1、Chapter 13General EquilibriumTopics to be DiscussedGeneral Equilibrium AnalysisEfficiency in ExchangeEquity and EfficiencyEfficiency in ProductionTopics to be DiscussedThe Gains from Free TradeAn Overview:The Efficiency of Competitive MarketsWhy Markets FailGeneral Equilibrium AnalysisUp to this poi
2、nt,we have been focused on partial equilibrium analysis Activity in one market has little or no effect on other marketsMarket interrelationships can be important Complements and substitutes Increase in firms input demand can cause market price of the input and product to riseGeneral Equilibrium Anal
3、ysisTo study how markets interrelate,we can use general equilibrium analysis Simultaneous determination of the prices and quantities in all relevant markets,taking into account feedback effectsThe feedback effect is the price or quantity adjustment in one market caused by price and quantity adjustme
4、nts in related marketsEfficiency in ExchangeWe showed before that competitive markets are efficient because consumer and producer surpluses are maximizedWe can study this in more detail by examining an exchange economy Market in which two or more consumers trade two goods among themselves Same for t
5、wo countriesEfficiency in ExchangeAn efficient allocation of goods is one where no one can be made better off without making someone else worse off Pareto efficiencyVoluntary trade between two parties is mutually beneficial and increases economic efficiencyGain from TradeAssumptions Two consumers(co
6、untries)Two goods Both people know each others preferences Exchanging goods involves zero transaction costs James and Karen have a total of 10 units of food and 6 units of clothingGain from TradeTo determine if they are better off,we need to know the preferences for food and clothingIndividualInitia
7、l EndowmentTradeFinal AllocationJames7F,1C-1F,+1C6F,2CKaren3F,5C+1F,-1C4F,4CGain from TradeJames MRS of food for clothing is only He will give up unit of clothing for 1 unit of foodKaren has a lot of clothing and little food MRS of food for clothing is 3 To get 1 unit of food,she will give up 3 unit
8、s of clothingGain from TradeThere is room for trade James values clothing more than Karen Karen values food more than James Karen is willing to give up 3 units of clothing to get 1 unit of food,but James is willing to take only unit of clothing for 1 unit of foodActual terms of trade are determined
9、through bargaining Trade for 1 unit of food will fall between and 3 units of clothingGain from TradeSuppose Karen offers James 1 unit of clothing for 1 unit of food James will have more clothing,which he values more than food Karen will have more food,which she values moreWhenever two consumers MRSs
10、 are different,there is room for mutually beneficial trade Allocation of resources is inefficientGain from TradeFrom this analysis we obtain an important result:An allocation of goods is efficient only if the goods are distributed so that the marginal rate of substitution between any pair of goods i
11、s the same for all consumersThe Edgeworth Box DiagramA diagram showing all possible allocations of either two goods between two people or of two inputs between two production processes is called an Edgeworth BoxLets consider an exchange economyThe Edgeworth Box10F0K0J6C10F6CJamesClothingKarensClothi
12、ngJames FoodKarens Food1C5C3F7FAThe initial allocation before trade is A:Jameshas 7F and 1C&Karen has 3F and 5C.Exchange in an Edgeworth BoxJames FoodKarens Food10F0K0J6C10F6CJamesClothingKarensClothing1C5C3F7FAThe allocation after trade is B:Jameshas 6F and 2C&Karen has 4F and 4C.4F6F+1C-1F2C4CBGai
13、ns from TradeA:UJ1=UK1,but the MRSis not equal.All combinationsin the shadedarea arepreferred to A.KarensClothingKarens FoodUK1JamessClothingJamess FoodUJ110F0K0J6C10F6CGains fromtradeAEfficiency in ExchangeKarensClothingKarens FoodJamessClothingJamess Food10F0K0J6C10F6CUK1UJ1APoint B is on higher I
