Academic literature on the topic 'Mathematization of Economic'

Historians of economic thought have long debated about the methodological position adopted by Alfred Marshall (1842–1924) concerning the mathematization of economics. While Francis Y. Edgeworth and Marshall's pupils, most notably A. C. Pigou and J. M. Keynes, agreed that it was mainly through him that mathematical economics has since become respectable (see Pigou 1925, p. 66) and proclaimed him the founder of modern diagrammatic economics (ibid., p. 24), more recent commentators have criticized his failure to give proper credit to mathematics, and have even depicted him as an enemy of such an approach (see, for example, Schumpeter 1951, p. 97; Coase 1975; Brems 1975; Creedy 1986, p. 126; Schabas 1989; Huriot 1994, p. 17).

Historians of the social sciences and historians of economics have come to agree that, in the United States, the 1940s transformation of economics from political economy to economic science was associated with economists’ engagements with other disciplines—e.g., mathematics, statistics, operations research, physics, engineering, cybernetics—during and immediately after World War II. More controversially, some historians have also argued that the transformation was accelerated by economists’ desires to be safe, to seek the protective coloration of mathematics and statistics, during the McCarthy period. This paper argues that that particular claim 1) is generally accepted, but 2) is unsupported by good evidence, and 3) what evidence there is suggests that the claim is false.

In an interview with the Nobel prize winner K. Arrow the authors discuss social preferences and interests, mathematization of economics, development of innovations, economic forecasting, regulation of financial institutions, and energy policy. Future forms and features of economics and the consequences of the global economic crisis are also touched upon.

The transformation of economics through its mathematization has been of interest to historians of economics and economic thought. While considering aspects of this history, Philip Mirowski (1986a, 1992) and Lionel Punzo (1989, 1991) have introduced David Hilbert's work, the Hilbert program, formalism, and Kurt GddePs results into their discussions in a way that is inconsistent with the mathematical community's understanding of mathematical history.

The utility function has long been the main tool used by many economists due to the mathematization of economics. Some textbooks on mathematical economics state that the application of mathematics in economics imposes greater rigor, precision, and transparency of assumptions, not significantly different from the non-mathematical method. When analyzing utility function, it can be noticed that its application influences the economic analysis by imposing certain behaviors on people and giving them a mechanical character, primarily by introducing a constant relationship between the goods or goals considered by the person. For this reason, it is almost impossible to take into account the real uncertainty in theoretical research, which overly mechanizes the description of decision-making and economic processes.

The article is devoted to the problems of applying economic and mathematical methods in the organization of production in conditions of digitalization. The reasons and necessity of the formation of economic and mathematical methods in the domestic and foreign literature are considered, the reasons for the mathematization of economic methods are reflected. The problems of economic and mathematical methods and economic and mathematical models in the conditions of constant growth of information and digitalization are established. The main task of the research is to identify problems and study the application of economic and mathematical methods in the organization of production in modern conditions of digitalization, as well as to identify trends in their development.

Many economists show certain nonconformity relative to the excessive mathematical formalization of economics. This stems from dissatisfaction with the old debate about the lack of correspondence between mainstream theoretical models and reality. Although we do not propose to settle this debate here, this article seeks to associate the mismatch of mathematized models with the reality of the adoption of the hypothetical-deductive method as reproduced by general equilibrium. We begin by defining the main benefits of the mathematization of economics. Secondly, we address traditional criticism leveled against it. We then focus on more recent criticism from Gillies (2005) and Bresser-Pereira (2008). Finally, we attempt to associate the reproduction of the hypothetical-deductive method with a metatheoretical process triggered by Debreu's general equilibrium theory. In this respect, we appropriate the ideas of Weintraub (2002), Punzo (1991), and mainly Woo (1986) to support our hypothesis.

The usage of quantitative tools for creating the mathematical models of functioning different economic facilities abounds the opportunity for better understanding and acquaintance of the surrounding reality. A lot of thinkers identify even universality of the particular branch of knowledge with the extent of its ‘mathematization’. Applying mathematical methods so called quantitative provide great and not to overestimate services not only in the science research of technique, physics, astronomy, biology and medicine, but also – within the qualitative methods- in the field of social science in the sphere of the control of the quality of production or in the process of service management or decision making. Complex nature of the social and economic phenomena requires making the usage of the most modern means and the ubiquitous computerization significantly confirms the usefulness of these methods. Progressing ‘mathematization’ and computerization of the science forces creating and applying quantitative (mathematical) models including economic science. The model of operating of studied system was considered in two variants. I. when the process of the product delivery to the store represents inclusively the subsystem of production and the subsystem of the transportation – it could be then said that the level of filling the store up is controlled by the aggregated process of the delivery of the product. when the process of the product delivery to the store takes into account explicate both the production process and also the operating of transportation subsystem, so it is then the structural process of the product delivery. Both in the aggregated and structural version, the analyses of the functioning of the system was made in three variants of the store filling: intermediate state of the store filling; zero state of the store filling that is lower barrier; the state of full storage of the store, that is the upper barrier. The result of my analyses are two proprietary probabilistic models of system operation which are presented through the system of differential equations both in the aggregated and structural variant. Probabilistic models of functioning of the system in both variants presented throughout the probabilistic model also enable determining sizing prognosis which are characteristic for the functioning of this system. These prognoses are transferred to the unit of the management system and they provide the premises to the streamline of its functioning. These tools create the basics of theoretical and methodological constructed computer programmes of the informative systems of decision-making support.

