Theory Of General Economic Equilibrium Research Articles

Towards the theory of general economic equilibrium

The paper proposes a model of general economic equilibrium, when some firms can influence prices by their actions. Their primitives (that is, the description of production, distribution, and consumption) of the proposed model are the same as those of the Arrow–Debreu model. The difference lies in the behavior of oligopolistic firms: it is assumed that they (as in the original Cournot model) assign their production plans. The main innovation is the description of the decision-making process on production plans by oligopolistic firms. In previous models, it was assumed that oligopolistic firms seek to maximize profits at current prices. Here, a more natural assumption is made that oligopolistic firms make decisions about production plans through a vote of shareholders. It is shown how the Arrow–Debreu model can be modified to account for this circumstance. The concept of Condorcet–Cournot–Walras equilibrium is introduced, combining the ideas of these three classics. The question of the existence of equilibria is discussed. A simplified version of the model is also considered, in which each firm is owned by one agent. The simplification is that there is no need to turn to the voting.

Макроэкономическая стабильность: теория и реальность

This article explores the concept of macroeconomic stability originated from the theory of general economic equilibrium (GEE) by L. Walras. Modern macroeconomic models that do not contradict the GEE, a implement the principles of consistency of micro- and macroeconomic analysis, the interrelation of markets, and the effectiveness of market mechanism. Economic fluctuations generated by shocks are in dialectical unity with the state of equilibrium. The aim of macroeconomic policy is to maintain equilibrium (macroeconomic stability) through inflation targeting and effective public debt management. Within the framework of this policy a number of goals are met including the control over inflationary expectations, strengthening confidence in the central bank, and overcoming inflation. However, low inflation rates can produce liquidity traps, thus causing a need to adjust monetary policy and develop its new instruments. At the same time, the global crises of the 21st century, the Great Recession of 2008 and the COVID-19 pandemic, prompts to re-evaluate the contradictions between the theoretical concept of equilibrium and the real state of the economy, as well as measures needed to stabilize it during a recession. The policy of overcoming the crisis in 2020 includes large-scale discretionary fiscal and monetary stimulus according to Keynesian recipes, in the absence of which the loss of jobs, closure of enterprises, and lack of financial stability are inevitable. The gap between theory and reality, as it happened during the Great Depression almost a hundred years ago, once again raises the questions of further development of macroeconomics. The article may be of interest to teachers and students interested in the prospects for the development of scientific knowledge in this area.

Walrasian equilibrium behavior in nature

The interaction between land plants and mycorrhizal fungi (MF) forms perhaps the world's most prevalent biological market. Most plants participate in such markets, in which MF collect nutrients from the soil and trade them with host plants in exchange for carbon. In a recent study, M. D. Whiteside et al. [Curr. Biol. 29, 2043-2050.e8 (2019)] conducted experiments that allowed them to quantify the behavior of arbuscular MF when trading phosphorus with their host roots. Their experimental techniques enabled the researchers to infer the quantities traded under multiple scenarios involving different amounts of phosphorus resources initially held by different MF patches. We use these observations to confirm a revealed preference hypothesis, which characterizes behavior in Walrasian equilibrium, a centerpiece of general economic equilibrium theory.

A Regional Economy-Energy-Transport Model of the EU for Assessing Decarbonization in Transport

The EU decarbonization strategy foresees deep cuts in CO2 in the transport sector. Investment in infrastructure, manufacturing of new technology vehicles and production of alternative fuels induce macroeconomic changes in activity and employment for both national and regional economies. The objective of the paper is to present a newly built macroeconomic-regional model (GEM-E3-R general equilibrium model for economy, energy and environment for regions) for assessing impacts of transport sector restructuring on regional economies of the entire EU, segmented following NUTS-3 (nomenclature of territorial units of statistics). The model combines general economic equilibrium theory with location choice and New Economic Geography and implements a dynamic, fully endogenous agglomeration-dispersion mechanism for people and industries coupled with a gravity model for bilateral interregional flows. A novelty of the model is a two-layers structure: (i) the country-wide layer formulated as a global multi-sector, multi-country and multi-period computable general equilibrium (CGE) model; and (ii) the regional economy layer, which simulates impacts on regional economies, while considering country-wide economic trends as boundary conditions. The paper presents a use of the model in the assessment of regional economic effects of electrification of car mobility in Europe and wide use of domestically produced advanced biofuels.

