General equilibrium
General equilibrium theory isbranchtheoretical microeconomics. It seeksexplain production, consumptionprices inwhole economy. This article considers neoclassical approachesgeneral equilibrium. Investigations intointeractionmarkets arguably outsideneoclassical theorytakenbe outsidescopethis article. In particular, ClassicalMarxist analysesnatural prices or pricesproduction, Wassily Leontief's Input-Output analysis,John von Neumann's Linear Programming modelgrowthnot otherwise discussed.General equilibrium triesgive an understanding ofwhole economy usingbottom-up approach, startingindividual marketsagents. Macroeconomics, as developed by so-called Keynesian economists, usestop-down approach whereanalysis startslarger aggregates. Since modern macroeconomics has emphasized microeconomic foundations, this distinction has been slightly blurred. However, many macroeconomic models simply have'goods market'study its interaction withinstancefinancial market. General equilibrium models typically modelmultitudedifferent goods markets. Modern general equilibrium modelstypically complexrequire computershelpnumerical solutions.
Under capitalism,pricesproductionall goodsinterrelated. A change inpriceone good, say bread, may affect another price,example,wagesbakers. If bakers differtastes from others,demandbread might be affected bychangebakers' wages, withconsequent effect onpricebread. Calculatingequilibrium pricejust one good,theory, requires an analysis that accountsall ofmillionsdifferent goods thatavailable.
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2 Modern Conceptgeneral equilibriumeconomics 3 Unresolved problemsgeneral equilibrium |
HistoryGeneral Equilibrium Modeling
The first attemptNeoclassical economicsmodel prices forwhole economy was made by Leon Walras. Walras' ElementsPure Economics providessuccessionmodels, each taking into account more aspects ofreal economy (two commodities, many commodities, production, growth, money). Many think Walras was unsuccessful andlater modelsthis series inconsistent. Nevertheless, Walras first laid downresearch program much followed by 20th century economists. In particular, Walras' agenda includedinvestigationwhen equilibriauniquestable.
Walras also first introducedrestriction into general equilibrium theory that some think has never been overcome, that oftatonnement or groping process. The tatonnement process istoolinvestigating stabilityequilibria. Pricescried,agents register how mucheach goodwould like to offer (supply) or purchase (demand). No transactionsno production take place at disequilibrium prices. Instead, pricesloweredgoods with positive pricesexcess supply. Pricesraisedgoods with excess demand. The question formathematicianunder what conditions suchprocess will terminateequilibriumwhich demand equates to supplygoodspositive pricesdemand does not exceed supply for goods withpricezero. Walras was not ableprovidedefinitive answerthis question.
In partial equilibrium analysis,determination ofprice ofgoodsimplified by just looking atpriceone good,assuming thatpricesall other goods remain constant. The Marshallian theorysupplydemandan examplepartial equilibrium analysis. Partial equilibrium analysisadequate whenfirst-order effects ofshift in, say,demand curve do not shiftsupply curve. Anglo-American economists became more interestedgeneral equilibrium inlate 1920s1930s after Piero Sraffa's demonstration that Marshallian economists cannot accountthe forces thoughtaccount forupward-slope ofsupply curvea consumer good.
If an industry uses little offactorproduction,small increase in the outputthat industry will not bidpricethat factor up. To a first order approximation, firms inindustry will not experience decreasing costs andindustry supply curves will not slope up. If an uses an appreciable amountthat factorproduction, an increase inoutputthat industry will exhibit increasing costs. But such a factorlikelybe usedsubstitutes forindustry's product, and an increased pricethat factor will have effects onsupply of those substitutes. Consequently,first order effects ofshift insupply curve oforiginal industry under these assumptions includeshift inoriginal industry's demand curve. General equilibriumdesignedinvestigate such interactions between markets.
Continential European economists made important advances in1930s. Walras' proofs ofexistencegeneral equilibrium often were based oncountingequationsvariables. Such arguments are inadequatenon-linear systemsequationsdo not imply that equilibrium pricesquantities cannot be negative,meaningless solutionhis models. The replacementcertain equations by inequalities andusemore rigorous mathematics improved general equilibrium modeling.
Modern Conceptgeneral equilibriumeconomics
The modern conceptiongeneral equilibriumprovided by a model developed jointly by Kenneth ArrowGerard Debreu in1950s. Gerard Debreu presents this modelTheoryValue (1959) as an axiomatic model, following the stylemathematics promoted by Bourbaki. In such an approach, the interpretation ofterms intheory (e.g., goods, prices) are not fixed byaxioms.