In this paper, we show that Paul Samuelson (1915–2009), renowned as one of the main advocates of the mathematization of economics, has also contributed to the change of the place of visual representation in the discipline. In his early works (e.g. Foundations of Economic Analysis published in 1947), he rejected diagrammatic analysis as a relevant tool of theorizing but used diagrams extensively, both as a pedagogic tool in his introductory textbook Economics (1948) and as a way of clarifying his theory of public expenditure (1954-5). We show that Samuelson’s reluctance to use diagrams in his early works can be explained by his training at Chicago and Harvard and his rejecting Marshall’s economics, whereas his adoption of visual language in Economics was a product of the peculiar context affecting American mass-education after WWII. A methodological debate which opposed him to Kenneth Boulding in 1948 led him to reconsider the place of visual representation in order to clarify conceptual controversies during subsequent debates on mathematical economics. Therefore, it can be said that the prominent place of visual language in the diffusion of economic ideas was stabilized in the mid-1950s, as mathematical language became the prevailing tool of economic theorizing. From this, we conclude that the idea that algebra simply upstaged geometry in the making of economic analysis must be qualified.

The thesis takes as its starting point the alleged “founder” of “scientific” economics, Lionel Robbins, and investigates how economics has evolved in time, detaching itself ever more from the richer texture of Robbins’ view which was more akin to classical political economy. I argue that the top journals of economics were key players in the significant epistemological changes the discipline underwent after the 1940s, first with the increasing mathematical formalization, and later with the rise of empiricism in an attempt to mimic the natural sciences. If the 1940s and 1950s marked the rise of formalization in economics, there has been a more recent shift from the Cowles econometric approach to quasi-experimental methods, which have grown considerably in importance since 1990. This shift originated with the disarray in which the simultaneous equations approach fell during the 1980s, with its contested reliance on economic theories based on the optimization of agents or firms. If economics has certainly been relying less on theoretical models and becoming more data-driven in recent decades, hence more applicable to policy matters, this does not necessarily mean that political economy is resurfacing. Economics may be turning into a more useful instrument for designing public policies, but it remains to be seen whether the social, political and institutional elements that were extruded in the transition from political economy to economics will have any important role to play in the new era ofdata-driven economics. Chapter one argues that parallel to the mathematization of economics there was a redefinition of the methodology of economics. In order to do so I assess the influence of British classical economists on Lionel Robbins in what concerns the demarcation between the epistemology of the natural and the social sciences. With the mathematization of economics this distinction was displaced and economists increasingly started to mimic the methods of natural sciences, leading to the dehistorization and desocialization of economics. Lionel Robbins provides an interesting window into investigations of the changing nature of economics not only because he was concerned about the methodology of economics, but also because he wrote in a period when economics was quickly becoming more quantitative. In this sense the lingering influence of British classical economists on Lionel Robbins shows that the mathematization of economics after the 1930s happened in tandem with an epistemological change whereby economists increasingly endorsed the methods of the natural sciences as the proper way to approach their subject matter. In recent years the role of top journals of economics in molding research has been widely debated and the chapters 2 and 3 of the thesis contribute to this debate by examining how the language used by economists evolved since the foundation of Econometrica in 1933 until recent years. The second chapter focuses on the consolidation of mathematical economics between the 1930s and the 1960s. I argue that one of the drivers of the mathematization of economics was the ideological context of the period. As a response to totalitarian tendencies taking place in Europe, quantitative methods grew in importance because they were perceived as being value-free. Using latent semantic analysis I show that there was a convergence in the language used by the top journals of economics and in this sense the origins of the so-called top five journals can be traced back to the 1960s when they endorsed the methods championed by the Econometric Society. Chapter three then investigates the role of the American Economic Review, the Journal of Political Economy, and the Quarterly Journal of Economics in the development of mathematical economics. Using bibliometrics it is shown that the papers published in these journals are strikingly similar between 1940 and 2010. In this sense I argue that mathematical economics was increasingly incorporated by the top general journals and the rest of the profession followed suit, not least because the creation of citation metrics in the 1960s created a hierarchy within

