Economics as a Science: The resolution of the microeconomic problem of market demand

Title	Economics as a Science: The resolution of the microeconomic problem of market demand
Authors	V. K. Gorbunov¹ ¹Ulyanovsk State University
Annotation	The purpose of this report is to acquaint applied mathematicians solving real problems of economic analysis, as well as economists, both theoretical and applied, with our solution, published mainly in Russian-language books and economic journals, of a valuable problem in economic theory and practice. The problem is that modern neoclassical economics, which is studied in most universities around the world and forms the majority of economic investigations contains an unrealistic mathematical axiomatic individual demand theory (IDTh) in multi-product consumer markets, but does not contain a realistic market demand theory (MDTh), which is of real interest to economic practitioners and governments. The consequences of this failure are the lack of founded mathematical methods for analysing market demand, in particular, the calculation of economic (analytical) consumer demand indexes that reflect the consumers preferences of the population, and a theory of economic equilibrium that determines prices that are effective for real economies. The realistic MDTh has created by the author as a revision of the IDTh within scientific methodology. Also, we have developed a verification method of this MDTh on the basis of Afriat-Varian’s nonparametric (individual) demand analysis. The problem of verifying an applied mathematical theory is the inverse problem of that theory, and the latter is usually ill-posed and generally has many solutions. The solution of such problems consists in their regularization with involvement of additional information about the desired solution, and to regularize the MDTh inverse problem we use economic indexes, which makes it possible to obtain solutions with various meaningful properties.
Keywords	market demand problem, methodological analysis, statistical ensemble of consumers, verification, Konus indexes.
Citation	Gorbunov V. K. ''Economics as a Science: The resolution of the microeconomic problem of market demand'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 26-28, 2024). Saransk: SVMO Publ, 2024. - pp. 222-225. Available at: https://conf.svmo.ru/files/2024/papers/paper43.pdf. - Date of access: 21.11.2024.

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Economics as a Science: The resolution of the microeconomic problem of market demand

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