14、C but is not efficient UJ2UK2BAt point C,MRSs are equal and allocation is efficientUK3CD is also a possible efficient allocation depending on bargaining UJ3DEfficient AllocationsHow do these parties reach an efficient allocation?When there is no more room for trade When their MRSs are equal They wil
15、l keep trading,reaching higher indifference curves,until they can no longer do so and still make each better off This is when indifference curves are tangent they have the same slope and same MRSEfficiency in ExchangeAny move outside the shaded area will make one person worse off(closer to their ori
16、gin)B is a mutually beneficial trade-higher indifference curve for each personTrade may be beneficial but not efficientMRS is equal when indifference curves are tangent and the allocation is efficientAKarensClothingKarens FoodUK1UK2UK3JamesClothingJames FoodUJ1UJ2UJ3BCD10F0K0J6C10F6CThe Contract Cur
17、veTo find all possible efficient allocations of food and clothing between Karen and James,we would look for all points of tangency between each of their indifference curvesThe contract curve shows all the efficient allocations of goods between two consumers,or of two inputs between two production fu
18、nctionsThe Contract Curve0JJamesClothingKarensClothing0KKarens FoodJames FoodEFGContractCurveE,F,&G arePareto efficient.Contract CurveAll points of tangency between the indifference curves are efficient MRS of individuals is the same No more room for tradeThe contract curve shows all allocations tha
19、t are Pareto efficient Pareto efficient allocation occurs when further trade will make someone worse off Pareto set itself does not depend on the initial endowmentMarket TradeWhat would happen if the two persons are in a competitive market?Both are price-takersSuppose we have a third party who acts
20、as an“auctioneer”for the two agentsAt any prices announced by the auctioneer,if there is excess demand or supply,then she will change the prices such that demand equals demand for any goodConsumer Equilibrium in a Competitive MarketPrice Line10F0K0J6C10F6CJamesClothingKarensClothingKarens FoodJames
21、FoodCABegin at A:Each James buys 2C and sells 2Fmoving from UJ1to UJ2,which is preferred(A to C).Begin at A:Each Karen buys 2F and sells 2C moving fromUK1to UK2,which is preferred(A to C).PPUJ2UJ1UK1UK2Walrasian Equilibrium A market equilibrium or Walrasianequilibrium is a set of prices at which the
22、 quantity demanded equals the quantity supplied in every market Also called competitive equilibriumIn the market equilibrium,all consumers are facing the same price,so all consumers will have the same marginal rate of substitution between any two goodsWalrasian EquilibriumAt the equilibrium prices p
23、*,we should haveThis means thatLet us denote the excess demand for good i by agent j byThen,we get Z(p1,p2)represents the aggregate excess demand for good i)2,1(),(),(*2*1*2*1iWWppXppXiBiAiBiA0)*()*(iBiBiAiAWXWX),(),(21BAjWppXeijijij),(),(),(212121ppeppeppziBiAiWalrasian EquilibriumThe prices are eq
24、uilibrium prices ifThe equilibrium prices will clear all markets simultaneouslyIn order to understand the nature of these conditions,we need to know Walras Law),(*2*1pp0),(,0),(*2*12*2*11ppzppzThe Walras LawKkkkBABABBBBBBAAAAAAAApzpgenerallyMoreppzpppzpeepeepepepWpWppXppXpepepWpWppXppXppXpXbundlesop
25、timaltheAtppzpppzp12122211122211122112211221122112211221121212221110)(,0),(),(0)()(0)()(0)()()(),(0),(),(ImplicationsIf(K-1)markets clear,then the last market will also clearThere are only(K-1)independent pricesNote that p*and tp*are both equilibrium prices,and by setting t=1/p1,then there are only(
