Slonimsky's view on Antoine-Augustin Cournot∗

Abstract

In 1878 the Russian Liudvig Zinov'sevich Slonimsky published a lengthy article on the mathematization of economics. To defend the legacy of applying mathematics in the study of economics, he made ample uses of both von Thünen and Cournot's works. The article published in Russian and in the Russian Vestnik Evropy (Journal of Europe) has passed virtually ignored by economists. This notes gives a complete account of Slonimsky's references to Cournot's work.     

INTERTEMPORAL COURNOT AND WALRAS EQUILIBRIA: AN ILLUSTRATION*

In an intertemporal general equilibrium framework, we compare a Cournot equilibrium to the Walras equilibrium. The Cournot agents trade and invest less than the Walras agents. This generates an inefficiency that does not vanish as the number of Cournot agents tends to infinity. A larger number of strategic Cournot agents implies that the amount of trade (relative to their aggregate consumption) increases (i.e., it moves towards the Walrasian amount), but their investment (relative to the stock) decreases (i.e., it moves away from the Walrasian amount). "S'il y avait 3, 4, ...n producteurs en concurrence [...] la valeur de p, qui en résulte, diminuerait indéfiniment par l'accroissement indéfini du nombre n,”A. A. Cournot (1838, p. 63)."     

Can you put free will into an equation? The debate on determinism and mathematics at the end of the nineteenth century†

Mathematics and determinism may seem two very different topics, especially when mathematics is associated with the social sciences and economics. Nonetheless, this has not always been the case. In 1873 a curious debate took place in Paris between a young Léon Walras and Pierre Emile Levasseur concerning the compatibility of mathematics, economics, and free will. It was the consequence of a Laplacian view of mathematics that Walras inherited from physics, a view that associated mathematics with a peculiar philosophical conception. We reconstruct the historical context of the debate, the particular view of mathematics that lead to it, and then analyse the attitudes of Cournot, Walras, and Levasseur on the issue. We show that the mathematisation of economics was deeply influenced by how physicists understood mathematics.     

On the second optimality theorem of welfare economics

To what extent does the second optimality theorem of welfare economics (every Pareto optimal allocation can be repesented as a Walras equilibrium allocation) remain valid when preferences are allowed to be locally satiated? It is always valid for an exchange economy, and is valid for a production economy if there is a consumer who is not locally satiated, but not in general for a production economy where all consumers are locally satiated. A generalized equilibrium is defined, which includes the Walras equilibrium as a special case. Every Pareto optimum can be represented as a generalized equilibrium allocation. Furthermore, every Pareto optimal utility distribution can be realized by a Walras equilibrium allocation.     

Foucault on the Marginal Revolution in Economics: Language and the Cartesian Legacy

Scholars have long debated the ‘revolutionary’ character of the ‘Marginal Revolution’ in economics, focusing on theoretical foundations, methodological devices, social context and political aspects. This article offers a new perspective by investigating ontological and epistemological conditions of that intellectual movement. This requires, in turn, a characterization of those conditions, for which purpose we will draw on Foucault's configurations of thought into ‘epistemes’ in The Order of Things. Although not mentioning those conditions, there have been few references in economics to Foucault's approach. They have mainly claimed that he neglected its importance because he did not see it as a ‘revolution’ in The Order of Things. It is argued here that he actually considered it a ‘revolution’ in The Archaeology of Knowledge. A revision of Foucault's account provides some ideas regarding deep philosophical conditions of the emergence of neoclassical theory and defies some usual interpretations of the circumstances that led to the mathematization of economics. The main conclusion is that its revolutionary character did not stem from a change of ontological beliefs, but—just as many historians of economics have defended—it was a methodological revolution. This study suggests a reinterpretation of that event, claiming that it resulted from a new conception of language and a crisis of Descartes's project of a mathematical unifying science. Going beyond that debate, these reflections proffer ideas that deserve an appraisal in economics.     

The Bertrand Paradox,the Useless Auctioneer and the Launhardt Model

We revisit the Cournot–Bertrand debate in the light of Cournot, Edgeworth and Launhardt, tracing back to Launhardt the origin of price competition in duopoly models with constant returns to scale. Then, we discuss the formalisation of consumer utility function for differentiated products, first appearing in Launhardt and then in Bowley. This allows us to point out that assuming that firms know the demand function(s) is equivalent to assuming that they know the structure of consumer preferences. Therefore, we argue that there is no role for the auctioneer, either in Cournot or in Walras.     

Ugo Broggi: a precursor in mathematical economics

The concern for the existence of solution to the Walras - Cassel model is usually dated at the beginning of the 1930s, and one decade later the proof of existence of utility function. Ugo Broggi, however, posed both issues in 1923 and 1919, respectively, and even hinted at modern ways of solving them. He was an outstanding mathematician, a former disciple of David Hilbert and collaborator with the Giornale degli Economisti. Broggi's achievements are also linked to a critical reading of Osorio's treatise on Paretian economics.     

