General equilibrium reaches North America: The hydraulic simulation model in Irving Fisher's Mathematical Investigations in the Theory of Value and Prices (1891)

Abstract

General equilibrium was independently developed in Irving Fisher's 1891 Yale PhD dissertation in economics and mathematics, Mathematical Investigations in the Theory of Value and Prices (published the next year), which was the basis for his pioneering course "The Mathematical Theory of Prices" in Yale's Mathematics Department in the 1890s. As part of his dissertation, Fisher constructed a hydraulic mechanism to simulate the computation of general equilibrium prices and quantities. Paul Samuelson modestly declared Fisher's thesis the greatest dissertation in economics, but Robert Dorfman suggested that Fisher was fortunate his thesis was not rejected for inadequate knowledge of the literature, since, knowing only Jevons and Auspitz and Lieben, Fisher discovered the writings of Walras and Edgeworth just a few weeks before submitting his final draft. Beyond independently rediscovering general equilibrium, Fisher took an ordinalist approach to preferences and utility, stating that the "foisting of Psychology on Economics [by Gossen, Jevons, and Edgeworth] seems to me inappropriate and vicious" and presenting total utility surfaces that would be termed indifference curves. Most of all, Fisher differed from his contemporaries in his emphasis on general equilibrium analysis that, at least in principle, would be computable and applicable. As William Brainard and Herbert Scarf [14] emphasize, the Fisher machine, the ingenious hydraulic mechanism constructed by Fisher to illustrate his dissertation by solving for equilibrium prices and quantities in a model economy, is a landmark both in the history of economic modeling and the history of pre-electronic computing. This paper examines the theory of general economic equilibrium presented in Fisher's dissertation, of which the celebrated Fisher machine was a greatly simplified attempt at implementation. Fisher's version of the theory is compared with the work of Walras, Edgeworth, and Pareto, with particular attention to Fisher's emphasis on ordinalism and computability. The paper also investigates the reception of Fisher [27] by Pareto and reviewers such as Edgeworth, Fiske, Kinley, and Phillips (collected in Dimand, ed., Irving Fisher: Critical Responses [21]), and its later influence and lack thereof. With regard to later influence, the paper investigates the extent of acquaintance with Fisher [27] in two institutions he helped create, the Econometric Society and the Cowles Commission for Research in Economics (and its successor the Cowles Foundation at Yale), as well as the problematic relationship of Fisher's early general equilibrium analysis to his later work in capital theory and monetary economics.