General equilibrium theory
In 1874, French economist Léon Walras published Elements of Pure Economics. This work marked the first serious attempt to model prices for an entire economy simultaneously. Walras constructed a series of models that added complexity with each iteration. He began with two commodities and expanded to many commodities, then included production and growth. Later he introduced money into his framework. Some scholars argue these later models were inconsistent with earlier ones. Walras assumed capital goods quantities were fixed in arbitrary ratios while their prices remained equal across all industries. This created tension between long-run price assumptions and short-run quantity data. His research program asked when equilibria would be unique or stable. Lesson 7 of his book showed neither uniqueness nor stability was guaranteed. Walras proposed a dynamic process called tâtonnement to reach equilibrium. Prices announced by an auctioneer triggered supply and demand responses. No actual transactions occurred at disequilibrium prices. The auctioneer adjusted prices downward for goods with excess supply and upward for those with excess demand. Mathematicians still debate whether this process always terminates in true equilibrium.
Kenneth Arrow, Gérard Debreu, and Lionel W. McKenzie developed the modern version of general equilibrium theory during the 1950s. Debreu presented this model in Theory of Value published in 1959. They followed mathematical styles promoted by Nicolas Bourbaki using axiomatic methods. Three interpretations emerged for how commodities functioned within the system. First, goods could be distinguished by delivery location creating spatial trade models. Second, commodities could be differentiated by delivery time forming intertemporal markets. Third, contracts specified states of nature affecting conditional transfers without probability concepts. These interpretations combined into complete sets of prices for complex contracts like winter wheat delivered in January if hurricanes struck Florida in December. Such complete market systems seemed distant from real economies yet remained useful guides. Recent work explored incomplete markets where uncertainty prevents full wealth allocation across time periods. Economies lacking adequate means to transfer wealth through risky futures may fail Pareto optimality. Inefficiency might result from underdeveloped financial institutions or credit constraints facing public members. Research continues examining these implications today.
The First Fundamental Welfare Theorem asserts that market equilibria achieve Pareto efficiency. No reallocation leaves one consumer better off without harming another. A sufficient condition requires preferences to be locally nonsatiated in pure exchange economies. This theorem holds even with production regardless of production function properties. Implicitly it assumes complete markets and perfect information. Externalities can create inefficient equilibria despite this rule. When equilibria arise that are not efficient, market failure rather than the system itself bears blame. The Second Fundamental Welfare Theorem states every Pareto efficient allocation can support as an equilibrium through price adjustments. All required is redistribution of initial endowments after which markets operate freely. Efficiency and equity issues separate without trade-offs. Conditions for the second theorem prove stronger than those for the first. Consumers' preferences and production sets must now exhibit convexity. Convexity roughly corresponds to diminishing marginal rates of substitution meaning averages outperform extremes. These theorems inform sources of inefficiency but do not guarantee existence of any equilibrium at all.
Proofs of equilibrium existence traditionally rely on fixed-point theorems like Brouwer or Kakutani. Lionel McKenzie and Kenneth Arrow developed these proofs alongside Gérard Debreu. Uzawa derived Brouwer's theorem from Walras's law making existence a deeper result than welfare theorems. Global analysis methods using Sard's lemma and Baire category theorem were pioneered by Debreu and Stephen Smale. Sonnenschein-Mantel-Debreu results proven in the 1970s show aggregate excess demand functions inherit only continuity homogeneity degree zero Walras law and boundary behavior properties. Any such function represents rational utility-maximizing individuals. Equilibrium uniqueness requires much stronger conditions than mere existence. Under mild assumptions equilibria remain finite and odd according to index theorems. Revealed preference property or gross substitute property ensure unique outcomes. Michael Mandler challenged claims that most economies are regular in 1999 work. Indeterminacy undermines price-taking assumptions since arbitrary factor supply manipulations dramatically increase prices. Factor owners will not treat prices as parametric when indeterminacy exists. Stability depends on adjustment processes guiding price changes beyond simple equilibrium counts. Some researchers focus on plausible processes guaranteeing convergence despite multiple stable equilibria where starting points determine final allocations.
