Landmarks in General Equilibrium Theory - A Chronology -

Contents

• 1870s
• 1880s
• 1890s
• 1900s
• 1910s
• 1920s
• 1930s
• 1940s
• 1950s
• 1960s
• 1970s
• 1980s
• 1990s

Landmarks in General Equilibrium Theory, 1870-2000

1870s - Revolution

1871 

• William Stanley Jevons introduces pure exchange economic model, achieving general equilibrium without price-taking behavior.
• Carl Menger differentiates between economic & non-economic goods.

1874 

• Léon Walras's Elements of Pure Economics - first Neoclassical "General Equilibrium" system with price-taking behavior.

1880s

1881

•  Francis Y. Edgeworth's Mathematical Psychics - introduces generalized utility functions, coalitional bargaining and the core.

1886

• Giovanni B. Antonelli identifies integrability problem; introduces indirect utility function; discusses aggregation and "representative agent".

1889

• Friedrich von Wieser introduces alternative cost and imputation theory
• Rudolf Auspitz and Richard Lieben introduce substitution and complementarity.

1890s

1892

• Irving Fisher introduces ordinal utility.

1893

• Knut Wicksell's synthesis of Austrian and Walrasian theories.

1894

• Philip H. Wicksteed introduces marginal productivity theory of distribution.

1896 

• Vilfredo Pareto's Cours d'economie politique - introduction of profit-maximization, choice-theoretic demand, etc.
• Enrico Barone introduces variable production coefficients into Walras's system.

1900s

1901

• Knut Wicksell's Lectures on Political Economy, vol. I - continues Lausanne-Austrian fusion.

1906

• Vilfredo Pareto's Manual of Political Economy - develops Lausanne theory of general equilibrium.

1908

• Enrico Barone launches "socialist calculation" debate.

1910s

1913

• William E. Johnson derives demand functions from indifference curves.

1914

• Karl Schlesinger attempts to integrate money into general equilibrium theory.

• Eugen Slutsky decomposes demand into substitution and income effects

1918

• Gustav Cassel's Theory of Social Economy: resurrects Walras's G.E. equations; introduces steady-state growth equilibrium into Neoclassical economics.

1920s - Resurrection

1924

• Arthur L. Bowley introduces the Paretian mathematical structure to English-speaking world.

1926 

• Ragnar Frisch begins axiomatization of consumer theory. Followed up by Frisch (1932).

1928 

• Friedrich A. von Hayek initiates concept of intertemporal equilibrium.

1929

• Erik Lindahl introduces temporary equilibrium and intertemporal equilibrium independently in an formal model. Followed up by Lindahl (1932).

1930s - Paretian Revival

1930

• Irving Fisher's Theory of Interest introduces simple intertemporal economy, the Fisher Separation Theorem, and a host of other results.

1932 -

• Lionel Robbins's Essay - popular methodological manifesto enshrining approach of the Austrian and Lausanne schools
• Harold Hotelling introduces notions of duality in consumer theory, in particular, the indirect utility function. Followed up in Hotelling (1935).
• Roy G.D. Allen develops demand theory without utility function.
• Hans Neisser's critique of Walras-Cassel system; beginning of the "existence" question.

1933

• Critiques of Walras-Cassel by Heinrich von Stackelberg and Frederik Zeuthen.

• John Hicks and R.G.D. Allen  embed demand function in ordinal utility, resurrect the Slutsky decomposition of demand.
• Abba P. Lerner introduces "Fundamental Welfare Theorems" and the marginal conditions for efficiency.

1935 

• Karl Schlesinger introduces inequalities & "slack" conditions for equilibrium.
• Abraham Wald's first proof of existence of equilibrium using "slack" conditions.
• John Hicks's attempt to situate money in a general equilibrium framework.

1936 

• Abraham Wald cleans up proof of existence of equilibrium; introduces WARP.
• Franz Alt and Nicholas Georgescu-Roegen independently continue axiomatization of preferences and demand.

1937

• John von Neumann introduces his expanding economy model: introduces activity analysis, duality theorems and fixed-point existence proof.

1938 - (a year of controversial contributions!)