Economic theories in competition: A new narrative of the debate on the General Economic Equilibrium theory in the 1930s

The paper deals with the debate on the General Economic Equilibrium (GEE) in the 1930s in Vienna and at the London School of Economics and offers an interpretation of it different from that of the traditional narratives. It interprets the debate as a renewed confrontation between the two different classical methodological paths of research in GEE, the Paretian and the Walrasian ones. What emerges from this examination is a picture of different approaches and theories in competition, in particular on the issue of the relationship between theory and the real world. This was the fundamental issue at stake. Herein lies also the interest in those distant controversies for the current debate in economics.

Optimization of Financial Flow Management Based on Estimates of Regional Multiplicative Effects

The article deals with questions of increasing the management efficiency of the regional financial resources. As the main hypothesis, the idea of the optimization of the management of the regional financial flows based on the multiplicative economic effect is proved. This measure will allow to evaluate more efficiently the impact of the regional socio-economic policy. The article presents a multifactor model of the management of the regional financial flows on the regional level — the matrix of financial flows, based on the principles of the general economic equilibrium theory, the balance method of «input-output» and the methodology of national accounts. The paper introduces a methodology for the integration of the regional consolidated budget balance in a matrix of financial flows. Matrix multipliers of the consolidated budget balance are calculated for some regions of the Russian Federation allowing to model the economic multiplicative effects resulting from impact of different types of exogenous factors on the economic development of the regions, such as to predict the impact of fiscal redistribution on the GRP and income, to assess the impact of foreign investment on economic growth, to explore the effectiveness of the federal tax policy at the regional level. The article shows that the multiplier effect depends on several factors, including the foreign trade relations of the region, its dependence on imports, the share of value added in gross output, as well as the household savings. Various levels of government can use the author’s approach during development of strategies for socio-economic development, in assessing the extent and direction of the influence of exogenous factors on the economy of the territory, as well as in analyzing the investment initiatives from the private sector applying for state financial support for projects. In the conclusion, the ways of improving the management of financial flows on the basis of maximizing the multiplicative economic effects in the short and medium term for regions with a different level of budgetary provision are proposed.

Optimizing the management of financial flows based on assessment of regional multiplier effects

This article examines the issues of improving the effectiveness in the management of regional financial flows. As their main hypothesis, the authors provide a rationale for the argument that the management of regional financial flows must be optimized on the basis of multiplier economic effects that allow to better assess the performance of regional socio-economic policy. The article presents a multifactor model for managing the financial flows at the regional level, or the matrix of financial flows based on the principles of general economic equilibrium theory, Input—Output balancing method and methodology of national accounts system. The consolidated budgetary balance sheet of the region is presented as an important structural element of the model. A methodology has been developed for integrating the consolidated budgetary balance sheet of the region in the matrix of financial flows. By using the example of individual subjects of the Russian Federation, the authors calculated the matrix multipliers of consolidated budgetary balance sheet that allow to simulate the multiplier economic effects resulting from the impact of different types of exogenous economic factors on the development of regions, and to forecast the impact of changes in the fiscal reallocation on GRP and household income, assess the impact of external investment on the economic growth of the regions and study the effectiveness of federal tax policy at the regional level. The article demonstrates that the value of multiplier effect depends on several factors, including the external trade relations of the region, its dependence on imports, the share of value added in gross output, as well as the propensity of households to savings. The approach proposed by the authors can be used by the government authorities at different levels in the development of their strategies of socio-economic development, assessment of the extent and areas of impact made by various exogenous factors on the economy of the region, as well as in the analysis of the investment initiatives of the private sector seeking the financial support for its projects from the state. The authors propose the areas for improving the management of financial flows based on maximizing the multiplier economic effects in the short and medium term for the regions with a different level of fiscal capacity.