Friedrich Hayek published The Use of Knowledge in Society essay in 1945 articulating fundamental challenges to general equilibrium informational assumptions. He argued economic knowledge disperses across countless individuals existing tacitly context-specific forms unaggregatable or centralizable. This posed problems for models presuming complete information gathering capabilities. Hayek proposed market prices serve decentralized signals distilling complex local preferences resources opportunities into summary statistics coordinating decisions without centralized direction. While predating full Arrow-Debreu formalization his essay interpreted subsequent economists both as critique feasibility limitations perfect-information equilibrium models explanations real-world coordination mechanisms despite pervasive ignorance uncertainty. Perspectives emphasize economic processes discovery over static equilibrium states. Critics hold necessary assumptions include perfect rationality complete information about all prices now and future conditions required perfect competition. Experimental economics suggests even few imperfectly informed agents produce prices resembling perfectly competitive markets though certainly not stable general equilibrium across all markets. Frank Hahn defends modeling providing negative function showing economy requirements for unregulated Pareto efficiency.
Until the 1970s general equilibrium analysis remained purely theoretical. Advances in computing power combined with input-output tables enabled national world economy modeling attempts solving equilibrium prices quantities empirically. Herbert Scarf pioneered Applied General Equilibrium models in 1967 offering numerical solution methods for Arrow-Debreu systems. John Shoven and John Whalley implemented these first at Yale during 1972 and 1973 becoming popular through that decade. AGE models faded popularity mid-1980s unable provide precise solutions high computation costs. Computable General Equilibrium models surpassed them replacing AGE frameworks by mid-1980s. CGE provided relatively quick large computable whole-economy models preferred by governments World Bank. These heavily used today while AGE and CGE terms interchanged literature Scarf-type AGE constructions ceased after mid-1980s current CGE literature not based on Arrow-Debreu discussed here. Instead they rely static simultaneously solved macro balancing equations from standard Keynesian models giving precise explicitly computable results.
General equilibrium theory remains central contention between neoclassical school other economic thought schools varying views. Keynesian Post-Keynesian economists strongly reject it as misleading useless arguing economies never reach equilibrium slow painful achievement possible resulting theory guide particularly understanding economic crises. Robert Clower argued reformulation toward disequilibrium analysis incorporating monetary exchange fundamentally altering barter system representation. Jean-Pascal Bénassy developed Non-Walrasian Equilibria Money Macroeconomics Handbook chapters covering non-clearing markets microeconomic concepts macroeconomic applications. New classical macroeconomics builds macroeconomic theory on general equilibrium bases assuming unique equilibrium full employment potential output always achieved via price wage adjustment market clearing. Real business-cycle theory considers business cycles largely real economy changes unemployment due to equilibrium potential output fallen rather than market failure achieving potential output. Socialist economics critiques given Anti-Equilibrium based János Kornai Communist central planning failures though Michael Albert Robin Hahnel later based Parecon model same theory. Structural equilibrium matrix-form Computable General Equilibrium new structural economics extends John von Neumann's model using R package GE enabling intertemporal analysis time labels differentiating commodity firm types including taxes money endogenous production functions institutions excess tax burdens potentially non-Pareto optimal equilibria.
Common questions
When did Léon Walras publish Elements of Pure Economics?
Léon Walras published Elements of Pure Economics in 1874. This work marked the first serious attempt to model prices for an entire economy simultaneously.
Who developed the modern version of general equilibrium theory during the 1950s?
Kenneth Arrow, Gérard Debreu, and Lionel W. McKenzie developed the modern version of general equilibrium theory during the 1950s. Debreu presented this model in Theory of Value published on the 2nd of May 1959.
What does the First Fundamental Welfare Theorem assert about market equilibria?
The First Fundamental Welfare Theorem asserts that market equilibria achieve Pareto efficiency. No reallocation leaves one consumer better off without harming another.
Why did Herbert Scarf pioneer Applied General Equilibrium models in 1967?
Herbert Scarf pioneered Applied General Equilibrium models in 1967 offering numerical solution methods for Arrow-Debreu systems. Advances in computing power combined with input-output tables enabled national world economy modeling attempts solving equilibrium prices quantities empirically.
How do Computable General Equilibrium models differ from AGE frameworks after the mid-1980s?
