that improves the welfare of a consumer without reducing the
12、 welfare of another is a Pareto-improving allocation.uWhere are the Pareto-improving allocations?2023-1-9中级微观经济学Edgeworths Box 2A 1AxA2xA1OA 2B 1BxB1xB2OB2023-1-9中级微观经济学Pareto-Improvements 2A 1AxA2xA1OA 2B 1BxB1xB2OBThe set of Pareto-improving allocations2023-1-9中级微观经济学Pareto-ImprovementsuSince each
13、 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?2023-1-9中级微观经济学Pareto-Improvements 2A 1AxA2xA1OA 2B 1BxB1xB2OBThe set of Pareto-improving reallocations2023-1-9中级微观经济
14、学Pareto-Improvements2023-1-9中级微观经济学Pareto-Improvements2023-1-9中级微观经济学Pareto-ImprovementsTradeimproves bothAs and Bs welfares.This is a Pareto-improvementover the endowment allocation.2023-1-9中级微观经济学Pareto-ImprovementsNew mutual gains-to-trade region is the set of all further Pareto-improving realloc
15、ations.Tradeimproves bothAs and Bs welfares.This is a Pareto-improvementover the endowment allocation.2023-1-9中级微观经济学Pareto-ImprovementsFurther trade cannot improve both A and Bs welfares.2023-1-9中级微观经济学Pareto-OptimalityBetter forconsumer BBetter forconsumer A2023-1-9中级微观经济学Pareto-OptimalityA is str
16、ictly better off but B is strictly worse off2023-1-9中级微观经济学Pareto-OptimalityA is strictly better off but B is strictly worse offB is strictly betteroff but A is strictlyworse off2023-1-9中级微观经济学Pareto-OptimalityA is strictly better off but B is strictly worse offB is strictly betteroff but A is stric
17、tlyworse offBoth A andB are worseoff2023-1-9中级微观经济学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 worseoff2023-1-9中级微观经济学Pareto-OptimalityThe allocation isPareto-optimal since theonly way
18、 one consumerswelfare can be increased is todecrease the welfare of the otherconsumer.2023-1-9中级微观经济学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 a
19、re“only just back-to-back”is Pareto-optimal.2023-1-9中级微观经济学Pareto-OptimalityuWhere are all of the Pareto-optimal allocations of the endowment?2023-1-9中级微观经济学Pareto-Optimality 2A 1AxA2xA1OA 2B 1BxB1xB2OB2023-1-9中级微观经济学Pareto-Optimality 2A 1AxA2xA1OA 2B 1BxB1xB2OBAll the allocations marked bya are Par
20、eto-optimal.2023-1-9中级微观经济学Pareto-OptimalityuThe contract curve is the set of all Pareto-optimal allocations.2023-1-9中级微观经济学Pareto-Optimality 2A 1AxA2xA1OA 2B 1BxB1xB2OBAll the allocations marked bya are Pareto-optimal.The contract curve2023-1-9中级微观经济学Pareto-OptimalityuBut to which of the many alloc
21、ations on the contract curve will consumers trade?uThat depends upon how trade is conducted.uIn perfectly competitive markets?By one-on-one bargaining?2023-1-9中级微观经济学The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OBThe set of Pareto-improving reallocations2023-1-9中级微观经济学The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OB2023-1
22、-9中级微观经济学The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OBPareto-optimal trades blocked by BPareto-optimal trades blocked by A2023-1-9中级微观经济学The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OBPareto-optimal trades not blocked by A or B2023-1-9中级微观经济学The Core 2A 1AxA2xA1OA 2B 1BxB1xB2OBPareto-optimal trades not blocked by A or
23、B are the core.2023-1-9中级微观经济学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.2023-1-9中级微观经济学The CoreuBut which core allocation?uAgain,that depends upon the
24、manner in which trade is conducted.2023-1-9中级微观经济学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,.2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OAFor co
25、nsumer A.p xp xppAAAA1 12 21122 xA2*xA1*2023-1-9中级微观经济学Trade in Competitive MarketsuSo given p1 and p2,consumer As net demands for commodities 1 and 2 arexAA11*xAA22*.and2023-1-9中级微观经济学Trade in Competitive MarketsuAnd,similarly,for consumer B 2023-1-9中级微观经济学Trade in Competitive Markets 2B 1BxB2xB1Fo
26、r consumer B.OBxB1*xB2*p xp xppBBBB1 12 21122 2023-1-9中级微观经济学Trade in Competitive MarketsuSo given p1 and p2,consumer Bs net demands for commodities 1 and 2 arexBB11*xBB22*.and2023-1-9中级微观经济学Trade in Competitive MarketsuA general equilibrium occurs when prices p1 and p2 cause both the markets for co