• Harold Hotelling introduces marginal cost pricing equilibrium.
• Oskar Lange's examination and defense of "socialist calculation".
• Abram Bergson introduces his "social welfare function".
• Paul A. Samuelson independently introduces WARP.

1939 

• John Hicks's Value and Capital presents Walrasian and Paretian G.E. to English-speaking world; introduces concept of "temporary equilibrium" , analysis of local stability of equilibrium with multiple markets, composite commodities and a host of other results.
• Nicholas Kaldor and John Hicks introduce the compensation criteria for welfare comparisons.

1940s - Programming

1941 

• Wassily Leontief introduces input-output models.
• Shizuo Kakutani generalizes von Neumann's fixed-point theorem for correspondences.
• Paul A. Samuelson introduces stability of equilibrium as a system of differential equations; discusses "correspondence principle" between dynamic stability and comparative statics.
• Tibor de Scitovsky introduces his "reversal paradox" in welfare theory.
• S. Eilenberg attempts formal derivation of utility representation of preferences.

1942 

• Oskar Lange provides general proof of First and Second Welfare Theorems.
• Oskar Lange defines "Walras's Law" and "Say's Law", criticism of monetary theory.

1943 -

• Maurice Allais's treatise, A la Recherche d'une discipline economique.; proves Welfare Theorems independently; introduces utility possibilities frontier.
• Rene Roy introduces relationship between demand and indirect utility (Roy's Identity).
• Herman Wold's work on relationship between preferences, utility and demand.

1944 -

• John von Neumann's and Oskar Morgenstern's Theory of Games and Economic Behavior; introduce game theory, axiomatization of choice under uncertainty; representation by utility function.
• Oskar Lange and Paul Samuelson's continued attack on Hicksian stability.
• Jacob Mosak introduces notion of gross substitution as stability condition.
• Abba Lerner's Economics of Control - enshrines marginal cost pricing, the fundamental welfare theorems and advances the socialist calculation debate.

1945 -

• Lloyd A. Metzler proves that gross substitution is sufficient for local stability of equilibrium.

1947 -

• Paul Samuelson's Foundations of Economic Analysis - popularization of mathematical economics, includes finalized statements on demand and production theory, dynamics and welfare economics.
• Maurice Allais's Economie et Intérêt: introduce overlapping generations model; capital and interest into G.E.

1949 -

• David Hawkins and Herbert A. Simon introduce the famous "Hawkins-Simon" conditions for equilibrium in linear production models.

1950s - The Glory Years

1950 -

• John Nash uses Kakutani's fixed point-theorem to prove existence of an equilibrium in non-zero-sum games ("Nash Equilibrium").
• Paul A. Samuelson rediscovers utility possibilities frontier; also, attempts to solve integrability problem.
• Hendrik Houthakker introduces SARP and helps solve integrability problem.

1951 - (the year of mathematical programming!)

• Kenneth J. Arrow introduces his impossibility theorem for social welfare orderings.
• Kenneth J. Arrow and Gérard Debreu independently prove fundamental welfare theorems using convex analysis (separating hyperplane theorem).
• H.W. Kuhn and A.W. Tucker introduce non-linear programming and the Kuhn-Tucker conditions for an optimum.
• Tjalling C. Koopmans introduces activity analysis models of production; proves equivalence between technical efficiency and profit maximization.
• George Dantzig introduces the "simplex" algorithm to solving linear programming problems.
• Nicholas Georgescu-Roegen extends Hawkins-Simon conditions to variable production coefficients.

1952 -

• Gérard Debreu  proves existence of Nash equilibrium for a "generalized game".
• Michio Morishima introduces conditions for stability with some complementarity.

1953 - (the year of deep insights)

• Kenneth J. Arrow introduces state-preference approach to uncertainty and rationale for incorporating financial assets in equilibrium.
• Edmond Malinvaud incorporates capital goods formally into general equilibrium; defines and proves intertemporal efficiency.
• R. Shephard provides synthesis and rigorous formalization of duality relationship between profit-maximization and cost-minimization in production.
• William Gorman and A. Nataf independently introduce conditions when aggregate demand functions can be treated as if there was a representative agent.
• Israel N. Herstein and John Milnor provide simpler axiomatization choice under uncertainty using "mixture sets"; provide first proof of representation of preferences by a continuous utility function.
• Paul A. Samuelson attempts to prove uniqueness of equilibrium via Jacobian matrix of global univalence mapping.

