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Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Microeconomics,General Equilibrium: price taking,Excess Demand,Decentralis-ation,and Trade,A many-person economy,Robinson Crusoes Problem,Excess Demand,Decentralis-ation,and Trade,Robinson Crusoes Problem,General Equilibrium,Why price-taking?,A many-person economy,Overview.,So far weve focused on competitive equilibrium analysis. But why?,Why concentrate on,equilibrium?,Why assume competitive behaviour?,Lets start by having another look at the,exchange economy.,Well redraw the Edgeworth box,Some puzzles in competitive equilibrium analysis,General equilibrium,Robinson,Crusoes,problem,Decentrali-,sation and,Trade,A many-person Economy,Why price-taking?,Excess demand,The solution concept,Prices and the Core,The solution concept,An exchange economy,Prices and the Core,Why price-taking?,D,E,O,a,x,2,a,x,1,a,D,E,x,1,a,x,2,a,x,1,b,O,b,O,a,D,E,x,2,b,x,1,b,O,b,What would I do out of equilibrium?,And what would he do?,Lets look at the inner workings.,Building an Edgeworth box,x,1,a,R,1,a,R,2,a,x,2,a,O,a,The situation from Alfs point of view,How Alf responds as,p,1,/,p,2,changes.,x,1,a,R,1,a,R,2,a,x,2,a,O,a,Alfs offer curve,What about Bill?,x,1,b,R,1,b,R,2,b,x,2,b,O,b,The situation from his point of view,.,as an Australian,x,1,b,R,1,b,R,2,b,x,2,b,O,b,How Bill responds as,p,1,/,p,2,changes.,x,1,b,R,1,b,R,2,b,x,2,b,O,b,Bills offer curve,The two offer curves,1,x,2,b,O,b,x,1,a,x,2,a,O,a,x,1,b,R,1,b,R,1,a,R,2,a,R,2,b,Offers are only consistent where curves intersect,But, by construction.,This is the competitive equilibrium,Satisfies materials balance,E,D,equilibrium,here,endowment,here,Price-taking utility-maximising Bill,endowment,here,equilibrium,here,Price-taking utility-maximising Alf,But why competitive behaviour?,Why should Alf and Bill behave that way?,Where do the prices come from?,Given competitive behaviour, the CE is the only consistent allocation,subject to,h h,S,p,i,x,i,M,i,=1,U,(,x,),max,n h h,S,p,i,x,i,M,So where do the prices come from?,We need a more general solution concept,Then examine how price-taking equilibrium relates to this.,Lets develop the approach for the exchange economy, though it could apply to more interesting economies.,A fresh approach,General equilibrium,Robinson,Crusoes,problem,Decentrali-,sation and,Trade,A many-person Economy,Why price-taking?,Excess demand,The solution concept,Prices and the Core,An exchange economy,Prices and the Core,An exchange economy,Why price-taking?,View the population.,Q,2,Q,1,.,as,n,separate individuals,Q,0,A coalition.,The coalition concept gives us an important clue,.,.,is formed by any subgroup,weve got our endowments with us,One day you take your bundle along to the swap shop.,.and some bossy person is there who proposes (insists on?) a particular feasible allocation,.,You and some others dont like the,x,bundle you would get under this allocation,.,.and you find that by using just the resources you all own you could all get a utility level at least as high as that offered to you under the proposed allocation,.,You guys therefore refuse to accept it.,your coalition has,blocked,the proposed allocation,The idea of,blocking,: a little story,An allocation is,blocked,.,Q,2,x,b,x,c,x,d,x,a,x,e,x,f,x,g,x,l,x,k,.,which can do better for itself,if we can find a coalition.,A proposed allocation for the,whole economy,h h,U,(,x,),h h,U,(,x,),.,and that are feasible,Q ,1,2,.,n,h,h,x, is,blocked,by,Q,h,Q, for some,h,h,Q,h,S,x,h,S,R,h,Q,A coalition,Bundles that are preferred by members of the coalition.,h,x,A formal approach,The Core,is the set of