1、Excess DemandDecentralis-ationand TradeA many-person economyRobinson Crusoes ProblemExcess DemandDecentralis-ationand TradeRobinson Crusoes ProblemGeneral EquilibriumWhy price-taking?Why price-taking?Overview.lTheres only one economic actorlTherefore there can be no interactionlPrices are either exo
2、genous(from the mainland?the world?Mars?)or hypotheticalWhy is Robinson Crusoe so boring?lMany actors in the economy.l.and the possibility of their interaction.lThe endogenisation of prices in the economy.lBut what do we mean by an economy.?we need this to give meaning to equilibriumOnward from Crus
3、oe.These encapsulate almost all the steps in the course so farresource stockstechnologypeoples tastesThree major componentsnResourcesnh of thesenHouseholds(preferences)U1,U2,.nFirms(technologies)F1,F2,.nf of thesen of theseR1,R2,.What is an economy?General equilibriumRobinsonCrusoesproblemDecentrali
4、-sation andTradeA many-person EconomyWhy price-taking?Excess demandIncomesEquilibriumIncomesAllocationsEquilibriumA many-person economyof consumption basketsfor each household.Think of this as two collections.and of net outputs for each firm.like this.x1,x2,x3,.y1,y2,y3,.The state of an economy is d
5、escribed by an allocation.Formally,an allocation is.nA collection of bundles(one for each household)nA collection of net-output vectors(one for each firm)nA set of prices(used by households and firms)pxhyfprofit-maximisingutility-maximising.and a competitive allocation is.p yf(p)(profit maximisation
6、)yf(p):f=1,2,.,nfEach firms behavioural response maps prices into net outputsp,Mhxh(p)(utilitymaximisation)xh(p):h=1,2,.,nhEach households behavioural response maps prices and incomes into demandsThe allocation ajust a minute!where dothese incomes come from?How does a competitive allocation work?Gen
7、eral equilibriumRobinsonCrusoesproblemDecentrali-sation andTradeA many-person EconomyWhy price-taking?Excess demandIncomesEquilibriumAllocationsAllocationsEquilibriumA many-person economyownershiprights ofeverythingon the island Where did R.Crusoes income come from.?nResourcesR1h,R2h,.V1h,V2h,.nShar
8、es infirms profitsSo what does household h possess?0Vfh1 Rih0nResourcesnShares in firmsnNet outputsnPricesProfitsRentsThe components of incomelets look atthe role ofpricesIncomesNet outputs depend on prices.yif =yif(p)(supply of net outputs)P f(p):=S pi yif(p)n i=1directlyindirectlyAnd so profits de
9、pend on prices.and Incomes=resource rents+profits Mh=S pi Rih+S Vfh P f(p)n nf i=1 f=1P f(p):=S pi yif(p)n i=1Mh=Mh(p).so incomes depend on pricesProfits are a function of prices.yf(p):f=1,2,.,nfxh(p):h=1,2,.,nhSo,take the allocation as a collection of responses.pp,MhThe allocation a.and substitute
10、the price-income relation into household responses.p.which implies:Mh=Mh(p)yf(p)xh(p)The allocation apLets look at the whole process.Written more simply.dR1a,R2a,.R1b,R2b,.V1a,V2a,.V1b,V2b,.Propertydistributionm resource distribution m share ownershipCompetitive system takes as given.and through the
11、 price mechanismdresource distributionshare ownershippriceshousehold incomesaconsumption bundlesnet output vectors.determines an allocationd apricesa summary of the processGeneral equilibriumRobinsonCrusoesproblemDecentrali-sation andTradeA many-person EconomyWhy price-taking?Excess demandIncomesEqu
12、ilibriumAllocationsAllocationsIncomesA many-person economyCrusoe again.lMust be utility-maximising(consumption).l.profit-maximising(production).l.and satisfy materials balance(the facts of life)OK,lets do this for the many-person case.What kind of allocation is an equilibrium?for each householdsubje
13、ct toUh(xh)maxS pi xih Mhn i=1subject toFf(yf)0maxS pi yifn i=1for each firmxi yi+Riand for each good.But what determines these aggregates?The basics of competitive equilibriumCan we add upacross households like this.?S S xih=xinh h=1Yes if i is a rival goodCounterexamples:goods like TV,national def
14、ence.Aggregate consumption of good i.?S S yif=:yinf f=1definitionif all the yfare feasible willy be feasible?Yes if thereare no productionexternalitiesCounterexample:production withcongestion.Aggregate net outputlAssume incomes are determined privately lall goods are rival commoditieslThere are no e
15、xternalitiesTo make life simple:(a)nIt must be a competitive allocationx y+RnThe materials balance condition must holdCompetitive equilibrium:a summarylExchange economy(no production)l2 traders(Alf,Bill)l2 GoodsAn exampleresourceendowmentconsumptionutilityUa(x1a,x2a)(x1a,x2a)(R1a,R2a)Alf sells some
16、of his endowment of 2 forgood 1 by trading with.A description of Alf.Bill,of course,sells good 1 in exchange for 2Ub(x1b,x2b)(x1b,x2b)(R1b,R2b)resourceendowmentconsumptionutility.Billx1aR1aR2ax2aOaAlfs optimisation problemIncreasing preferenceAlfs budget constraintl endowment point l Bills budget co
17、nstraintx1bR1bR2bx2bObl Increasing preferenceBills optimisation probleml endowment point Dx2aOax1al n E equilibriumendowmentThe equilibrium of Alfx1bR1bR2bx2bObl n E equilibriumendowmentDThe equilibrium of Billx1bR1bR2bx2bObl n E DFlipped.R1bR2bObx2bx1bl n E DFlipped.to give the Edgeworth BoxDEx2bOb
18、x1bx2aOax1aR1a+R1bR2a+R2bThe size of the Edgeworth BoxDEx1ax2ax2bx1bObOaendowmentcompetition takes Alf&Bill from here.l EDx1ax2ax2bx1bObOaequilibrium.to here.n EDx1ax2ax2bx1bObOaIncomes in the distributionmatch expenditures in the allocationThe role of prices is central.The Crusoe equilibrium story
19、translates to a many-person economy.Role of prices in allocations and equilibrium is crucial.Equilibrium depends on distribution of endowments.Main features are in the model of Alf and Bill.But,why,why,why do these guys just accept the going prices.?thats for next time.Alf and Bill as a microcosm.2020/11/543谢谢观赏！