26、K-1)relative pricesIn general we call good 1 as numenaire goodNote that the Walras law is conditional only on optimality of choices,not equilibriumEquilibrium and EfficiencyAs shown before,we can see that the allocation in a competitive equilibrium is economically efficient The efficient point must
27、occur where the two indifference curves are tangent If not,one of the consumers can increase their utility and be better offA Proof of Efficiency in Market EquilibriumThis can be proven by way of counter argumentSuppose a market equilibrium is NOT efficient,then it implies that there is another feas
28、ible allocation such that),(BAyy),(),(),(),()2,1(21212121BBBBBAAAAAiBiAiBiAXXyyXXyyandiWWyyA Proof of Efficiency in Market EquilibriumIf (yA)is better than the bundle(xA)A is choosing,then it must cost more than A can afford,similarly for BThat is,Adding these two equations,we getThis contradicts wi
29、th the feasibility condition with equality),(22112211BAjWpWpypypjjjj)()()()(222111222111BABABABAWWpWWpyypyypFirst Theorem of Welfare EconomicsMarket equilibria are Pareto efficientIf everyone trades in a competitive marketplace,all mutually beneficial trades will be completed and the resulting equil
30、ibrium allocation of resources will be economically efficient Welfare economics involves the normative evaluation of markets and economic policyEquilibrium and EfficiencyThe first welfare theorem is the best illustration of Adam Smiths invisible hand Economy will automatically allocate all resources
31、 efficiently without need for regulatory control Supports argument for less government intervention and more highly competitive marketsMarkets use minimum information to function well(compare this with the centralized planning)看不见的手：亚当斯密的表述“他只是盘算他自己的安全；由于他管理产业的方式目的在于使其生产物的价值能达到最大程度，他所盘算的也只是他自己的利益。在这
32、场合，像在其他许多场合一样，他受着一只看不见的看不见的手手的指导，去尽力达到一个并非他本意想要达到的目的。也并不因为事非出于本意，就对社会有害。他追求自己的利益，往往使他追求自己的利益，往往使他能比真正出于本意的情况下更有效地促进社会的利益他能比真正出于本意的情况下更有效地促进社会的利益”“我们每天所需的食物和饮料，不是出自屠户、酒家或面包师的我们每天所需的食物和饮料，不是出自屠户、酒家或面包师的恩惠，而是出于他们自利的打算恩惠，而是出于他们自利的打算”；“我们不能借着向肉贩、啤酒商、或面包师傅诉诸兄弟之情而获得免费的晚餐，相反的我们必须诉诸于他们自身的利益。我们填饱肚子的方式，并非诉诸于我们
33、填饱肚子的方式，并非诉诸于他们的慈善之心，而是诉诸于他们的自私。他们的慈善之心，而是诉诸于他们的自私。我们不会向他们诉诸我们的处境为何，相反的我们会诉诸于他们的获利”看不见的手：韩非子的表述“人为婴儿也，父母养之简，子长而怨；子盛壮成人，其供养薄，父母怒而诮之。子、父，至亲也，而或谯或怨者，皆挟相为而不周于为己也。夫卖庸而播耕者，主人费家而美食，调布而求易钱者，非爱庸客也，曰：如是，耕者且深，耨者熟耘也。庸客致力而疾耘耕者，尽巧而正畦陌者，非爱主人也，曰：如是，羹且美，钱布且易云也。此其养功力，有父子之泽矣，而此其养功力，有父子之泽矣，而心调于用者，皆挟自为心也。故人行事施予，以利之为心，则心
34、调于用者，皆挟自为心也。故人行事施予，以利之为心，则越人易和；以害之为心，则父子离且怨越人易和；以害之为心，则父子离且怨”-外储说左上“故明主之治国也，适其时事以致财物，论其税赋以均贫富，厚其爵禄以尽贤能，重其刑罚以禁奸邪。使民以力得富，以过受罪，以力得富，以过受罪，以功致赏，而不念慈惠之赐以功致赏，而不念慈惠之赐。此帝王之政也。”-六反Underlying AssumptionsFor the first theorem to hold,there are several implicit assumptions:No externality or public goods No monop
35、oly power in setting prices No asymmetric information:markets can be missing due to the asymmetric informationEquity and EfficiencyAlthough there are many efficient allocations,some may be more fair than othersThe difficult question is,what is the most equitable allocation?We can show that there is
36、no reason to believe that efficient allocation from competitive markets will give an equitable allocationThe Utility Possibilities FrontierFrom the Edgeworth Box,we showed a two person exchangeThe utility possibilities frontierrepresents all allocations that are efficient in terms of the utility lev
37、els of the two individuals Shows the levels of satisfaction that are achieved when the two individuals have reached the contract curveThe Utility Possibilities FrontierJames UtilityKarens UtilityEFGOKLOJHOJ James has zero utilityOK Karen has zero utilityE,F,G points on contract curveH inefficient ca
38、n do better in shaded areaL-unobtainableThe Utility Possibilities FrontierFrom previous example,one can see that an inefficient allocation might be more equitable than an efficient oneBut how do we define an equitable allocation?It depends on what we believe equity to entail Requires interpersonal c
