The classical tradition

The tradition of using algebra to develop the classical theory of Ricardo (and, after him, Karl Marx) was revived towards the end of the century, most prominently with the contributions of Vladimir K.

Dmitriev (1974, first published 1898) and Ladislaus von Bortkiewicz (1906-07 [1952]). Using systems of equations, Dmitriev defended Ricardo against Walras’s accusation of circular reasoning by demonstrating that the current conditions of production are sufficient to determine prices and the rate of profit in a logically consistent way - without any need for a “historical regress” to determine the quantities of labour embodied in the capital goods used in production, as was believed to be necessary. Dmitriev also made precise Ricardo’s intuition of a negative relationship between the rate of profit and the real wage rate at given conditions of production. Bortkievicz built on, and extended, Dmitriev’s framework of analysis to solve the Marxian problem of the transformation of values into prices of production.

By disambiguating and making more explicit the pillars of the classical theory of prices and distribution, these first contributions laid the foundations for richer developments in the twentieth century, from Wassily Leontief’s input-output framework for applied analysis (Leontief 1966), to the more theoretical contributions of Sraffa (1960), John von Neumann whose well-known growth model (1945) shares a classical filiation (Kurz and Salvadori 1993, 2000), and the recently re-discovered Maurice Potron (Bidard et al. 2009). The interested reader is invited to consult relevant entries of this volume for more information.

Some concluding remarks on pre-1925 mathematical economics are in order. In spite of remaining weaknesses, the economic thought of this time placed greater emphasis on mathematics than before, and showed mounting enthusiasm about its use; indications of this tendency are the re-naming of the discipline, from the older “political economy” to “economics”, rhyming with “mathematics” and primarily due to the initiative of Marshall; and the first bibliographies of mathematical economics, established by Jevons (1879 [1888]) and Irving Fisher (1892).

A possible explanation of the increased penetration of mathematics into economics may be found in Philip Mirowski’s controversial claim that the economists of this time period deliberately tried to imitate physics (1989).

It is certainly true that some margin- alist writers explicitly mentioned physics as a source of inspiration; yet some of these mentions are misleading and fail to convey the real originality of the economic thought of these authors (see, for example, Donzelli 1997). Others refrained from using mechanical analogies and Marshall, in particular, privileged biological metaphors. Notice that at the time, mathematical methods - even those ultimately based on physics too, specifically those of Newton - were often taught and researched independently of any physical application (see Weintraub 2002: ch. 1).

It must also be mentioned that many economists of this time still privileged the verbal form, some overtly criticizing the use of mathematics (the most prominent example being the German Historical School), and even the most motivated mathematical economists were cautious, preferring to communicate in literary form wherever possible. Towards the end of his life, Marshall himself recommended prudence:

(1) Use mathematics as a shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can’t succeed in (4), burn (3). (Marshall 1925 [1966]: 427)

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Source: Faccarello G., Kurz H.-D.. Handbook on the history of economic analysis. Volume III, Developments in major fields of economics. Edward Elgar,2016. — 659 p. 2016

The classical tradition

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