This article is cited in 1 paper

Mathematical Modelling

Probabilistic solutions to the problem of rational consumer choice with random income

G. A. Timofeeva^ab, O. N. Ie<sup>ab

a</sup> Ural State University of Railway Transport, Ekaterinburg, Russian Federation
^b Ural Federal University, Ekaterinburg, Russian Federation

Abstract: Probabilistic solutions are used when the amount of decision-makers is large. Each of them chooses the optimal solution independently of the others by solving his optimization problem. In this case, the optimal solution constructed by a randomly selected person (e.g. a consumer of goods) can be considered as a random vector. In particular, probabilistic solutions arise naturally in the rational consumer choice problem if income is assumed to be random. The problem of the utility function maximization at a time when the income of a randomly selected consumer is described as a random variable is considered as the stochastic optimization problem. The properties and distribution of the probabilistic solution of the consumer choice problem for various types of the utility function and income distribution are studied.

Keywords: stochastic optimization, probabilistic solution, the problem of consumer choice, random income, utility function.

UDC: 519.8

MSC: 91B16

Received: 08.01.2021

Language: English

DOI: 10.14529/mmp210202