General Economic Equilibrium with Financial Markets and Retainability

A theory of general economic equilibrium with incomplete financial markets is developed with many new features, including currency-denominated prices which enable treatment of currency-based derivative instruments and collateralized Prices in such models with standard market structure have previously been articulated only in of which have no link to an actual currency and are subject to indeterminancy in scaling. That shortcoming, which prevents ordinary comparisons between different states, present and future, has stemmed from a focus on consumption as the sole source of economic value, but here retention of is allowed to influence their utility as well.The goods are not just commodities and thus can encompass other elements essential to finance. The framework is that of an economy operating in a currency agents find attractive to retain, in balance with other needs. The attractiveness comes from Keynesian considerations about uncertainty which until now have not been brought in. An altered view of time and states helps by loosening the grip of perfect foresight in future markets. Existence is established with a single currency denominating the units of account in all states, and indeterminancy is thereby removed. All contracts issued in the financial markets can be interpreted then as real contracts. Endogenously generated transaction costs on sales of contracts keep the financial markets from getting out of hand and lead to bid-ask spreads, including a gap between interest rates for lending and borrowing money. To this end, equilibrium is given a variational formulation that brings fresh tools to the subject. A different way of proving existence in that setting, not merely in a generic sense and without normalizing to a simplex or arbitrarily fixing price levels in the future states, makes use of duality bounds for the budget constraints. In the currency framework of the model, the proof of equilibrium is able moreover to proceed under far weaker assumptions than usual on the agents' preferences and endowments.

Victor Valentinovich Novozhilov: A Marxian Mathematical Economist in Honour of the 120th Anniversary of His Birth

This article attempts to present the important contribution of Victor V. Novozhilov to Marxian economic theory, the proof that the theory of optimal planning is the proper field of general economic equilibrium theory and that this theory, by fully respecting the objective law of value, leads to planned prices which equalize supply and demand and for which the labour theory of value holds: prices of production are proportional to marginal labour values. In Novozhilov's and Soviet terminology marginal labour values are differentially socially necessary labour which includes not only the socially necessary labour needed to produce a unit of a given product, as it is commonly understood by bourgeois and many Marxian economists, but also the socially necessary accumulation of the means of production. In mathematical programming this is the rational for the Lagrange multipliers and norms of effectiveness. Novozhilov in fact proofs that in an optimal plan (Pareto optimum), prices are proportional to marginal labour values and use values.

Habits and Expectations: Dynamic General Equilibrium in the Italian Paretian School

Between the two world wars, the theory of general economic equilibrium received notable impetus in Italy from the work of the Paretian School. This consisted of a small, but very active, group of economists, whose best-known members at the time were Luigi Amoroso and Giulio La Volpe. One of the main aspects of the research program carried out by the followers of Pareto was their attempt to dynamize the theory of general economic equilibrium. These economists believed that research on static economics was by then complete although they were well aware that some analytical problems were still unsolved, and they advanced the construction of dynamic models using new and sophisticated mathematical tools such as functional calculus. However, despite its originality, the Paretian approach to dynamics, at least in the fields of pure theorizing, did not have a significant impact on the understanding of economic dynamics in the postwar period; we attempt to explore why.

Rolf Mantel and the Computability of General Equilibria: On the Origins of the Sonnenschein-Mantel-Debreu Theorem

Research Article| December 01 2006 Rolf Mantel and the Computability of General Equilibria: On the Origins of the Sonnenschein-Mantel-Debreu Theorem Fernando Tohmé Fernando Tohmé Search for other works by this author on: This Site Google History of Political Economy (2006) 38 (Suppl_1): 213–227. https://doi.org/10.1215/00182702-2005-023 Cite Icon Cite Share Icon Share Facebook Twitter LinkedIn MailTo Permissions Search Site Citation Fernando Tohmé; Rolf Mantel and the Computability of General Equilibria: On the Origins of the Sonnenschein-Mantel-Debreu Theorem. History of Political Economy 1 December 2006; 38 (Suppl_1): 213–227. doi: https://doi.org/10.1215/00182702-2005-023 Download citation file: Zotero Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search Books & JournalsAll JournalsHistory of Political Economy Search Advanced Search The text of this article is only available as a PDF. Duke University Press2006 Article PDF first page preview Close Modal You do not currently have access to this content.

