On no-envy and fair allocations in general equilibrium theory

In this article we address the story of developments in general equilibrium theory in the Soviet Union during the 1970s through the lens of a single biography. The Soviet advances in mathematical economics give an occasion to reflect on the extension of the Walrasian paradigm to nonmarket societies, as well as on the ideological effects of general equilibrium theory and its interpretations in a Soviet context. Our contribution is focused on the development of general equilibrium theorizing in the work of Victor Meerovich Polterovich (b. 1937), who has been one of the leading figures in mathematical economics and general equilibrium theory in the Soviet Union and post-Soviet Russia. His papers on the abstract models of exchange, dynamic general equilibrium and optimal growth theory, excess demand correspondences, monotonicity of demand functions, and disequilibrium theory were for the most part published in English and gained considerable attention within the field. We reconstruct the political and ideological basis of the general equilibrium concept and show how abstract mathematical models reflected the discursive shift from optimal centralized planning to various forms of decentralization. We argue that the Soviet work on general equilibrium was a part of the global development of mathematical economics but was not integrated into it institutionally.

In this paper we address the story of developments in general equilibrium theory (GET) in the USSR during the 1970s through the lens of a single biography. The Soviet advances in mathematical economics, only fragmentarily known in the West, give an occasion to reflect on the extension of the Walrasian paradigm to non-market societies, as well as on the ideological effects of GET and its interpretations in a Soviet context. Our contribution is focused on the development of general equilibrium theorizing in the work of Victor Meerovich Polterovich (b. 1937) who has been one of the leading figures in mathematical economics and general equilibrium theory in the USSR and post-Soviet Russia. His papers on the abstract models of exchange, dynamic general equilibrium and optimal growth theory, excess demand correspondences, monotonicity of demand functions, and disequilibrium theory were for the large part published in English and gained considerable attention within the field. We reconstruct the political and ideological basis of the general equilibrium concept and show how abstract mathematical models reflected the discursive shift from optimal centralized planning to various forms of decentralization. We argue that the Soviet work on general equilibrium was a part of the global development of mathematical economics but was not integrated into it institutionally.

This chapter generalizes the Walrasian theory. The traditional theory is for a stationary economic system. Walras introduced saving and capital accumulation in his general equilibrium theory. But his treatments of capital accumulation are not proper, especially in the light of modern neoclassical growth theory. Ricardo’s On the Principles of Political Economy and Taxation of 1817 makes a valuable contribution to economics. Applying the law of diminishing returns in agriculture, he makes important development of the theory of rent. His study shows how wages, interest rate, and rent can be determined within a compact theory. This chapter integrates Walrasian general equilibrium, Ricardian distribution, and neoclassical growth theories as an extension of the basic model proposed in Chap. 2. The chapter also introduces exogenous shocks to the general equilibrium and demonstrates how various business cycles are generated by different exogenous changes. The appendix generalizes the model in cases of multiple capital and consumer goods.

Although this chapter is mainly concerned with the international contributions by Japanese theoretical economists in the post-World War II period (after 1945), in this section, we shall briefly refer to some important contributions before 1945. Until the end of World War II, Japan was a pure importer of economic theory and had nothing to export except only a few exceptional contributions.1 Kei Shibata and Masazo Sono are two such exceptional Japanese scholars who were able to add something new to modern economic theory of that period. Shibata was a very creative theoretical economist at Kyoto University. He studied mathematical Walrasian/Casselian general equilibrium theory as well as Marxian economic theory. In 1930, he found that Cassel’s (1918) system of equations of general economic equilibrium may not have a meaningful solution because there is the possibility that a subsystem becomes overdeterminate. Unfortunately, his paper (Shibata 1930) was written in Japanese, so that his contribution remained unknown amongst western economists. But his assertion was in fact the same as that of von Stackelberg (1933), which appeared three years after the publication of Shibata (1930).2 Shibata (1933), which was written in English, tried to formulate Marx’s scheme of reproduction by means of a simplified two sector Walrasian general equilibrium system of equations, and this paper was referred to by Oscar Lange (1935). He also published a critical review of Keynes’ General Theory (Keynes 1936) in English only a year after the publication of Keynes’ book (cf. Shibata 1937). Masazo Sono was a mathematician rather than economist, but his mathematical analysis of the ‘separable goods’ problem, which was done during World War II, is an important contribution to consumer theory (cf. Sono 1943).3 The contributions by such economists as Shibata and Sono were the pioneering works which foreshowed the striking international contributions by several Japanese theoretical economists after World War II, especially in the period between the 1940s and the 1970s. In the following sections, we shall consider international contributions by Japanese economists to the development of economic theory after World War II, especially focusing on the development of dynamic economic theories from the1940s to the 1970s. We take up the theoretical contributions by Takuma Yasui, Michio Morishima, Hirofumi Uzawa, Takashi Negishi, Nobuo Okishio and Hukukane Nikaido.4