unblocked, feasible allocations,Use the idea of blocking to introduce a basic solution concept,Alf & Bill,Alf,Bill,In a 2-person world there are very few coalitions possible,Use the Edgeworth box.,x,2,b,O,b,x,1,a,x,2,a,O,a,x,1,b,.,to get the,contract curve,Alf blocks these allocations.,D,Bill blocks these allocations.,Alf, Bill (together) block these.,Endowment,No-one can block an allocation here,The 2-person core,General equilibrium,Robinson,Crusoes,problem,Decentrali-,sation and,Trade,A many-person Economy,Why price-taking?,Excess demand,The solution concept,Prices and the Core,An exchange economy,The solution concept,An exchange economy,Why price-taking?,x,2,b,O,b,x,1,a,x,2,a,O,a,x,1,b,D,E,The competitive equilibrium again,x,2,b,O,b,x,1,a,x,2,a,O,a,x,1,b,D,E,Any competitive equilibrium must lie in the core,Every CE allocation must belong to the core,Of course it is possible that no CE exists (see next lecture),But what of other core allocations which are,not,CE?,Lets take a close-up look,A simple result,D,B,Alf,Bill,Alf,Bill,A,The extremes of the 2-person core,Core,CE,Introducing Alf and Bills long-lost twin brothers.,Remember we are dealing with a 2-person model,But will there always be non-CE points in the core?,A basic relation.,Alf and his twin brother Arthur have the same preferences and endowments,Likewise the twins Bill and Ben,Now of course there are more possibilities of forming coalitions,So lets,clone,the economy,Arthur & Ben,Arthur,Ben,Alf & Arthur,etc, etc,Bill&Ben,Alf & Bill,Alf,Bill,Alf, Arthur &Bill,.,plus some new ones,All the old coalitions are possible.,Will these still be core allocations in the 4-person economy?,B,A,Alf n Arthur,Bill n Ben,Alf n Arthur,Bill n Ben,D,Alf, Arthur,Ben,Bill,G,.,leaving the Ben twin outside the coalition,This allocation is not a,solution,.,But it shows that the core has become smaller,No. Alf-Arthur-Bill can block A.,Alf ,x,a,+,R,a, (G),Arthur,x,a,+,R,a, (G),Bill,x,b,(A),Ben,R,b,(D),2,R,a,+,R,b,The coalition,Feasible,How the blocking coalition works,A,B,D,Can this allocation be blocked?,An A-person would be better off somewhere here,Bingo!,What if there were 500 of each type.?,500,of the A tribe,450,of the B tribe,500,of the A tribe,400,of the B tribe,500,of the A tribe,360,of the B tribe,500,of the A tribe,310,of the B tribe,500,of the A tribe,250,of the B tribe,If,N,is bigger there may be more blocking coalitions,A,B,D,E,The only allocation left in the 2,N-,person core (eventually).,As you clone the economy the core becomes smaller.,In the limit it contains,only,competitive equilibrium allocations.,But notice that this requires balanced replication of the Alf and Bill tribes,And it assumes that all these various coalitions are somehow relevant,A powerful result: the shrinking core,Endowments,Preferences,Allocations,Coalitions,Blocking,Answer to question: why price-taking?,In a large economy with suitably small agents.,.its the only thing to do.,A final reminder: Basic conceptsof the core,Aggregating firms,Aggregating consumers,WARP,Properties of demand systems,The Separation Theorem,Firm #4 slides 18-26,Consumer #4 slides 39-44,Consumer #1 slides 23.24,Consumer #3 slides 5,6,Gen Eqm #2 slides 14-20,24,25,.,演讲完毕，谢谢观看！,内容总结,Microeconomics。A many-person Economy。.as an Australian。Bills offer curve。But, by construction.。View the population.。.as n separate individuals。.and that are feasible。A formal approach。Alf & Bill。Use the Edgeworth box.。Bill blocks these allocations.。Alf, Bill (together) block these.。Lets take a close-up look。A basic relation.。Alf, Arthur &Bill。The Separation Theorem。演讲完毕，谢谢观看,
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