Equilibrium, Disequilibrium and Time in Walras' Economics

Walras' theory of general economic equilibrium undergoes deep changes over the twenty-six years elapsing from the date when Walras' first significant theoretical contribution is published (1874) and the date when the fourth edition of his fundamental work, the Elements d'economie politique pure, eventually appears (1900). In this paper we reconstruct the many steps characterizing the twisted evolution of Walras' thought concerning equilibrium, disequilibrium, and time in economics. Our reconstruction shows how difficult it is for Walras to free his analysis from the constraints initially imposed on it by a pre-analytic vision marked by a strong, almost naif, descriptive realism, at least as far as the representation of the competitive market mechanism is concerned. As a matter of fact, Walras very early, albeit only confusedly, arrives at perceiving the theoretical, analytical and epistemological difficulties undermining his analysis of the tâtonnement processes associated to his various equilibrium models, but he hesitates to face such issues squarely lest this would force him to give up the allegedly realistic justifications of his theory. As far as the pure exchange model is concerned, Walras, under the pressure of external criticism, soon enough (i.e., since 1885) yields to the requirements of the analysis, by explicitly endorsing the so-called no-trade-out-of-equilibrium assumption, as well as the associated interpretation of the tâtonnement process in exchange as a purely virtual equilibration process in time, supporting an instantaneous equilibrium notion. As far as the production models are concerned, on the contrary, Walras strenuously resists giving up the pseudo-realistic assumptions permeating his analysis of the tâtonnement process in production at least up to the third edition of the Elements (1896): such analysis is essentially based on the idea that the tâtonnement process in production should be interpreted as actual equilibration process in real time, supporting a stationary equilibrium notion. Yet, due to his late realization of the logical contradictions engendered by his assumptions concerning this sort of tâtonnement process and equilibrium notion, hardly (if at all) compensated by a few dubious gains in terms of descriptive realism, Walras eventually resolves, in the fourth edition of the Elements, to renounce all pseudo-realistic pretence: in the 1900 edition, in fact, he adopts a novel, openly unrealistic assumption, the so-called hypothese des bons, which turns all tâtonnement processes, including the one concerning production, into virtual processes in time, supporting a generalized notion of instantaneous equilibrium of the temporary type.

Smith and Newton: some methodological issues concerning general economic equilibrium theory

This paper argues that the generally shared interpretation of what can be labelled ‘Smithian Newtonianism’ is spurious on two counts. I suggest not only that Smith was not a Newtonian in the sense that this is commonly understood, but also that Newton was not ‘Newtonian’ either. Specifically, it is argued that neither did Smith have an atomistic‐mechanistic conception of the world like that of neoclassical and modern mainstream economics, and nor did Newton simply conform to the axiomatic‐deductive methodology emulated by economic theory. In particular, Walras's explicit idealism as the architect of general equilibrium theory is contrasted with Smith's evident realism. The latter allows a possible connection between Smith's broader project and critical realism. It is concluded that the popular view of Smith as a forerunner or founder of general economic equilibrium theory must be laid to rest.

The evolution of socioeconomic order in the move to a market economy

Abstract This paper addresses the problem of the formation of order in sodoeconomic systems in transition. One approach, stemming from interpretations of the writings of Bernard Mandeville and Adam Smith, culminates in modern general equilibrium theory in economics. However, no coherent and adequate formal model of the generation of social order and economic equilibrium has yet been produced on the basis of its atomistic and individualistic assumptions. Furthermore, general equilibrium theory does not deal with economic systems in an adequate sense. It can represent neither true markets, nor money, nor key types of knowledge and uncertainty, nor real time. Finally, it does not support a policy of laissez‐faire. In sum, the general equilibrium project now lies in ruins. It is argued here that rather than the interactions of atomistic and self‐seeking individuals, real capitalist economies depend on complex relations of loyalty and trust, pervading civil society and its interpersonal relationships. The over...

Economic Equilibrium in the History of Science: Reviewing the Invisible Hand

The Invisible Hand, by Bruna Ingrao and Giorgio Israel (iggo),, contains a discussion of the present state of general-equilibrium theory from a historical perspective, with far-reaching implications. The authors argue that generations of economists have been unable to supply an adequate mathematical foundation for general equilibrium and that the time may have come to change the strategy in economics, abandoning the long-cultivated concern with equilibrium. The book is important also because it is an expression of a widely shared feeling of discomfort, endorsed by recent economic events.2 It will be recognised as a serious attempt to expose the fragility of general equilibrium theory because it enters into the heart of the matter: mathematics. The Invisible Hand deals with the development of general economic equilibrium theory. It traces the developments in the formalisation of the concept of equilibrium through the history of economics from the French Enlightenment up to the last decade. This is, indeed, an enormous task and the authors should certainly be given credit for their excellent account of almost a quarter of a millennium of economic equilibrium theory. In a dozen chapters the reader is given a fair impression of the basic concepts and prime problems of general-equilibrium theory. An extensive and well-chosen set of notes gives the book an extra dimension. The Invisible Hand is well documented, the extensive bibliography containing items that go beyond the boundaries of the history of economics. As Ingrao and Israel observe, the history of economics 'reveals gross shortcomings in the interdisciplinary field'. The authors have tried to eliminate some of these shortcomings by including elements of science in the book, as expressed by its subtitle: 'economic equilibrium in the history of science'. The Invisible Hand therefore claims to address a wide audience: economists, mathematicians, historians of science, historians of philosophy. Whether this is a correct judgment, however, may be questioned: the details of generalequilibrium theory may appeal only to a minority of the authors' intended audience.