Recent evidence of entrepreneurship's significant contribution to economic growth and development challenges the dominance of general equilibrium theory in macroeconomic thought. Microeconomics has long criticized the assumptions of the neoclassical economic model which underlies general equilibrium theory but has not swayed the grasp that general equilibrium theory has over macroeconomic policy formulation. Yet, general equilibrium theory does not incorporate entrepreneurship; on the contrary, the assumptions of this model exclude entrepreneurship as an economic variable. Now, however, as microeconomic research finds more and more evidence confirming the importance of new business formation and growth, general equilibrium theory remains incapable of adapting to this reality. And, this theory frequently produces policy prescriptions that favor large, established firms over new, small firms. This paper describes the weaknesses of general equilibrium theory that are relevant to entrepreneurship. Then, after reviewing the growing evidence supporting entrepreneurship, it describes Schumpeter's model of creative destruction and demonstrates how entrepreneurship empirical research supports this model. It concludes by urging economists to desert general equilibrium theory and search for a new macro-theory that incorporates entrepreneurship.

The firm fits into general equilibrium theory as a balloon fits into an envelope: flattened out! Try with a blown-up balloon: the envelope may tear, or fly away: at best, it will be hard to seal and impossible to mail... . Instead, burst the balloon flat, and everything becomes easy. Similarly with the firm and general equilibrium though the analogy requires a word of explanation. General equilibrium theory GET for short has two attributes. First, it defines clearly the boundary between economic analysis and the exogenous primitive data or assumptions from which it proceeds; that is, it defines a precise, self-contained 'model'. Second, it verifies the overall consistency of the economic analysis. A natural step in verifying overall consistency is to exhibit sufficient conditions for the existence of the proposed solutions, or 'equilibria'. This step is usually amenable to mathematical reasoning. Still, I do not mean to identify general equilibrium theory with that potent cocktail of economics and mathematics known as mathematical economics. (To some, mathematical economics is merely a pleonasm; to others, it is a branch of mathematical pornography; the word cocktail, with its element of pornographic pleonasm, is purposedly neutral.) Work in mathematical economics lacking the GET attributes is abundant. Conversely, let me remind you of our friend Harry Johnson: He was a beautiful member of our GET-set, for he was skilful at integrating partial contributions into consistent general pictures; yet he needed little algebra, because he was a master at the declining art of expressing complex rigorous arguments in literate English. The two attributes of General Equilibrium Theory stand out, for instance, in the classic work Theory of Value hereafter referred to as TV (not inappropriately, given the recent successes of its author as a TV-star). In Theory of Value, an 'economy' is defined by a set of commodities; a set of consumers, individually described by their needs and abilities (consumption sets), their initial assets, and their tastes (preferences); and a set of producers of firms, individually described by their technological possibilities (production sets). These are the primitive data, which the economist treats as exogenous and does not seek to explain. Basically, they correspond to the opportunities and motivations of all agents a structure which is even clearer in the 'abstract economies' approach; see Shafer and Sonnenschein (1975).

We generalize the concept of Nash equilibrium to the concept of general Nash equilibrium such that it becomes applicable to more general games. We also generalize the concept of general equilibrium in general equilibrium theory to a more general concept of general equilibrium such that it becomes applicable to any game. To illustrate the usefulness of these generalized concepts, we apply them to industrial organizations and general equilibrium theory.

There are two independent lines of equilibrium concepts. To unify these two lines, we generalize the concept of Nash equilibrium to the concept of general Nash equilibrium such that it becomes applicable to all games. We also generalize the concept of general equilibrium in general equilibrium theory to a more general concept of general equilibrium such that it becomes applicable to all games. To illustrate the usefulness of these generalized concepts, we apply them to industrial organizations and general equilibrium theory.

The Inexact and Separate Science of Economics (ISSE) offers an overview of standard microeconomics and general equilibrium theory. These are not the whole of orthodox economics, and orthodox economics is not the whole of economics. But orthodox economics dominates the profession, and the theoretical core of microeconomics and general equilibrium theory – what I called ‘equilibrium theory’ – is central to most orthodox economics. Unlike many methodological works, which focus almost exclusively on the empirical problems of equilibrium theory and its applications, ISSE is also concerned with the structure, strategy and heuristics of equilibrium theorizing, and it attempts to link questions about theory appraisal to questions about structure and strategy. It is addressed both to philosophers interested in epistemological questions posed by the social sciences and to economists interested in reflecting on and improving their discipline. Its inspiration lies in the work of John Stuart Mill.

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.

Modern economic theory has experienced a persistent shift away from partial equilibrium modelling and towards the theory of general competitive equilibrium. Spatial economic analysis, however, has by and large remained rooted in the older approach. This conservatism may be explained in part by the stringently aspatial manner in which general equilibrium theory is conventionally expressed. This paper attempts to redress this imbalance by considering general equilibrium in an explicitly geographic setting. In this particular context, space manifests itself primarily through transportation costs, and the major concern is to ascertain the pattern of transportation costs which the axioms of general equilibrium theory imply.