27、mmodities 1 and 2 to clear;i.e.xxABAB1111*xxABAB2222*.and2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OB2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBCan this PO allocation beachieved?2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1x
28、B2OBBudget constraint for consumer A2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer AxA2*xA1*2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer BxA2*xA1*2023-1-9中级微观经济学Trade in Competitive Market
29、s 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer BxA2*xA1*xB1*xB2*2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBxA2*xA1*xB1*xB2*ButxxABAB1111*2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBxA2*xA1*xB1*xB2*andxxABAB2222*2023-1-9中级微观经济学Trade
30、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.2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBSo this PO allocatio
31、n cannot beachieved by competitive trading.2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved by competitive trading?2023-1-9中级微观经济学Trade in Competitive MarketsuSince there is an excess demand for commodity 2,p2 will rise.uSince there is an exc
32、ess 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.2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved by competitive trading?
33、2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved by competitive trading?2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBWhich PO allocations can beachieved by competitive trading?2023-1-9中级微观经济学Trade in Competitive Mark
34、ets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer A2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer AxA2*xA1*2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer BxA2*xA1*2023-1-9中级微观经济学
35、Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBBudget constraint for consumer BxA2*xA1*xB1*xB2*2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBxA2*xA1*xB1*xB2*SoxxABAB1111*2023-1-9中级微观经济学Trade in Competitive Markets 2A 1AxA2xA1OA 2B 1BxB1xB2OBxA2*xA1*xB1*xB2*andxxABAB
36、2222*2023-1-9中级微观经济学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.2
37、023-1-9中级微观经济学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.2023-1-9中级微观经济学Second Fundamental Theorem of Welfare EconomicsuThe First Theorem is
38、 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.2023-1-9中级微观经济学uGiven that consumers preferences are well-behav
39、ed,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 Economics2023-1-9中级微观经济学Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OB
40、The contract curve2023-1-9中级微观经济学Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OBA*2xB*2xA*1xB*1x2023-1-9中级微观经济学Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OBA*2xB*2xA*1xB*1xImplemented by competitivetrading from the endowment .2023-1-9中级微观经济学Second Fundamental Theorem 2A 1AxA2xA1OA 2B
41、 1BxB1xB2OBCan this allocation be implementedby competitive trading from?2023-1-9中级微观经济学Second Fundamental Theorem 2A 1AxA2xA1OA 2B 1BxB1xB2OBCan this allocation be implementedby competitive trading from?No.2023-1-9中级微观经济学Second Fundamental TheoremxA2xA1OAxB1xB2OBBut this allocation is implementedby
42、 competitive trading from q q.A1q qB2q qB1q qA2q q2023-1-9中级微观经济学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.2023-1-9中级微观经济学Walras LawuEvery consumers preferences are well-behaved so,for any positive pri
43、ces(p1,p2),each consumer spends all of his budget.uFor consumer A:For consumer B:p xp xppAAAA1 12 21122*p xp xppBBBB1 12 21122*2023-1-9中级微观经济学Walras Lawp xp xppAAAA1 12 21122*p xp xppBBBB1 12 21122*pxxpxxppABABABBB111222111222()()()().*Summing gives2023-1-9中级微观经济学Walras LawpxxpxxppABABABBB1112221112
44、22()()()().*Rearranged,pxxpxxABABABAB11111222220()().*That is,.2023-1-9中级微观经济学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 Walras Law.2023-1-9中级微观经济学Implications of Walras Law0)xx(p)xx(pB2A2B*2A*
45、22B1A1B*1A*11 Suppose the market for commodity Ais in equilibrium;that is,.0 xxB1A1B*1A*1 Thenimplies.0 xxB2A2B*2A*2 2023-1-9中级微观经济学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
46、inequilibrium.2023-1-9中级微观经济学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 2023-1-9中级微观经济学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.