1954 - (the breakthrough year)

• Kenneth J. Arrow and Gérard Debreu prove the existence of equilibrium (the "Arrow-Debreu" model).
• G. Debreu introduces "consumption set", extends fundamental welfare theorems to general linear topological spaces, thus highlighting the way to infinite commodities.
• Lionel W. McKenzie independently proves existence of equilibrium using Kakutani's fixed-point theorem, albeit based on demand functions rather than preferences.
• Leonard J. Savage's famous axiomatization of subjective expected utility.
• Henri Theil introduces notion of "certainty equivalence".

1955 -

• David Gale's independent proof of existence of equilibrium.
• L.W. McKenzie proves existence with externalities in consumption.
• William Gorman highlights intransitivity problems in welfare economics.

1956 -

• Hukukane Nikaido and H.W. Kuhn  provide independent proofs of existence of equilibrium.
• Don Patinkin's treatise Money, Interest and Prices; attempt at integrating monetary theory and Walrasian G.E.; introduces disequilibrium analysis and "microfoundations" of macroeconomics.
• G. Debreu weakens free disposibility axiom

• L.W. McKenzie shows duality between utility-maximizing and expenditure-minimizing approaches to demand.
• Tjalling C. Koopmans  publishes his Three Essays on State of Economic Science, an accessible and highly popular exposition of general equilibrium theory.

1958 -

• Robert Dorfman, Paul Samuelson and Robert M. Solow publish their influential Linear Programming and Economic Analysis.

• Paul Samuelson rediscovers the overlapping generations model.
• Three independent papers by Frank H. Hahn, Takashi Negishi and K.J. Arrow and Leonid Hurwicz, all proving that gross substitution actually implies the Hicksian conditions for local stability.
• Arrow and McManus introduce notion of "D-stability".

1959 - (a banner year!!)

• Gérard Debreu publishes his Theory of Value, the "definitive" statement of axiomatic general equilibrium theory. Particularly useful in extending the notion of time-state-contingent market equilibrium.
• Lionel W. McKenzie's proof of existence of equilibrium without free disposibility; introduces "irreducibility".
• K.J. Arrow, H.D. Block and L. Hurwicz provide conditions for global stability.
• Martin Shubik resurrects Edgeworth's "core"; proves core convergence to equilibrium albeit with transferable utility.
• Martin J. Farrell launches debate on "convexification by large numbers". Followed up by Jerome Rothenberg (1960) and Francis M. Bator (1961).

1960s - The Edgeworthian Revival

1960 -

• L. W. McKenzie introduces diagonal dominance and weak gross substitution as necessary and sufficient for local stability of equilibrium.
• Herbert E. Scarf provides example of a non-pathological economy which nonetheless has globally unstable equilibrium.
• David Gale's Theory of Linear Economic Models - classical textbook on convex analysis and linear programming.
• Takashi Negishi introduces proof of existence via second welfare theorem.
• Hirofumi Uzawa uses WARP as foundation of demand theory; solves integrability problem.
• H. Uzawa introduces non-linear programming representation of saddlepoint.
• K.J. Arrow, L. Hurwicz and H. Uzawa provide various results in linear and non-programming.

1961 -

• T. Negishi attempts to incorporate monopolistic competition into G.E.
• B. Eisenberg provide alternative conditions on individual agents for aggregation into a representative agent.

1962 - (ah, a year of new directions!)

• Frank H. Hahn and Takashi Negishi introduce the "Hahn process" of non-tatonnement stability.
• Hirofumi Uzawa introduces the "Edgeworth process" of non-tatonnement stability.
• H. Uzawa shows equivalence between Walras's existence theorem and Brouwer's fixed-point theorem.
• G. Debreu introduces notion of quasi-equilibrium; removes irreversibility and free disposal axioms.
• H. E. Scarf proves Edgeworth's conjecture on core convergence without transferable utility.
• Robert J. Aumann attempts to prove the existence of utility function with incomplete preferences

1963 -

• Gérard Debreu and Herbert Scarf  prove core convergence in a replicated economy
• F.J. Anscombe and R.J. Aumann provide simple formalization of subjective expected utility theory.
• David Gale provides example of a reasonable economy with globally unstable equilibrium.
• J. Trout Rader proves representability of intransitive preferences by utility function.

