Geodesic
Probabilistic solutions to the problem of rational consumer choice with random income
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 2, pp. 17-26

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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, the problem of consumer choice, random income, utility function.
Mots-clés : probabilistic solution 
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G. A. Timofeeva; O. N. Ie. Probabilistic solutions to the problem of rational consumer choice with random income. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 14 (2021) no. 2, pp. 17-26. http://geodesic.mathdoc.fr/item/VYURU_2021_14_2_a1/