On continuity and general equilibrium: Pareto, Cassel, and the foundations of neoclassical economics

Abstract

This article explores the application of the principle of continuity to general equilibrium theory by Vilfredo Pareto, Gustav Cassel, and Knut Wicksell. It begins by recapping Pareto’s early works based on cardinal utility and continuity. After that, Cassel’s proposal of an elementary framing for general equilibrium with discontinuous functions is presented. The next section covers some unpublished letters between Pareto, Maffeo Pantaleoni, and Cassel related to the issue. It is followed by a review of the reception of Cassel’s ideas advanced in his 1899 Grundriss. In the end, some reflections are offered on the scientific implications of the principle of continuity to neoclassical economics.

Keywords:

• Continuity
• pure theory
• utility
• general equilibrium
• scarcity

JEL CODES:

• B13
• B16
• B31

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No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

1 By the end of the nineteenth century, Pareto had been teaching political economy at the University of Lausanne since 1893, where he held the chair formerly occupied by Léon Walras (Mornati 2018, II, 2–14, 93–124). At that time, Cassel was searching for a post from which he could teach his novel ideas on economics. He would eventually take up the chair of political economy at the University of Stockholm in 1904 (Trautwein 2016, 404–409; Magnusson 1991, 122–140). Wicksell, for his part, after several years of academic studies, was finally appointed for a professorship at Lund University in 1901 (Uhr 1991, 76–121).

2 Alain Alcouffe and Donald A. Walker have covered similar ground, although centering their analyses on Walras’s, Cassel’s, and Pareto’s formal conceptions of general equilibrium (Alcouffe 2011, 113–131; Walker 2003, 278–293).

3 Transcription and translation of the correspondence between Cassel and Pantaleoni, originally in German, by Alphatrad. Remaining translations by the authors unless otherwise indicated.

4 The word ophelimité is Greek and Pareto introduced it to distinguish the subjective satisfaction each individual experiences by consuming certain goods from the more general meaning of utility, a term supposed to convey a sense of the material, moral, and scientific progress of society (Pareto 1896–1997, v. I, 4–14. see also McLure 2000, 347–371).

5 The expression had been originally coined by William S. Jevons in his Theory of Political Economy to denote what became known as marginal utility (Jevons [1871] 1888, 51).

6 Cassel here reiterates a point previously raised by Walras, who had argued, against Marshall’s concept of consumer’s surplus, that the demand for any commodity depends not only on its own price, but also on the entire price constellation prevailing within the economy (Walras [1900] 1965, 483–488). As others had commented as well, the idea of consumer’s surplus could only provide a safe measure of total welfare if the willingness to pay, that is, the demand price for each inframarginal unity of consumption, were supposed identical for every individual. Since personal incomes are different, welfare estimations required a constant marginal utility of money to everyone, as Marshall had conjectured, albeit in fairness only for the sake of simplification (Dooley 1983; Marshall [1890] 1920, 124–133).

7 Syll and Sandelin (2001, 292) have asserted that Cassel, together with Pasquale Boninsegni and Enrico Barone, was the first of the modern economists to advocate for the revealed preference approach. But it should be noted that Boninsegni (1902) is a development from Pareto’s Sunto, which puts together a mathematical formalization of insights previously delivered in a speech at the Stella students’ association in 1898 (Pareto [1898] 1963), while Barone’s article on the ‘ministry of production’ would come out only in 1908 (see Bradley and Mosca 2014). Consequently, the clear Paretian origin of revealed preference and choice theory pre-dates Cassel’s rather disputed contribution on this score (Schumpeter [1954] 2006, 1033 f.3).

8 Mentioned over thirty times in the Grundriss, curiously enough, as noticed by Joseph A. Schumpeter ([1954] 2006, 829 f.3, 919 f.1), Walras’ name does not come up even once in the Theory, the same happening with Pareto, whereas David Ricardo, Marshall, and Irving Fisher, among others, are mentioned several times throughout the book. Perhaps, as suggested by Eric Englund (1943), Cassel had just tried to be pedagogic and avoid intricate mathematical notation, even though that does not excuse weak scientific etiquette. In his autobiography, Cassel declared that, since the Grundriss, he had never opened Walras’s Elements again (Cassel 1941, 435).

9 At the Handwritten Section of the National Library of Sweden there are three letters from Pareto to Cassel in French, along with eight letters in German between Cassel (three) and Pantaleoni (five). Cassel’s notes to Pantaleoni are sketches riddled with stricken and added words and only one of these pieces is dated.

10 Probably Pareto’s “Le nuove teorie economiche: Appunti”, published by the Giornale in 1901, which ended with an appendix outlining the equations for dynamic equilibrium (Pareto 1901). Syll and Sandelin (2001, 283–297) provide an insightful research on why the work of Italian economists had a limited diffusion within Swedish universities at that time.

11 If a particular good happens to be produced beyond the amount necessary to its joint use with other complementary goods, then the whole surplus becomes “useless” or even “noxious,” in Pantaleoni’s wording, there being no price reduction sufficient to mitigate the excess supply through the substitution or income effects (Pantaleoni [1889] 1898, 81–85). That, of course, implies a discontinuity in the respective demand curve.

12 The same charge is levelled in Pure Economics against Carl Menger’s and Eugen von Böhm-Bawerk’s theory of costs predicated exclusively on the subjective value of final commodities, qualified as completely unoriginal since their ideas had presumably been already set forth in the works of Italian authors such as Giammaria Ortes (1713–1790) and Francesco Ferrara (1810–1900), among others (Pantaleoni [1889] 1898, 85 f.1, 169 f.1).

13 Pantaleoni was the most cited author in Swedish universities over the 1895–1945 period, appearing at least twice in Wicksell’s, Nils Stjernberg’s, and Erik Lindhal’s doctoral theses (Syll and Sandelin 2001, 288).

14 Although not for the study of welfare consequences of movements within the commodity space, not even in his mature works, as such studies typically represent ophelimity as a quantity.

Additional information

Funding

The authors thank the most valuable contributions from two EJHET anonymous referees. Financial support from CNPq is gratefully acknowledged, grant number 304978/2018-3.