1964 -

• Robert J. Aumann proves equivalence of core and equilibrium in an economy with a continuum of agents; introduction of measure-theoretic G.E.
• Karl Vind proves core equivalence in a coalitional economy with a large number of agents; introduction of Lyapunov's Theorem.
• Ivor F. Pearce provides general derivation of community indifference curves.

1965 - (a year of criticisms!)

• Karl Vind proves non-replica core convergence.
• F.H. Hahn's critique of integration of money and equilibrium theory ("Hahn Problem"); points the way to sequence economies.
• Robert M. Clower introduction of distinction between "effective" versus "notional" demand; Walrasian microfoundations for Keynesian macroeconomics.
• K.J. Arrow highlights implications of asymmetric information on existence of equilibrium.
• D. Gale and H. Nikaido prove Samuelson's global univalence mapping fails to prove uniqueness.

1966 -

• Robert J. Aumann  proves existence of equilibrium in continuum economy.
• Kelvin J. Lancaster introduces "characteristics" theory of demand.
• Lloyd S. Shapley and Martin Shubik introduce "approximate core" or "e -core".
• Richter shows integrability without integration of partial differentials.

1967 - (a tentative year towards new directions)

• Duncan K. Foley provides "no envy" or "anonymous" characterization of equilibrium.
• Peter Diamond develops stock market equilibrium model; incomplete markets and "constrained efficiency" are introduced.
• Herbert E. Scarf proves the non-emptiness of core
• H.E. Scarf introduces algorithm for computation of equilibrium.
• Roy F. Radner introduces "rational expectations" equilibrium.
• Robert Clower introduces his "cash-in-advance" constraint in an effort to integrate money in general equilibrium.
• G. Debreu proves equivalence of Vind and Aumann approaches to the continuum economy.

1968 -

• Roy Radner introduces G.E. model where agents have different information sets; defines equilibrium conditional on information.
• Werner Hildenbrand proves core equivalence for production economies.
• G. Debreu introduces a metric on the space of preferences as a way of measuring how "similar" agents are.
• Jean Jaskold Gabszewicz's proof of core equivalence with a continuum of commodities (unpublished).

1969 -

• Ross M. Starr shows the convexification effect of increasing agents; discusses the "approximate" decentralization of an equilibrium by prices; proves Shapley-Folkman theorem.
• David K. Schmeidler proves existence of equilibria in continuum economy without complete preferences.
• Werner Hildenbrand proves fundamental welfare theorems in continuum economies.
• Bent P. Stigum attempts formalization of "temporary" equilibrium.
• Edmond Malinvaud formalizes notion of "first order certainty equivalence".
• Truman F. Bewley's first proof of existence of equilibrium with infinite commodities (unpublished)

1970s - Years of High Mathematics

1970 - (high mathematics for high results!)

• Gérard Debreu proves local uniquenes/finiteness of set of equilibria; introduces economists to Sard's Theorem which helps resurrect differentiability in G.E.; introduces notion of "regular" and "critical" economies.
• Duncan K. Foley introduces Lindahl equilibrium for general equilibrium economies with public goods.
• D.K. Foley introduces transactions costs into G.E. models.
• Bezalel Peleg and Menachem Yaari prove existence of equilibrium with a countably infinite number of commodities.
• Yakar Kannai introduces characterizes economies via distributions on spaces of preferences and endowments.
• Werner Hildenbrand's first proof of core convergence in measure. Followed up in Hildenbrand (1972).
• B. Peleg attempts to prove existence of utility function with incomplete preferences.
• Bent P. Stigum proves existence of equilibrium with infinite commodities. Followed up by Stigum (1973).
• M.J. Farrell incorporates collusive oligopoly theory into the general equilibrium.
• Jean Jaskold Gabszewcz and Jean-Phillippe Vial introduce non-cooperative oligopoly theory into general equilibrium.