Three important theorems have been provedthis framework. First, existence theorems show that equilibria exist under certain abstract conditions. The first fundamental theoremwelfare states that every market equilibriumPareto optimal under certain conditions. The second fundamental theoremwelfare states that every Pareto optimumsupported byprice system, again under certain conditions. These conditions were stated in language of mathematical topology. The proofs used such concepts as seperating hyperplanesfixed point theorems.
Three important interpretations ofterms oftheory have been often cited. First, supposed commoditiesdistinguished bylocation where theydelivered. ThenArrow-Debreu model isspatial model of,example, international trade.
Second, suppose commoditiesdistinguished by whenare delivered. That is, suppose all markets equilibriate at some initial instanttime. Agents inmodel purchasesell contracts, wherecontract specifies,example,good to be delivered anddate at whichisbe delivered. The Arrow-Debreu modelintertemporal equilibrium contains forward marketsall goods at all dates. No markets exist at any future dates.
Third, suppose contracts specify statesnature which affect whether or notcommodity isbe delivered: "A contract fortransfer ofcommodity now specifies,addition to its physical properties, its locationits date, an event on the occurrencewhichtransferconditional. This new definition ofcommodity allows oneobtaintheory[risk] free from any probability concept..." (Debreu 1959)
These interpretations can be combined. Socomplete Arrow-Debreu model can be saidapply when goodsidentified by when they arebe delivered, whereto be delivered,under what circumstances theyto be delivered, as well as their intrinsic nature. So there would becomplete setpricescontracts such as "1 tonWinter red wheat, delivered on 3rdJanuaryMinneapolis, if there ishurricaneFlorida during December". A general equilibrium modelcomplete marketsthis sort seemsbelong way from describingworkingsreal economies.
Unresolved problemsgeneral equilibrium
Research building onArrow-Debreu model has revealed some problemsthe model. The Sonnenschein-Mantel-Debreu results show that, essentially, any restrictions onshapeexcess demand functionsessentially arbitrary. Some think this implies thatArrow-Debreu model lacks empirical content. At any rate, Arrow-Debreu equilibria cannot be expectedbe unique, stable, or determinate.
A model organized aroundtatonnnement process has been saidbe a model ofcentrally planned economy, notdecentralized market economy. Some research has tried, not very successfully,develop general equibrium modelsother processes. In particular, some economists have developed modelswhich agents can trade at out-of-equilibrium pricessuch trades can affectequilibriawhicheconomy tends. Particularly noteworthy areHahn process,Edgeworth process, andFisher process.
The Arrow-Debreu modelintertemporal equilibrium,which forward markets exist atinitial instantgoodsbe delivered at each future pointtime, can be transformed intomodelsequences of temporary equilibrium. Sequencestemporary equilibrium contain spot markets at each pointtime. Roy Radner found thatorder for equilibriaexistsuch models, agents (e.g., firms and consumers) must have unlimited computational capabilities.
AlthoughArrow-Debreu modelset outtermssome arbitrary numeraire,model does not encompass money. Frank Hahn, for example, has investigated whether general equilibrium models can be developedwhich money enterssome essential way. The (unsatisfied) goal isfind modelswhich whether or not money exists alters equilibrium solutions, perhaps because the initial positionagents depends on monetary prices,example, whenhave debts.
Some criticsgeneral equilibrium modeling contend that much researchthese models constitutes exercisespure matheamtics with no connectionactual economies. "Thereendeavors that now pass formost desirable kind of economic contributions although theyjust plain mathematical exercises, not only without any economic substance but also without any mathematical value" (Nicholas Georgescu-Roegen 1979). Georescu-Roegen cites as an examplepaper that assumed more traders than therepoints onreal line.
Although modern modelsgeneral equilibrium theory demonstrate that under certain circumstances prices will indeed convergeequilibria, critics hold thatassumptions necessarythese resultscompletely unrealistic. The necessary assumptions include perfect rationalityindividuals; complete information about all prices both nowinfuture; andconditions necessaryperfect competition.
Frank Hahn defends general equilibrium modeling ongrounds that it providesnegative function. General equilibrium models show what the economy would havebe likean unregulated economybe Pareto efficient. Note that Hahn's defense drops any claim that general equilibrium models describe actual capitalist economies.
Some economists reject equilibrium theory outrightfavourmore pragmatic models based more closely on observation ofeconomy.
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