A Review of "Existence and Optimality of Competitive Equilibria" by C. D. Aliprantis, D. J. Brown, and O. Burkinshaw

The theory of general economic equilibrium is surely one of the central achievements of modern economics. Although economists hold a wide range of views about the theory's usefulness as a guide to understanding or ameliorating the behavior of actual economies, its theorems and results concerning the efficiencY'of price-taking be­ havior in appropriately decentralized economic environments will no doubt continue to plague, perplex, or perhaps delight graduate stu­ dents for years to come. General equilibr ium theory (GET) had its beginnings in the late nineteenth century in the work of L. Walras and F.Y. Edgeworth. It began to flower in the 1950's, with significant work done by K. Arrow, G. Debreu, and L. MacKenzie, among others. This body of work is perhaps most concisely articulated in Debreu's (1959 ) Theory of Value, which lays out theoretical results on the existence and effi­ ciency of competitive equilibria in particular environments as well as a general framework for future research. In this framework, economies are represented by mathematical objects independently susceptible to rigorous formal mathematical analysis. Thus, the means of analysis and the interpretation of analytical results are conceptually distinct, which has the benefit of allowing researchers to express and commu­ nicate their results in an unambiguous and widely understandable language, that of mathematics. A related cost is that these research results can appear intimidating at best, and arbitrary and misleading at worst, to the mathematically unsophisticated.

The Invisible Hand: Economic Equilibrium in the History of Science

This study of the fundamental theoretical underpinnings of modern economies examines how economists define and categorize the market. It suggests that modeling a social science such as economics on the physical/mathematical sciences has created intractable problems, and that the basic structure of the theory needs rethinking.A meticulously researched work in the field of mathematical economics and pure theory, Invisible Hand traces the evolution of general economic equilibrium theory in its rich interaction with the physical sciences over a period of more than 150 years. The authors discuss how the invisible hand that balances physical processes was inspiration and model for the creation of general economic equilibrium theory.Ingrao and Israel review fundamental concepts of the theory, showing how its early forms, strictly analogous to mechanical equilibrium, arose from the cultural atmosphere generated by Newtonianism and the French Enlightenment. They describe developments and changes in the theory from the work of Leon Walras and Vilfredo Pareto through restructuring by the Vienna group and John Von Neumann and the contributions of the Robbins group at the London School of Economics, to its current formulations in the work of Irving Fisher, Paul Samuelson, Kenneth Arrow, and Gerard Debreu.Concluding chapters survey the results obtained in attempts to deal with questions of the existence of equilibrium, its uniqueness, and the problem of global stability. Ingrao and Israel find that the theory has arrived at a dead end, which raises serious doubts about the internal consistency of the basic model.Bruna Ingrao is Associate Professor of Economics at the University of Sassari and Giorgio Israel is Associate Professor of Mathematics at the University of Rome.

BOOK REVIEWS

Book reviewed in this article:The Political Economy of International Economic Organization Inflation and Unemployment: Theory, Experience and Policy‐Making. Edited by Victor Argy and John Nevile Restoring Europe's Prosperity. Edited by Olivier Blanchard, Rudiger Dornbusch and Richard Layard The Legacy of Ricardo. Edited by G. A. Caravale Industrial Economics. By Roger Clarke The Economic Decline of Northern Britain: The Debate Between Left and Right. Edited by David Coates and John Hillard Dynamics of Income Distribution. By John Creedy Advances in Monetary Economics. Edited by David Curie Horizontal Equity, Uncertainty, and Economic Well‐Being. Edited by Martin David and Timothy Smeeding The Economic Mind: The Social Psychology of Economic Behavior. By Adrlan Furnham and Alan Lewis Global Unemployment: The New Challenge to Economic Theory. By Martin Godfrey The Employment Effect of Technical Change. By Yanns Katsoulacos Labour and Employment in the U.S.S.R. Edited by David Lane The Theory of General Economic Equilibrium: A Differentiable Approach. By Anderu Mas‐Colell Macroeconomics': A Micro‐Macro Analysis. By Yew‐Kwang Ng Industrial Relations: Orgins and Patterns of National Diversity. By Michael Poole