1971 -

• K.J. Arrow & F.H. Hahn publish General Competitive Analysis, an influential textbook on general equilibrium.
• Frank H. Hahn continues with transactions costs in a G.E. economy, and obtains a sequence economy.
• Hugo Sonnenschein proves existence and continuity of demand, in spite of intransitive preferences.
• Jacob Marschak's introduction of information theory.
• Jean J. Gabszewicz and Jean-François Mertens prove that we still obtain core equivalence in continuum economies with atoms.
• P.A. Diamond introduces "search" theory of price adjustment.
• Egbert Dierker characterizes equilibrium with indivisible commodities.
• Werner Hildenbrand analyzes general equilibrium economy where agents have random preferences.

1972 - (a year for pathbreaking)

• Roy Radner incorporates uncertainty and financial markets into a general equilibrium sequence economy; obtains an equilibrium of "prices, plans and price expectations" (i.e. Radner Equilibrium).
• Hugo Sonnenschein's first paper on the indeterminacy of aggregate excess demand functions.
• Truman F. Bewley proves existence of equilibrium with an infinite number of commodities; introduces Mackey-Arens topology.
• Egbert Dierker provides conditions for uniqueness of equilibrium.
• G. Debreu's introduces notion of differentiable or "smooth" preferences.
• Egbert Dierker and Hildegaard Dierker provide new definition of "regular" economy.
• Donald J. Brown and Abraham Robinson introduce non-standard analysis into economics with a proof of core equivalence.
• W. Hildenbrand and J.F. Mertens analyze the relationship between equilibrium prices and distributions of agent characteristics.
• Robert E. Lucas's highly influential paper on rational expectations equilibrium.
• Edmond Malinvaud analyzes relationship between individual and aggregate risks, particularly in when there are a large number of agents in a general equilibrium economy.
• Franklin M. Fisher analyzes the relationship between preferences and WARP; also introduces non-tatonnement theory with agents setting prices themselves.
• David Schmeidler shows that the e -core coincides with the conventional core in continuum economies. Followed up by K. Vind (1972) and Birgit Grodal (1972).
• Jacob Marschak and Roy Radner's Economic Theory of Teams - popularizes the idea of equilibrium contingent on information.
• Jean-Michel Grandmont and Yves Younès formalize the cash-in-advance G.E. economy.

1973 - (a year of sequences)

• Independently, F.H. Hahn (1973) and David Starrett (1973) examine the efficiency properties of sequence economies with transactions costs, and the role of money in such economies.
• H.E. Scarf's Computation of Economic Equilibrium popularizes algorithm for finding fixed points of mappings that satisfy Brouwer's fixed point theorem.
• Hugo Sonnenschein's second paper on aggregation of excess demand functions.
• Jerry R. Green's long-germinating paper on rational expectations equilibrium finally appears.
• D. Schmeidler and K. Vind's paper on fair net trades.
• Truman Bewley's proof of core convergence in mean and measure.
• Truman Bewley's proof of core equivalence in large square economies.
• Benyamin Shitovitz proves core equivalence in a continuum economy with atoms.
• W. Hildenbrand, D. Schmeilder and S. Zamir prove existence of "approximate" equilibria without complete preferences.
• Joseph M. Ostroy introduces sequential bilateral trading system to explain money. Followed up by Ostroy and Starr (1974).
• Allan Feldman introduces notion of "pairwise optimality" in bilateral exchange economies.
• Maurice Allais introduces a "no surplus" characterization of equilibrium and optimality and introduces multi-price, multi-market dynamics of surplus elimination. Followed up by Allais (1977, 1981).

