537 ISSN 1064-5624, Doklady Mathematics, 2018, Vol. 98, No. 2, pp. 537–539. © Pleiades Publishing, Ltd., 2018. Original Russian Text © V.K. Gorbunov, 2018, published in Doklady Akademii Nauk, 2018, Vol. 482, No. 3. Holistic Theory of Economic Equilibrium: Modified Cassel–Wald Model V. K. Gorbunov Presented by Foreign Member of the RAS A.A. Akaev February 14, 2018 Received February 8, 2018 Abstract—A modified Cassel–Wald model is used as an example of the holistic approach to creating a math- ematical theory of market demand and economic equilibrium that is an alternative to methodological indi- vidualism (sociological reductionism). A theorem on the existence and uniqueness of equilibrium is proved. DOI: 10.1134/S1064562418060121 1. The neoclassical economic equilibrium theory (EET) was created by Léon Walras in the 1870s within the framework of his and, independently, W. Jevons’s program of reconstructing economic theory, which was then a conglomerate of different treatises, incon- sistent internally and mutually, by analogy with the scientific discipline of mechanics. Walras and Jevons began with the construction of a mathematical theory of individual consumer demand that maximizes the “utility” of bought goods, assuming that the theory of market demand, which is of practical interest, would be similar. The goal of EET is to determine equilib- rium prices at which the market demand for various goods is equal to their aggregate supply. Such prices can be used as a reference point in analyzing and reg- ulating an economy and foreign trade. The Walrasian model of equilibrium was revisited as a system of individual consumers and manufactur- ing firms in Arrow and Debreu’s work [1], which determined the subsequent development of EET until now [2, 3]. Failures of this reductionistic approach in the market demand and prices theory are well known [2, Chapter 4, Section 17.E; 4–7]. These failures have generated skepticism among researchers about EET and led to a series of projects revising the neoclassical economic theory. However, the problem of equilib- rium prices is not considered there as contradicting the globalization principle, which, in turn, is debat- able and politically loaded. 2. A contemporary of Walras, Gustav Cassel rejected the individualistic demand theory, which is not confirmed by facts, and proposed a modification of the Walrasian model in which market demand rep- resents an initial holistic object; however, Cassel did not elaborate any theory [8, Chapter 4]. In the 1930s, Cassel’s model was refined, and Abraham Wald proved the existence and uniqueness of equilibrium in a modified model [9]. Moreover, he introduced an assumption about market demand that was later redis- covered by P. Samuelson as a rationality principle in the context of individual consumer choice and is now known as the Weak Axiom of Revealed Preference (WARP). Cassel’s approach to an economy as a social phenomenon contradicted the methodological indi- vidualism of the 20th-century neoclassical theory, and the established contradiction between the rationality of individual and market demands was solved in neo- classical theory (which has prevailed until now) in favor of an individual. The Cassel–Wald holistic model remained at the periphery of EET. It was for- mally developed with respect to production in linear programming [10, Chapter 13], but the Wald condi- tion for market demand was used (if at all) only as a formal “economically illegitimate” exercise to demonstrate the possible uniqueness of equilibrium [11, Section 9.4]. Michio Morishima further advanced this model by incorporating the Leontief production model [12, Chapter 2]. Up till now, many mathemati- cians have continued developing the Arrow–Debreu model, its algorithmization, and investigation of pathologies of possible equilibrium sets [3]. In [13, 14] the demand theory is revisited on a holistic basis and this holistic approach is justified. Here, an initial object is a “statistical ensemble of mar- ket consumers” observed in terms of trade statistics, and the axioms of the formal theory of individual demand [2, Chapter 3] become scientific hypotheses of collective rationality, which are tested statistically. The model apparatus of neoclassical theory is retained. The solution of the market demand problem CONTROL THEORY Ulyanovsk State University, Ulyanovsk, Russia e-mail: vkgorbunov@mail.ru