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The possibility of the economy becoming more mathematicized began with the marginalist revolution in the late nineteenth century. However, effectively, the process of mathematization of economic discourse would only become widespread, according to MIROWSKI (1991), from 1925 onwards. In an attempt to elucidate how this process took place and when it occurred in Brazil, we wrote three critical essays on the subject. The goal of the first essay is to make more accessible to Brazilian students and researchers a discussion that is held somewhat dispersedly in our country, and also to encourage further research on the subject. This subject is the discussion about the influence of the crisis in mathematics and physics of the early twentieth century on economic discourse. To see how this happened, we investigated the texts of some of the main authors who dealt with the subject. So we seek to elucidate the differences in rigor between the different models in Economics before and after the creation by mathematical physicists of quantum physics and non-Euclidean geometry, as well as its impact on general equilibrium theory. In the second essay, we begin by presenting the main benefits generated by the mathematization of economics, according to what is proclaimed by some of the advocates of the progress of the mathematical formalization of the economic discourse. After that, we point out the more traditional criticism to this mathematization process. Then we focus on the recent criticism of GILLIES (2005) about the the prevalence of operational numbers in economics. Later we analyze the criticism presented by BRESSER-PEREIRA (2008), who considers that the hypothetical-deductive method used by the "mainstream" is inadequate for economics. Finally, bearing in mind the definitions of BRESSER-PEREIRA (2008), we tentatively associate the reproduction of the hypothetical-deductive method to a metatheoretical process triggered by the theory of general equilibrium. In our third essay, we check how mathematical formalization in economics advanced in Brazil in the last three decades. To see this, we classified into several categories all the articles published in three major economic journals of the country (Revista Brasileira de Economia, Estudos Econômicos and Revista de Economia Política) and also the papers presented at the meetings of ANPEC (Associação Nacional dos Centros de Pós Graduação em Economia) from 1981 to 2010, according to the type of argument used. The total of articles analyzed was 5733. We try to notice if there was a turning point in the trajectory of economic discourse, making it more mathematical. Finally, in order to reinforce our analysis, we focus on the process of mathematization through the observation of a quantitative variable: equations per article.
A possibilidade da economia se tornar mais matematizada se iniciou com a revolução marginalista no final do século XIX. Entretanto, efetivamente, o processo de matematização do discurso econômico apenas teria se propagado, segundo MIROWSKI (1991), a partir de 1925. A fim de tentar elucidar como se deu esse processo e quando teria ocorrido no Brasil é que escrevemos três ensaios críticos sobre o tema. O objetivo do primeiro ensaio é o de tornar mais acessível aos estudantes e pesquisadores brasileiros uma questão que é tratada de maneira pouco orgânica em nosso país, e também incentivar novas pesquisas. Trata-se da discussão sobre as principais influências da crise da matemática e da física do final do século XX sobre o discurso econômico. Para verificar como isso se deu, investigamos os textos de alguns dos principais autores que tratam do tema. E daí buscamos elucidar as diferenças de rigor entre os diferentes modelos físicos matemáticos antes e depois da física quântica e da geometria não euclidiana, bem como seus impactos na teoria do equilíbrio geral. No segundo ensaio, iniciamos definindo os principais benefícios gerados pela matematização da economia, proclamados por alguns dos defensores do avanço do processo de formalização matemática sobre o discurso econômico. Em seguida, apontamos as críticas mais tradicionais a esse processo de matematização. Depois nos concentramos nas críticas mais recentes de GILLIES (2005) sobre a prevalência de números operacionais em economia. Para afinal, analisarmos a crítica de BRESSER-PEREIRA (2008) que considera o método hipotético-dedutivo utilizado pelo 'mainstream' inadequado à economia. Por último, de maneira tentativa, tendo em mente as definições de BRESSER-PEREIRA (2008), buscamos associar a reprodução do método hipotético-dedutivo a um processo metateórico deflagrado pela teoria do equilíbrio geral. No nosso terceiro ensaio, buscamos verificar como a formalização matemática avançou na ciência econômica brasileira nas três últimas décadas. Para observar isso, classificamos em diversas categorias todos os artigos publicados em três das principais revistas de economia do país (Revista Brasileira de Economia, Estudos Econômicos e Revista de Economia Política), bem como as publicações efetuadas nos encontros da ANPEC (Associação Nacional dos Centros de Pós-graduação em Economia) desde 1981 até 2010, de acordo com o tipo de argumentação utilizada. O total de artigos analisados soma 5.733. Procuramos observar quando houve um ponto de inflexão na trajetória do discurso econômico, tornando-o mais matemático. Por fim, para atestar nossas conclusões, focamos o processo de matematização na observação da variável quantitativa: equações por artigo.

Abstract The second chapter on the Mathematics of the Practitioners attempts to show how mathematical knowledge circulated through the realm of practice, primarily in activities of measurement. Memory techniques were central to the circulation and transmission of such practices, helping them transmit beyond the practitioner to non-practitioners. This chapter argues that the mathematical practice of the practitioners in this tradition was grounded in political economy of resource distribution and remained central to that social order. It also points out how the canonical tradition’s practices were distant from these transactions, and hence raise the question about the character of abstraction in mathematization in precolonial Tamil country by situating it in social segregation and fragmentation.