Announcement

The paper focuses on Blaug's distinction between rational and historical reconstruction within the historiography of economics. Blaug's distinction is shown to be sterile and misleading and his definitions of no avail to clear thinking. Historical reconstruction (as defined by Blaug) is en empty box for reasons which are basically theoretical and not simply practical (as Blaug seems to hold). Moreover, Blaug's primary polemical target is Whig historiography and not rational reconstruction: the two concepts coincide only by means of an ad hoc definition. Blaug's criticism does not apply to other uses of the concept of rational reconstruction such as that proposed by Lakatos.     

Factors Affecting the Content of High School Economics

Several years ago there was great interest in the high school economics course. Studies were being made of the effectiveness of high school economics, of the relationship between the student's high school economics background and his or her performance in the college principles course, and of the economic knowledge of precollege teachers. Strom's article may bring about a revival of interest in secondary school economic instruction. He has considered variables not previously taken into account, he has addressed the problem of defining the high school course, and—perhaps most important—he has suggested that the two-step factor analysis/regression procedure may be superior to the standard regression analysis in economic education research.     

The Institutional Theory of Radhamakal Mukerjee: Lessons for Modern Nonprofit Economics

This paper examines the way the institutional economics of Radhamakal Mukerjee can inform modern nonprofit economics. A brief survey of Mukerjee's work highlights several elements of his theory that yield useful implications understanding the nonprofit sector. First, Mukerjee's theory implies that this sector's role is in helping the economies to better accommodate broader societal values, rather than in addressing market failure. Second, his theory suggests that the nonprofit sector provides an institutional framework for the pursuit of common interests that are not reducible to individual utility maximization. Finally, as he considered the state to be inherently coercive, he believed the nonprofit sector to be the only meaningful outlet for citizenship behavior, thus advancing an original theory of complementary state-nonprofit relationship. The paper concludes with calling for more institutionalist research on the economics of the nonprofit sector.     

Why it Pays to Major in Economics

In this article, the authors use a large, recent, and accessible data set to examine the effect of economics major on individual earnings. They find a significant positive earnings gain for economics majors relative to other majors, and this advantage increases with the level of education. Their findings are consistent with Black, Sanders, and Taylor (2003), documenting that about two-thirds of the bachelor's degree premium for economics majors can be attributed to the type of job economics majors perform, and about one-third is a premium that economics majors earn over other workers within the same job.     

Instrumentalism and Economic Policy: The Quest for Reasonable Value

Neuroeconomics and behavioral economics (NEBE) is one of the most dynamic fields in contemporary economics. However, from the viewpoint of economic methodology there are still substantial reasons why NEBE is irrelevant for economic theory. This paper argues that they will only become an essential part of economics if they are embedded into a fully-fledged institutional and evolutionary paradigm. I develop a Neo-Veblenian theory of the individual that starts out from the observation that modern brain sciences do not support the notion of the brain to be an integrated and consistent rational decision apparatus. An evolutionary explanation is offered for this, which reinstates Veblen's distinction between adaptation as engineering optima and social selection. Individual identity does only emerge through communication and interaction among brains, in particular via language. The concept of the "extended brain" is proposed, which is applied to define human individuality as a social phenomenon. Thus, the systematic unity of neuroeconomics and institutional economics is established.     

The fault line of axiomatization: Walras' linkage of physics with economics

Abstract

Economists have often aligned the field of economics with physics; in the process seeking to enhance the rigor of economics by mathematizing it. In the late nineteenth century there was no more ardent champion of this view of what economics should become than Leon Walras. His own writings, though, betray a tension between comprehending this mathematization as proceeding in parallel with physics or through a metaphorical analogy with physics. The limitations in Walras' ability to axiomatize economics reveal a flawed effort to establish the foundations of economics by analogy; this difficulty has persisted through the twentieth century.     

The distance between Buchanan's “An Economic Theory of Clubs” and Tiebout's “A Pure Theory of Local Public Expenditures”. New insights based on an unpublished manuscript

This article introduces Buchanan's comment on Tiebout's “A Pure Theory of Local Public Expenditures”. It helps us to understand the nature of the relationship between Buchanan and Tiebout. Usually, it is claimed that Buchanan modelled Tiebout's insights, that there exists a Buchanan-Tiebout hypothesis, and that Buchanan in 1965 complemented what Tiebout had written in 1956. We show that Buchanan could not have written “An Economic Theory of Clubs” as a complement of “A Pure Theory of Local Public Expenditures”. He disagreed with Tiebout's ideas on mobility because he saw mobility as a cause of inefficiencies and not a cause of homogeneity in groups. This is what we show by putting Buchanan's comment on Tiebout into historical perspective. It appears that Buchanan interpreted Tiebout 1956 from the perspective of his works on fiscal federalism from the early 1950s. We show that there is a continuity between Buchanan's work from the early 1950s and his works in the early 1970s; and Buchanan's way of reading Tiebout is part of it. Hence, when he wrote “An Economic Theory of Clubs”, Buchanan was convinced that Tiebout was wrong and that he was offering an alternative framework for public economics.     