Economic Theory in the Mathematical Mode

IIf a symbolic date were to be chosen for the birth of mathematical economics, our profession, in rare unanimous agreement, would select 1838, the year in which Augustin Cournot published his Recherches sur les Principes Mathematiques de la Thetorie des Richesses. Students of the history of economic analysis could point out contributions made to mathematical economics as early as the beginning of the eighteenth century. They could also point out Johann Heinrich von Thunen's Der isolierte Staat, 1826, a prototypical example of the use of mathematical reasoning in economic theory with little mathematical formalism. But Cournot stands out as the first great builder of mathematical models explaining economic phenomena. Among his successors in the nineteenth century and the early twentieth century, the highest prominence will be given in this lecture to Leon Walras (1834-1910), the founder of the mathematical theory of general economic equilibrium, to Francis Y. Edgeworth (1845-1926), and to Vilfredo Pareto (1848-1923). All three lived long enough into the twentieth century to have increased, for all Nobel Laureates, the value of the economics prize, had it, like the other prizes, been initiated in 1901. If 1838 is the symbolic birthdate of mathematical economics, 1944 is the symbolic beginning of its contemporary period. In that year, John von Neumann and Oskar Morgenstern published the first edition of the Theory of Games and Economic Behavior, an event that announced a profound and extensive transformation of economic theory. In the following decade, powerful intellectual stimuli also came from many other directions. In addition to von Neumann and Morgenstern's book, Wassily Leontiefs input-output analysis, Paul Samuelson's Foundations of Economic Analysis, Tjalling Koopmans' activity analysis of production, and George Dant

Job Matching, Coalition Formation, and Gross Substitutes

Competitive adjustment processes in labor markets with perfect information but heterogeneous firms and workers are studied. Generalizing results of Shapley and Shubik [7], and of Crawford and Knoer [1], we show that equilibrium in such markets exists and is stable, in spite of workers' discrete choices among jobs, provided that all workers are gross substitutes from each firm's standpoint. We also generalize Gale and Shapley's [3] result that the equilibrium to which the adjustment process converges is biased in favor of agents on the side of the market that makes offers, beyond the class of economies to which it was extended by Crawford and Knoer [1]. Finally, we use our techniques to establish the existence of equilibrium in a wider class of markets, and some sensible comparative statics results about the effects of adding agents to the market are obtained. THE ARROW-DEBREU THEORY of general economic equilibrium has long been recognized as a powerful and elegant tool for the analysis of resource allocation in market economies. Not all markets fit equally well into the Arrow-Debreu framework, however. Consider, for example, the labor market-or the housing market, which provides an equally good example for most of our purposes. Essential features of the labor market are pervasive uncertainty about market opportunities on the part of participants, extensive heterogeneity, in the sense that job satisfaction and productivity generally differ (and are expected to differ) interactively and significantly across workers and jobs, and large set-up costs and returns to specialization that typically limit workers to one job. All of these features can be fitted formally into the Arrow-Debreu framework. State-contingent general equilibrium theory, for example, provides a starting point for studying the effects of uncertainty. But this analysis has been made richer and its explanatory power broadened by the examination of equilibrium with incomplete markets, search theory, and market signaling theory. The purpose of this paper is to attempt some improvements in another dimension: we study the outcome of competitive sorting processes in markets where complete heterogeneity prevails (or may prevail). To do this, we take as given the implications of set-up costs and returns to specialization by assuming that, while firms can hire any number of workers, workers can take at most one job. We also return to the simplification of perfect information. In the customary view of competitive markets, agents take market prices as given and respond noncooperatively to them. In this framework equilibrium cannot exist in general unless the goods traded in each market are truly homogeneous; heterogeneity therefore generally requires a very large number of markets. And since these markets are necessarily extremely thin-in many cases containing only a single agent on each side-the traditional stories supporting the plausibility of price-taking behavior are quite strained.