Mathematical economics and economic calculation
Say’s legacy went far beyond the group of liberal economists. The contributions of Antoine-Augustin Cournot (1801-1877) and Jules Dupuit (1804-1866) were also extensively influenced by Say’s thought, even though they differed from him methodologically (by using mathematical tools) as well as on certain theoretical issues (in particular the theory of value).
Later, the work of Leon Walras (1834-1910), influenced by his father Auguste Walras (1801-1866), would also bear the mark of Say’s political economy, especially regarding the issues of equilibrium and competition (Potier 2019). These three economists, to whom this volume devotes a chapter each, are in their own ways the heirs of a tradition of mathematisation of social and economic questions inherited from the eighteenth century (see Vol. I, Chapter 8). Each of them, in a very distinctive way, made major contributions to economic theory, which were ground-breaking steps in the development of modern economic analysis.Antoine-Augustin Cournot’s intellectual portrait is quite unique: he was a distinguished mathematician (initially specialised in mechanics and astronomy) and developed from his midlife a strong interest in the history and philosophy of science, and in economics. If Cournot’s economic works were relatively ignored by his contemporaries, his contributions were considered in retrospect to be of major importance by the most eminent subsequent economists, notably Leon Walras, William-Stanley Jevons and Alfred Marshall. Indeed, he was the first to make explicit a decreasing function of demand with respect to price (his “loi du debit”), and to present a mathematical theory of price determination taking into account the possibility of different market structures, from monopoly to “unlimited competition”, in partial equilibrium; his analysis of the duopoly is, in this respect, singularly ground-breaking.
In his analysis of monopoly, he introduced the concept of marginal cost - although without naming it so - and the principle of profit maximisation. Finally, another of his key achievements was his analysis of the effect of taxation on consumers and producers, and his introduction of the notion of social income, distinguishing its nominal and real variations. In his late writings, Cournot distanced himself from liberal principles and took a critical stance towards some liberal economists, especially towards Frederic Bastiat’s (1801-1850) optimistic views.Jules Dupuit belonged to a distinct current of authors, that of the French engineereconomists, whose roots go back to the creation of the corps des Ponts et Chaussees in 1716 and the Ecole Royale des Ponts et Chaussees in 1747, the ramifications of which go as far as the most prestigious French economists of the recent period. In contrast to Cournot, who primarily addressed theoretical problems, Dupuit was a practitioner of public economics, who aimed at solving concrete issues related to the building or maintenance of public infrastructure. The context in which he contributed to political economy was also quite different from that of Cournot: although he was deeply involved in the liberal networks mentioned above, his most path-breaking contributions were expressed in other circles, those of the engineers of the Polytechnique and Ponts et Chaussees. He renewed the method for measuring utility, introducing the concept of public utility and the principle of economic surplus with the meaning that welfare economics would later give to it. This is why he was considered by the commentators as a pioneer, to whom the “secret origins of modern microeconomics” (Ekelund and Hebert 1999) could be traced back, long before the marginalist authors of the 1870s.
Finally, Leon Walras’s profile is again different. After a phase of professional uncertainty, during which he had some difficulty in finding his place among engineers, liberals and socialists, he succeeded in obtaining the Chair of political economy in Lausanne (1870).
From the perspective of economic analysis, Walras’s masterpiece is undoubtedly his formulation of general equilibrium analysis, in his Elements d’economie politique pure (1874-77), whilst other marginalists limited themselves to partial equilibrium analysis. Walras’ approach is, like Cournot’s, that of a theorist applying a rational method, whose aim was therefore to study the interdependencies between markets - expressed through systems of equations - and the resulting formation of a general equilibrium. His formalisation has become the “Magna Carta of economic theory”, as Joseph Schumpeter noted (1954, 233). Nevertheless, Walras’s political economy cannot be reduced to its pure economics. Pure economics constitutes a trilogy with two other branches of economic science, social economics and applied economics, which he exposed in two later volumes: Etudes d’economie sociale (1896) and Etudes d’economie politique appliquee (1898), dealing respectively with production and the distribution of social wealth. Far from being a supporter of individualism, of which the Elements d’economie politique pure would be the prototype, Walras provided an analysis that reconciles the interests of the individual and those of society (Lallement 2017), and which attributes extensive functions to the State, including land ownership. As his Etudes show, he claimed throughout his life to be a “liberal scientific socialist” (Potier 2019).At the end of the century, Walras found a successor in Albert Aupetit (18761944), while Clement Colson continued Dupuit’s work on public economics. Other engineers investigated different fields: Marcel Lenoir (1881-1927) used the most advanced developments in statistics to study the formation and dynamics of prices, building an approach that would be now described as econometric, and Maurice Potron (1872-1942), who developed a pioneering input-output analysis. But the most spectacular innovations of the period certainly came from the mathematicians: Joseph Bertrand (1822-1900) renewed the analysis of oligopoly by rejecting some of Cournot’s hypotheses, and Jules Regnault (1834-1894) and Louis Bachelier (1870-1946) made decisive contributions to mathematical finance by introducing new concepts in the theory of probability.