Nash and Walras equilibrium via Brouwer

Summary. The existence of Nash and Walras equilibrium is proved via Brouwer's Fixed Point Theorem, without recourse to Kakutani's Fixed Point Theorem for correspondences. The domain of the Walras fixed point map is confined to the price simplex, even when there is production and weakly quasi-convex preferences. The key idea is to replace optimization with “satisficing improvement,” i.e., to replace the Maximum Principle with the “Satisficing Principle.” Received: July 9, 2001; revised version: February 25, 2002 RID="*" ID="*" I wish to thank Ken Arrow, Don Brown, and Andreu Mas-Colell for helpful comments. I first thought about using Brouwer's theorem without Kakutani's extension when I heard Herb Scarf's lectures on mathematical economics as an undergraduate in 1974, and then again when I read Tim Kehoe's 1980 Ph.D dissertation under Herb Scarf, but I did not resolve my confusion until I had to discuss Kehoe's presentation at the celebration for Herb Scarf's 65th birthday in September, 1995. RID="*" ID="*"Correspondence to: C. D. Aliprantis     

Annual Index

The author of this article expands the background theory of voting to incorporate the undergraduate majors of members of Congress. Examining nine votes on trade across the 109th and 110th Congresses reveals that economics majors are the only category of college major to vote in favor of free trade in a predictable way. Controls for a variety of factors including ideology, race, campaign contributions, and the inclusion of votes specifically on Cuba fail to diminish the effect. While economics majors are more likely to take a free trade position, not every vote that presupposes a free trade outcome is supported by economics majors. On the issue of sugar subsidies, being an economics major does not influence the direction of a congressional member's vote.     

The Issue of Efficiency and the Role of State in New Institutional Economics: A Critical Perspective

ABSTRACT

This article scrutinises and criticises the notion of efficiency and the role of state in the emergence and evolution of institutions and property rights within the tradition of new institutional economics. Specifically, the attempt is to criticise the efficiency view of the formation of property rights and institutions. It is shown that the efficiency concept cannot provide a sufficient rationale for explaining the origins of private property. Additionally, some recent developments of North's thought are critically scrutinised, showing that his theoretical apparatus could be conceived as a paradise for the eclectic. Further, the role of the state in different versions of the theory of property rights – with a special reference to North's treatment of the notion of state – is, also, critically examined. Although North’s work has virtues compared to the ‘naïve model’ of property rights by recognising and addressing the role of the state and the issue of power in the formation of property rights and institutions, he does not succeed in fully accounting for the existence of institutional arrangements, due to his adherence to an individualist framework.     

J.A. Schumpeter and T.B. Veblen on economic evolution: the dichotomy between statics and dynamics

At present, the discussion on the dichotomy between statics and dynamics is resolved by concentrating on its mathematical meaning. Yet, a simple formalisation masks the underlying methodological discussion. Overcoming this limitation, the paper discusses Schumpeter's and Veblen's viewpoint on dynamic economic systems as systems generating change from within. It contributes to an understanding on their ideas of how economics could become an evolutionary science and on their contributions to elaborate an evolutionary economics. It confronts Schumpeter's with Veblen's perspective on evolutionary economics and provides insight into their evolutionary economic theorising by discussing their ideas on the evolution of capitalism.     

Do economists have anything to contribute to the debate on urban sprawl? (and would anbody listen to them if they did?)

This essay explores reasons for the relative shortage of work by economists on the subject of urban sprawl. I argue that a correct economic understanding of the sprawl issue is difficult to communicate. Meanwhile, a simplified caricature of economic thinking on sprawl has emerged. It argues that decentralized, low-density development has been chosen by the “free market”, therefore the problem signified by the word sprawl does not exist. This argument, made in the name of economics but not always by economists, has served to polarize the detabe as much as to enlighten it. I propose an alternative understanding of the economics of sprawl that provides common ground for debate among economists, planners, and politicians. The author is associate director of the Center for Regional Economic Issues at Case Western Reserve University's Weatherhead School of Management. In a prior life, he studied cost-of-sprawl issues for the New Jersey Office of State Planning. Thanks go to Rachael Callanan for assistance on this paper.