1974 -

• Andreu Mas-Colell proves existence of equilibrium without the transitivity and completeness axioms on preferences.
• Conclusive papers by Gérard Debreu and Rudolf Mantel confirming the indeterminacy of the shape of aggregate excess demand functions.
• Werner Hildenbrand's Core and Equilibria in Large Economies - famous restatement of measure-theoretic G.E. and core convergence in measure.
• Jean-Michel Grandmont formalizes notion of "temporary" equilibrium.
• Jacques H. Drèze identifies problems multiple-agent ownership of firms impose on equilibrium in production economies; allows firms production decisions to be made after their shares are traded.
• Mordecai Kurz proves existence of equilibrium in sequence economy with transactions costs. Also Walter Heller .
• Franklin M. Fisher introduces "out-of-equilibrium" production into non-tatonnement models of stability.
• Jerry R. Green proves stability of a coalitional process of adjustment to the core.
• Wayne Shafer obtains continuous function representation of intransitive preferences.
• Steven Smale introduces global analysis into the analysis of general equilibrium; in a cascade of papers, reproduces practically all the results of general equilibrium via these means.
• D. J. Brown and A. Robinson (1974) prove core convergence by non-standard analysis. Followed up by M.A. Khan (1974).
• O.D. Hart proves existence of equilibrium in financial markets.
• S. Ekern and R. Wilson introduce concept of "partial spanning" for stock market equilibria.
• Joseph E. Stiglitz extends the Modigliani-Miller theorem to general equilibrium framework.

• Jacques H. Drèze and Jean-Pascal Bénassy independently introduce "Non-Walrasian" general equilibrium models with fixed prices and quantity signals to obtain "rationed" equilibria. Simultaneously, Yves Younès presents a similar result, albeit without quantity signals.
• Andreu Mas-Colell formalizes notion of an economy with differentiated commodities
• Oliver D. Hart gives examples of non-existence of Radner equilibrium when asset payoffs are in commodity bundles; provides other paradoxes with incomplete markets.
• Roger Guesnerie analyzes optimality in general equilibrium models with non-convex production sets; introduces non-smooth analysis into economics.
• Lloyd S. Shapley introduces examples where the rate of core convergence might be too slow. Gerard Debreu (1975), and more generally Birgit Grodal (1975), showed rate of convergence is at least 1/n, where n is number of agents.
• E. Dierker provides alternative proof of core convergence in mean.
• Yves Balasko introduces the equilibrium manifold - or "Walras Graph" - for differentiable exchange economies and analyzes its properties.
• Hildegaard Dierker connects smooth preferences with regular equilibria.
• Two papers, one by Wayne Shafer and H. Sonnenschein and another by David Gale and A. Mas-Colell, provide alternative proofs of the existence of equilibrium with intransitive and incomplete preferences.
• L. Hurwicz, R. Radner and Stanley Reiter extend the non-tatonnement "Edgeworth" process.
• Daniel A. Graham and E. Roy Weintraub prove stability of a "core process" with out-of-equilibrium exchange.
• D.J. Brown and A. Robinson prove equivalence of approximate cores with approximate equilibria in large economies via non-standard analysis.
• M. Ali Khan provides a characterization of approximate equilibria via non-standard analysis.

1976 -

• D. J. Brown proves existence of equilibria with infinite agents via non-standard analysis.
• Stephen A. Ross introduces the fundamental theorems of asset pricing and the notion of "pricing by arbitrage" in financial markets equilibrium; introduces spanning effect of derivative securities.
• J.P. Benassy connects "fixprice" equilibrium with theories of monopolistic competition.
• Hal Varian provides anonymous characterization for continuum economy.
• R. Kihlstrom, A. Mas-Colell and H. Sonnenschein examine relationship between WARP and gross substitution.
• Walter Heller and R.M. Starr prove existence of equilibrium in sequence economies with non-convex transactions costs.
• S. Smale connects methods of global analysis with dynamics and the computation of equilibrium; introduces the "Global Newton Method" to this end.
• D. John Roberts and Andrew Postlewaite introduce idea of truthful revelation of demand when there are large numbers of agents.

• Andreu Mas-Colell characterizes equilibrium with indivisible commodities (i.e. non-convex consumption sets).
• Sanford J. Grossman introduces concept of Nash social optimality.