Is intertemporal general equilibrium concerned by the Cambridge critique of the theory of capital? Many thought, and for a long time, that it was not the case, since there is no aggregate of capital in general equilibrium theory, at least not in a form which would be visible immediately in the Arrow-Debreu model with a finite horizon (Debreu, 1959). Others suspected that the problems of capital theory would affect all versions of neoclassical theory, without being able to indicate the consequences for general equilibrium. Burmeister (1980, p. 122) introduced the assumption of regularity, i.e. essentially the postulate that the total change in the values of capital goods employed falls whenever a rise of the rate of interest causes a switch of technique/A variant of this assumption was used by Epstein (1987) to demonstrate the convergence of an intertemporal equilibrium with an infinite horizon towards a steady state in which the rates of return on all assets became equal among themselves and equal to the (variable) rates of time preference of the consumers. Here, the relationship with the Cambridge debate was made explicit and it was remarked (see also Burmeister, 1980, p. 125; Schefold, 1997, chapter 18.1) that the absence of reswitching and reverse capital deepening were necessary conditions in neoclassical theory to exclude the specific instability discussed in Schefold (2005a, 2005b) which might prevent the economy from reaching a terminal state with a uniform rate of profit after starting from arbitrary initial endowments of capital goods.

Part 1 Introduction: Equilibrium Theory as an Approach to Macroeconomics A Preview of the Argument An Example Concluding Remarks. Part 2 Linear Difference Equations - Part 1 - Linearizing Nonlinear Models Solving First-Order Linear Models Solving Higher-Order Linear Models Concluding Remarks. Part 3 Linear Difference Equations - Part 2 - Linear Rational Expectations Models Solving Linear Rational Expectations Models Cross-Equation Restrictions and the Lucas Critique Concluding Remarks. Part 4 General Equilibrium Theory under Certainty: The Idea of Equilibrium The Theory of Consumer Choice Excess Demand Functions Equilibria and Their Properties General Equilibrium Theory and Efficient Allocations of Resources Concluding Remarks. Part 5 Infinite Horizon Economies and Representative Agents: The Representative Agent Economy Competitive Equilibrium and the Planner's Problem Using the Representative Agent Model to Explain Time Series Data Concluding Remarks. Part 6 Horizon Economies and Overlapping Generations: The Structure of the Overlapping Generations Economy The Consumer's Problem An Example of a Pareto Inferior Equilibrium Institutions That May Improve Allocations The Set of Equilibria in the Overlapping Generations Model Some Questions about the Model More General Examples of Overlapping Generations Economies Concluding Remarks. Part 7 Infinite Horizon Economies with Nonconvexities: A Growth Model with Increasing Returns Empirical Evidence for Increasing Returns Equilibria in the Increasing Returns Economy Comparing the Theoretical Properties of RA and IR Models Comparing Some Empirical Predictions of RA and IR Models Concluding Remarks. Part 8 General Equilibrium Theory and Uncertainty: Debreu's Formulation of the Problem Arrow's Formulation of the Problem Infinite Horizon Economies with Uncertainty Concluding Remarks. Part 9 Sunspots: Do Sunspots Matter? An Example of a Macroeconomic Model in Which Sunspots Matter Concluding Remarks. Part 10 Macroeconomic Models of Money: Models of Money The Dynamics of a Cash-in-Advance Model Equilibrium under Interest Rate Control Equilibrium under a Fixed Money Growth Rate Rule Concluding Remarks. Part 11 Applied Monetary Theory: The Monetary Facts - What There Is to Explain A Simple Monetary Model - Using Equilibrium Theory to Explain the Facts How Do Equilibria Behave?.

This paper aims at understanding social practices and institutions that ensured the transnational diffusion, recognition, and renewal of the research program in the General Equilibrium Theory (GET), in spite of multiple critics and apparent theoretical dead ends. First, we trace the main conceptual developments of the Walrasian GET program since the 1950s and thus elaborate on its intellectual identity. Then, based on a systematic study of the educational and professional trajectories typical for several generations of GET scholars, we analyze a social form taken by this transnational and multidisciplinary “scientific community”: an institutional dynamics of the Walrasian GET program, most common career patterns, and the forms of international and intergenerational transmission. We construct a database of GET theorists and apply to this dataset a technique of Multiple Correspondence Analysis (MCA) in order to investigate the relational patterns between attribution of scientific credit (symbolic capital) and biographical properties in a transnational space of the GET scholars.

The theory of money is a special theory of exchange. Since as we confine ourselves in this book to the case of a general economic equilibrium, the necessary foundations are provided by general equilibrium theory. It is generally said that money cannot be found in it. That is not quite correct. We have become accustomed to regard prices in terms of money also in general equilibrium, i.e., to regard money as an accounting unit, and it needs not much imagination to imagine in this model money used also as a means of payment. However in the traditional version of general equilibrium theory there are no cash holdings. They can only be explained if transaction costs are taken into consideration, which usually is not the case in general equilibrium theory. The appearance of transaction costs leads us into the midst of the problems discussed later in this book; they are of a fundamental nature.