Walras, general equilibrium and successive approximations
After initially dismissing the economic theory of Leon Walras as too metaphysical in orientation, Pareto was persuaded by Maffeo Pantaleoni to study Walras’s Elements d’Economie Politique Pure more carefully.
Having done so, he came to endorse Walras’s general equilibrium theories of exchange, production and capital formation, and the associated formal conditions of equilibrium, as the subject of “pure economics” for conditions of free competition. However, Pareto significantly de-emphasized the issue of the equilibration process by not following Walras in giving prominence to tatonnement within pure economics as the mechanism for establishing the path to equilibrium prices. The origin of Pareto’s concern with Walras’s approach to the equilibration process is implicitly discussed in 1892, in the first part of the five-part article “Considerazioni sui principii fondamentali dell’economia politica pura” (Pareto 1892-93 [2007]), when he drew attention to Walras’s paraphrasing of an interlocutor who had questioned the necessity of demonstrating how prices adjust in the face of excess demand and excess supply, and took the side of the interlocutor:in this case we must confess that it was his [Walras’s] interlocutor who was right, only he did not defend himself well. He should have said that it is from direct observation that we deduce the law about prices rising when demand is greater than supply, and vice versa. And he should also add: since these are elementary, simple direct observations, if you no longer wish to take them as the basis of your reasoning, but as its consequences, then you must show that the replacements are more elementary, simpler and more direct. (Pareto 1892 [2007]: 4)
Pareto makes reference to the equilibrating role of the haggling process in the Cours, although he used the French word marchandage instead of Walras’s term tatonnement (Lendjel 1999) and his support for treating this process in pure theory was brief and limited.
His almost ambivalent position on the issue was most likely due to his realization that a formal theory on the process of adjustments to equilibrium would require economic equations to be specified on a dynamic basis using functional calculus, but he was unable to develop such a study for economic analysis (Donzelli 2006: 513). As a consequence, he largely settled on a static representation of equilibrium for pure theory, with the haggling process briefly presented as an almost incidental justification for the use of given prices in pure theory under conditions of free competition. His contributions to economic theory in subsequent phases of his scholarship did not even include indirect allusions to tatonnement. As a consequence, the extensive secondary literature on taton- nement within the Walrasian system of equilibrium is not matched by an equivalent literature on marchandage in the Paretian economic system.To accommodate this reduction in emphasis on the equilibration process, with a corresponding increase in emphasis on applied economics, Pareto set general equilibrium within his own distinctly non-Walrasian methodological framework that he referred to as “successive approximations”, which he took directly from the physical and natural sciences. When the Cours was being published, Pareto wrote a letter to Maffeo Pantaleoni (19 February 1897) saying: “I recognize that I have taken the idea of equilibrium from Walras, to which I have added the idea of successive approximations” (Pareto 1960: 36).
Under the methodological approach outlined in the Cours, the concrete economic phenomenon is explained by a synthetic union of the theoretical analysis of the conditions of economic equilibrium (the first approximation) and applied economic studies (the second approximation), be it the application of pure theory to particular problems (for example, the theories of welfare economics, international trade and rent) or laws deduced from empirical uniformities derived from statistical observation (for example, the distribution of income). But Paretian successive approximation also has an explicit pluralistic dimension: it is not limited to a relationship between theoretical and empirical economic analysis, it also extends to a synthesis of theory and applied studies pertinent to the economic phenomenon but which come from the other social sciences.
So Pareto attempted to accommodate third, fourth and subsequent approximations, which were considered synthetically when uniting analyses from a range of disciplines when compiling a picture of the general economic phenomenon under particular circumstances.To accommodate the successive approximations approach, Pareto introduced his neologism, ophelimity, and set about distinguishing it from utility. The abstract quality of acts that lead to physical, intellectual and moral development is termed “utility”, which may be considered with respect to the individual, the social aggregate, or the species as a whole. However, Pareto regarded such a notion as having too many dimensions to be clearly defined for use in theoretical analysis, so he introduced the one-dimensional notion of ophelimity, which is a sub-class of utility that is limited to the subjective and abstract quality of acts that satisfy an individual’s needs or desires irrespective of their legitimacy or usefulness. This distinction supported the pluralistic approach to social science that Pareto tried to accommodate because utility, and its sub-class ophelimity, are divided into different species: economic utility concerns the development of material well-being and economic ophelimity concerns the satisfaction of material desires irrespective of whether they are useful; moral utility concerns the development of more perfect morals while moral ophelimity concerns the subjective benefit from satisfying moral needs and desires irrespective of whether it is useful; and so on. Within that context, the abstraction homo wconomicus - and not a real person - was the subject of Pareto’s pure economics, as its actions were undertaken solely in response to the economic forces of “elementary” (marginal) ophelimity.
From this, Pareto also recognized that the approximate relationship between fact and theory is not equally accurate across each of the general equilibrium theories of exchange, production and capital formation, as “disturbances” from errors of judgement are common, most especially in relation to capital formation and the transformation of savings into a diverse range of capital goods. Consequently, the Cours concedes that observed equilibrium modifies itself continuously as the technical and economic conditions of production change with the real state being one of continuous oscillations around a central point of equilibrium which also changes (Pareto 1896-97 [1971]: 177). This general conclusion mirrors Walras’s view of equilibrium, but, to Pareto, the difference between theory and fact served to reinforce the need for a methodology that is based on successive approximations, a methodology that Walras was reluctant to embrace.