Computable General Equilibrium models surpassed AGE frameworks by replacing them in the mid-1980s. These models rely on static simultaneously solved macro balancing equations from standard Keynesian models giving precise explicitly computable results.
All sources
37 references cited across the entry
- 1bookThe New Palgrave Dictionary of EconomicsLionel W. McKenzie — 2008
- 2bookElements of Pure EconomicsLéon Walras — Irwin — 1954
- 3journalThe Use of Knowledge in SocietyF. A. Hayek — 1945
- 5bookThe New Palgrave: A Dictionary of EconomicsJohn Eatwell — Macmillan — 1987
- 6journalWalras's Theory of Capital Formation in the Framework of his Theory of General EquilibriumWilliam Jaffe — 1953
- 7journalLosing Equilibrium: On the Existence of Abraham Wald's Fixed-Point Proof of 1935Till ((Düppe)) et al.
- 8bookGeneral Equilibrium Analysis: Studies in AppraisalE. Roy Weintraub — Cambridge University Press — 1985
- 9journalThe Existence of an Equilibrium for a Competitive EconomyK. J. Arrow et al. — 1954
- 10journalOn the Existence of General Equilibrium for a Competitive EconomyLionel W. McKenzie — 1959
- 11bookTheory of ValueG. Debreu — Wiley — 1959
- 12journalOn Equilibrium in Graham's Model of World Trade and Other Competitive SystemsLionel W. McKenzie — 1954
- 13journalExistence of an equilibrium for a competitive economyK. J. Arrow et al. — 1954
- 14journalWalras' Existence Theorem and Brouwer's Fixed-Point TheoremHirofumi Uzawa — 1962
- 15journalQuasi-equilibria in markets with non-convex preferencesRoss M. Starr — 1969
- 16bookContributions to Operations Research and Economics: The twentieth anniversary of CORE (Papers from the symposium held in Louvain-la-Neuve, January 1987)Roger Guesnerie — MIT Press — 1989
- 17bookGeneral Competitive AnalysisKenneth J. Arrow et al. — Holden-Day North-Holland — 1971
- 18bookThe Theory of General Economic Equilibrium: A Differentiable ApproachAndreu Mas-Colell — Cambridge University Press — 1985
- 19bookCore and Equilibria of a Large EconomyWerner Hildenbrand — Princeton University Press — 1974
- 20bookMicroeconomics of market failuresBernard Salanié — MIT Press — 2000
- 21bookFundamentals of Public EconomicsJean-Jacques Laffont — MIT — 1988
- 22journalRecent Advances on Uniqueness of Competitive EquilibriumAlexis Akira Toda et al. — 2024
- 23bookDilemmas in Economic Theory: Persisting Foundational Problems of MicroeconomicsMichael Mandler — Oxford University Press — 1999
- 24journalThe Sonnenschein-Mantel-Debreu Results after Thirty YearsS. Abu Turab Rizvi — 2006
- 25bookGeneral Equilibrium, Capital, and Macroeconomics: A Key to Recent Controversies in Equilibrium TheoryFabio Petri — Edward Elgar — 2004
- 26journalMethods in Economic ScienceNicholas Georgescu-Roegen — 1979
- 27journalGeneral Equilibrium in an Imperfect World: Incomplete MarketsFrank Hahn — 1991
- 28journalA General Equilibrium Calculation of the Effects of Differential Taxation of Income from Capital in the U.S.J. B. Shoven et al. — 1972
- 29journalGeneral Equilibrium with Taxes: A Computational Procedure and an Existence ProofJ. B. Shoven et al. — 1973
- 30journalDebunking the Myths of Computable General Equilibrium ModelsBenjamin H. Mitra-Kahn — 2008
- 31webDebtwatch No 34: The Confidence TrickSteve Keen — May 4, 2009
- 32webDebtWatch No 29 December 2008Steve Keen — November 30, 2008
- 34bookAnti-Equilibrium: On Economic Systems Theory and the Tasks of ResearchJános Kornai — North-Holland — 1971
- 35bookThe Political Economy of Participatory EconomicsMichael Albert et al. — Princeton University Press — 1991
- 37bookGeneral Equilibrium and Structural Dynamics: Perspectives of New Structural EconomicsWu Li — Economic Science Press — 2019
- 38webCRAN: Package GE