• F.H. Hahn introduces notion of "conjectural equilibrium".
• Robert M. Anderson provides a very clean proof of core convergence in mean.
• William Novshek and Hugo Sonnenschein attempt to characterize Walrasian equilibrium in production as the limiting case of a Cournot-Nash oligopoly model.
• Y. Balasko produces numerous results on the structure of the equilibrium manifold.
• Salim Rashid proves existence of equilibrium in an large economy with production using non-standard analysis.
• Akira Yamazaki ...

1979 -

• Sanford J. Grossman and Oliver D. Hart analyze stock market economies (i.e. production economies with multiple-agent ownership). Require firms production decisions to be made before shares are traded.
• J.M. Harrison and D.M. Kreps identify the risk-neutral/Martingale representation of asset prices.
• R. Radner analyzes Radner equilibrium with differential information.
• R. Mantel proves existence of marginal cost pricing equilibrium.

1980s - Incomplete Years

1980-

• Yves Balasko, David Cass and Karl Shell reformulate the overlapping generations model as a G.E. model.
• Journal of Economic Theory Symposium on relationship between non-cooperative game theory and Walrasian general equilibrium. Includes some of the following contributions.
• Joseph M. Ostroy introduces "no-surplus" characterization of perfectly competitive equilibrium. Also, equivalence of no surplus and perfectly elastic demands and supplies.
• Louis Makowski extends no-surplus approach to production economies; also perfectly competitive innovation.
• Timothy J. Kehoe analyzes regular economies with production.
• Truman Bewley proves existence of monetary equilibrium in infinite horizon economy.

• K.J. Arrow and M.D. Intriligator edited Handbook of Mathematical Economics begins to appear. Popular and influential summaries of the state of the art.
• R.M. Anderson provides another proof of equilibrium with intransitive and incomplete preferences.
• David M. Kreps analyzes financial market equilibrium with infinite markets

• David M. Kreps suggests that with repeated trading, one needs relatively few assets to span large state-returns spaces.
• J.P. Benassy's Economics of Market Disequilibrium synthesizing Non-Walrasian equilibrium theory.
• Bernard Cornet analyzes non-smooth production sets using Clarke's normal cone as local approximation to derivatives.
• J.E. Stiglitz attempts to formalize the notion of constrained efficiency for incomplete markets.
• Richard Kihlstrom and Jean-Jacques Laffont develop stock market equilibrium model where agents can create their own firms.
• R.M. Anderson provides another characterization of approximate equilibrium.
• Journal of Economic Theory symposium on rational expectations equilibrium.

• Larry E. Jones's work on general equilibrium with differentiated commodities. Followed up by Jones (1984).
• Louis J. Makowski develops stock market equilibrium model where agents can create their own firms.
• W. Hildenbrand attempts to resurrect determinate shape for aggregate excess demand functions via consumer heterogeneity.
• Charalambous D. Aliprantis and Donald J. Brown introduce Riesz spaces as most primitive infinite commodity spaces.
• P. Beato and A. Mas-Colell provide example of inefficient marginal cost pricing equilibrium.
• Nicholas C. Yannelis and N.D. Prabakhar prove existence of equilibrium with incomplete and intransitive preferences in an infinite-commodity scenario.

• J.M. Ostroy shows that no surplus implies that adding up individual "marginal products" exhausts gains from trade.
• J.M. Ostroy proves existence of equilibrium in large square economies.
• David Cass introduces nominal unit of account (i.e. "cash") into Radner economy.
• M. Ali Khan and Rajiv Vohra prove existence of equilibrium with incomplete and intransitive preferences in economies with a large number of agents.
• Kim C. Border proves non-emptiness of core with incomplete and intransitive preferences.

• Andreu Mas-Colell's Theory of General Equilibrium appears: an authoritative statement of the differentiable approach to G.E.
• Darrell J. Duffie and Chi-Fu Huang prove that with repeated trading over time, only a finite number of assets are necessary to span an infinite set of states.
• D.J. Duffie and W. Shafer show generic existence of equilibrium for incomplete markets. Followed up by Duffie and Shafer (1986).
• Jan Werner proves existence of equilibrium in Radner economies with nominal units of account.
• David M. Cass detects indeterminacy in Radner economies with nominal units of account.
• Ariel Rubinstein and David Wolinsky develop sequential bargaining model to underpin Walrasian equilibrium.
• P. Beato and A. Mas-Colell prove existence of marginal cost pricing equilibrium with non-smooth, non-convex production sets.