39、omparisons of utilitySocial Welfare FunctionsWeights are often applied to individuals utility to determine what is socially desirable How these weights are applied comes from the social welfare functionsThe utilitarian function weights everyones utility to maximize utility for the whole societySocia
40、l Welfare FunctionsEach social welfare function is associated with a particular view of equitySome views of equity do not assign weights and cannot be represented by a welfare function Competitive market process is equitable because it rewards those who are most able and work hardest Believes compet
41、itive equilibrium would be most equitableSocial Welfare FunctionsThe Rawlsian view is that individuals dont know what their endowment will beRawls argues that if you dont know your own fate,you will opt for the system in which the least well-off person is treated reasonably wellThe most equitable al
42、location maximizes the utility of the least well-off person in societySocial Welfare FunctionsAn egalitarian view believes that goods should be equally shared by all individuals in societyCould have situation where more productive people are rewarded,thereby producing more goods and then having more
43、 to reallocate to all of societyFour Views of EquityEgalitarianAll members of society receive equal amount of goodsRawlsianMaximize the utility of the least-well-off personUtilitarianMaximize the total utility of all members of societyMarket-OrientedThe market outcome is the most equitableEquity and
44、 Perfect CompetitionA competitive equilibrium can occur at any point on the contract curve depending on the initial allocationSince not all competitive equilibria are equitable,we rely on the government to help reach equity by redistributing income Taxes Public servicesEfficiency and EquilibriumMust
45、 a society that wants to be more equitable necessarily operate in an inefficient world?Second Theorem of Welfare EconomicsIf individual preferences are convex,then every efficient allocation(every point on the contract curve)is a competitive equilibrium for some initial allocation of goodsEfficiency
46、 and EquilibriumPrice Line0K0JCAPPUJUKWWhy Are Convex Preferences?Price Line0K0JCAPPUKWUJImplications of the Second TheoremThe problem of distribution and efficiency can be separatedPrices play two roles in the market system:allocative vs.distributiveThe allocative role of prices is to reflect relat
47、ive scarcity while the distributive role is to determine the values of the endowmentsLet prices allocate resources and government redistribute wealth or income using(lump-sum)subsidy or taxesDont mix up these two rolesChapter 14General Equilibrium with ProductionAnnouncementProblem set 5 due on June
48、 11The Robinson Crusoe EconomyThis economy is characterized by one consumer,one firm,and two goodsRobinson Crusoe plays a dual role:consumer plus producerHe can spend time loafing on the beach by consuming leisure or gathering coconutsHow to allocate time on consumption and production?Leisure vs.Pro
49、ductionlaborCoconuts*L*cProductionfunctionExtended Robinson Crusoe EconomyConsider two marketsa labor market and a coconut market at the same timeCrusoe has multiple roles:Shareholder of the firm who collects profits Consumer who decides how much to consume Worker who decides how much labor to suppl
50、y Producer who decides the employment and productionThe Firm:Profit-maxlaborCoconuts*L*cProductionfunction*Isoprofitline0=c-wLc=f(L)Consumers ProblemlaborCoconuts*L*c*C=+wLBudget lineConsumers ProblemwLpcLwLLwpctsLLcuMax*)(.),(_Putting Them TogetherlaborCoconuts*L*cProductionfunction*Budget lineEffi