伦敦经济学院高微讲义-一般均衡.ppt

Microeconomics,General Equilibrium: price taking,Excess Demand,Decentralis-ation and Trade,A many-person economy,,,Robinson Crusoe's Problem,Excess Demand,Decentralis-ation and Trade,Robinson Crusoe's Problem,,General Equilibrium,Why price-taking?,A many-person economy,,Overview.,So far we've focused on competitive equilibrium analysis. But why? Why concentrate on equilibrium? Why assume competitive behaviour? Let's start by having another look at the exchange economy. We'll redraw the Edgeworth box,Some puzzles in competitive equilibrium analysis,,,,General equilibrium,,Robinson Crusoe’s 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?,,What would I do out of equilibrium? And what would he do?,Let's look at the inner workings.,Building an Edgeworth box,,,,x1a,R1a,R2a,x2a,Oa,,The situation from Alf's point of view,How Alf responds as p1/p2 changes.,,,,,,x1a,,,,,,,,,,,,,,,,,,,,R1a,R2a,x2a,Oa,,,,,,,,,,,,Alf's offer curve,What about Bill?,,,,,,x1b,R1b,R2b,x2b,Ob,,The situation from his point of view,.as an Australian,,,,,,,,,,x1b,R1b,R2b,x2b,Ob,,How Bill responds as p1/p2 changes.,,,,,,,,,,,,,,,,,,,,,,,,,x1b,R1b,R2b,x2b,Ob,,,,,,,,,,,,Bill's offer curve,,,,,,,,,The two offer curves,1,x2b,Ob,,,x1a,x2a,Oa,x1b,,R1b,R1a,R2a,R2b,Offers are only consistent where curves intersect,But, by construction.,,This is the competitive equilibrium,,Satisfies materials balance,E,D,Price-taking utility-maximising Bill,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 pixi £ M,i=1,U (x ),max,n h h,S pixi £ M,So where do the prices come from?,We need a more general solution concept Then examine how price-taking equilibrium relates to this. Let's develop the approach for the exchange economy, though it could apply to more interesting economies.,A fresh approach,,,,General equilibrium,,Robinson Crusoe’s 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.,,.as n separate individuals,A coalition.,.is formed by any subgroup,we've 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 don't 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.,,.which can do better for itself,if we can find a coalition.,,,,,,,A proposed allocation for the whole economy,.and that are feasible,Q Í {1,2,.,nh},“hÎQ, ““ for some h,A coalition,Bundles that are preferred by members of the coalition.,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.,,,,,,,,,,,x2b,Ob,x1a,x2a,Oa,x1b,.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 Crusoe’s 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?,,,,,,,,,,,x2b,Ob,x1a,x2a,Oa,x1b,,,,,,D,E,The competitive equilibrium again,,,,,,,,,,,,,,x2b,Ob,x1a,x2a,Oa,x1b,,,,,,,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? Let's take a close-up look,A simple result,,,,,,,,,,D,The extremes of the 2-person core,,CE,,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 let's clone the economy,{Arthur & Ben},{Arthur},{Ben},{Alf & Arthur},{etc, etc},{Bill&Ben},{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,。