2016, №4

Probabilistic and dynamical aspects of the consumer behavior and demand theory


The article examines the application of probabilistic and dynamic method to study the behavior of a consumer. The basis of presentation is the notion of the consumer as a dynamic system, phase variables which are meaningful components of the vector of decisions, and function of HaMilton acts as a measure of the ability of the system to the selection of solutions that form the optimal consumer behavior. The Hamilton function of the user is represented in the form of a diagonal quadratic form, the coefficients of which are the usefulness of the full set of consumption goods and each good as a function of the material component of the phase space. The resulting expression for the usefulness of the complete set in the form of modified functions von Neumann — Morgenstern expected utility, defined on a simple lottery of the elements of the set. Set the unit of utility — util, coinciding with the dimension of the Hamilton function and is equal to the unit of measurement of speed of Rota of funds to the system. Found the asymptotic of the functions of the utilities of each good in their saturation (asymptotic form of the first law of Gossen), which allowed to formulate the conditions of stable equilibrium consumption of the subject. It is shown that the equilibrium consumer behavior is a consequence of the optimality conditions and it is the homogeneity of the distribution of utility benefits, as the maximum value of the usefulness of the complete set. Studied extremely properties of the utility function of the full set of benefits describing the laws of optimal consumer demand in the conditions specified volume complete set, as well as known distributions of prices of goods and income of consumer. It is shown that in both cases, the requirement of optimality (equilibrium) behavior of the individual can be formulated in the form of the second law of Gossen on the invariance of marginal utility additionally introduced means of providing this consumer behavior. The results of the present study was carried out using the explicit expressions for the modified functions von Neumann-Morgenstern expected utility, allow to justify and extend the comparative statics of consumption, previously obtained within the model of methods of neoclassical theory.

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Vyacheslav A. Slavin — Cand. Sci. (Physical and Mathematical), Associate professor, Department of Higher Mathematics and Theoretical Mechanics, Chuvash State University (Cheboksary, Russian Federation; e-mail: slavin9297@mail.ru).

Irina N. Urusova – Cand. Sci. (Econ.), Chuvash State University, Associate Professor of the Department of Regional Economics and Entrepreneurship (CheboksaryRussian Federation;  e-mail: urusova_irina@mail.ru).