• A. Mas-Colell extends second welfare theorem and proves existence of equilibrium for economies with infinite commodities for far more vector spaces; introduces of the notion of "properness" of preferences.
• Douglas Gale underpins Walrasian equilibrium with a sequential bargaining structure.
• John D. Geanakoplos and Herakles M. Polemarchakis prove existence and constrained inefficiency of incomplete markets equilibrium with numeraire assets ("gold" model).
• Repullo proves generic existence of Radner equilibrium with complete markets.
• A. Mas-Colell introduces cross-dual composite dynamics for stability of equilibrium.
• Nicholas C. Yannelis and William R. Zame refine proof of the existence of equilibrium with infinite commodities without transitivity or completeness.

• J.M. Ostroy shows connection between no-surplus and the existence of incentive-compatible mechanism design.
• William R. Zame proves existence of equilibrium in infinite-dimensional production economies with incomplete and intransitive preferences.
• R.M. Anderson refines the rate of core convergence to a speedy 1/n².
• Hirsch, Magill and Mas-Colell prove generic existence of equilibrium in incomplete markets.
• D. Duffie multi-period equilibrium with generic incomplete markets
• J. Werner proves existence of equilibrium in financial markets, link between Radner and temporary equilibrium
• M.A. Khan and R. Vohra use Clarke normal cone to prove marginal cost pricing equilibrium in models of public goods with non-smooth, non-convex production sets.

• Jean-Marc Bonniseau and Bernard Cornet prove general existence of marginal cost pricing equilibrium with non-smooth, non-convex production sets; also extend second welfare theorem to infinite dimensions with similar properties.

• J.D. Geanakoplos and A. Mas-Colell confirm indeterminacy of equilibrium in economies with cash. Also Y. Balasko and D. Cass.
• J.M. Grandmont's attempts to resurrect determinate shape for aggregate excess demand curves via producer heterogeneity.
• S.F. Richard provides alternative proof of existence with infinite commodities.
• A. Mas-Colell analyzes relationship between bargaining set and Walrasian equilibrium

1990s

• M.J. Magill and W. Shafer prove generic existence of Radner equilibrium with complete markets.
• Incomplete Markets: further characterizations of equilibrium and efficiency by
• J.D. Geanakoplos and W. Shafer (1990)
• Michael Magill and W. Shafer (1990)
• M.D. Hirsch, M. Magill and A. Mas-Colell (1990)
• J. Werner (1990)
• C.D. Aliprantis, D.J. Brown and O. Burkinshaw publish Existence and Optimality of Competitive Equilibrium - popular summary of G.E. in finite and infinite dimensions.

1991

• W. Hildenbrand & H. Sonnenschein edited Handbook of Mathematical Economics, Vol. IV - popular summaries of the state of the art in G.E.
• Andrew McLennan and Hugo Sonnenschein
• Michael J. Magill and Martine Quinzii connect Radner economy with unit-of-account assets to conventional monetary theory.
• A. Mas-Colell and S.F. Richard generalize proof of existence of equilibrium with infinite commodities.
• Large Square Economies - existence and core-equivalence examined by
• Aldo Rustichini and N.C. Yannelis (1991)
• M.A. Khan and N.C. Yannelis (1991)
• T.F. Bewley (1991)
[]

1994

• J.M. Ostroy and W.R. Zame characterize perfectly competitive equilibrium in large square economy with differentiated commodities.

1996

• M. Magill and Martine Quinzii publish Theory of Incomplete Markets - popular summary of sequence economies with incomplete markets
• Incomplete Markets and Infinite State Spaces examined by:
  • Martin Hellwig (1996)
  • A. Mas-Colell and W.R. Zame (1996)
  • Paulo K. Monteiro (1996)
  •  A. Mas-Colell and P.K. Monteiro (1996)
  •  M. Magill and M. Quinzii (1996)

• R.M. Anderson and W.R. Zame prove core convergence in mean with infinite commodities.  Followed up in Anderson and Zame (1998).

To be completed.

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