On the Influence of the Price Dependence of a Goods Consumption Structure on the Equilibrium of an Economy
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ON THE INFLUENCE OF THE PRICE DEPENDENCE OF A GOODS CONSUMPTION STRUCTURE ON THE EQUILIBRIUM OF AN ECONOMY UDC 519.86
A. Ph. Makhort
Abstract. Equilibrium conditions for an open economy with monopolies are investigated. The presence of insatiable consumers in the economy is taken into account. The influence of the price dependence of a goods consumption structure on equilibrium states is investigated. The existence of equilibrium states in such an economy is proved. A relation is established between the selection of a taxation strategy and realization of a concrete equilibrium state of the economy. Keywords: economic equilibrium, demand, supply, monopoly, taxation. INTRODUCTION The description of reactions of economies to the influence of different factors is an important problem of mathematical modeling. It is well known that an economy evolves from one equilibrium state to another. In the general case, a sequence of realizations of different equilibrium states is not ordered with respect to time, which results in difficulties of an acceptable choice of equations for the dynamics of the economy. However, for a wide class of problems, it suffices to restrict our attention only to the description of equilibrium states without taking into account transitions between them. This approach is especially efficient if conditions should be specified that guarantee the realization of equilibrium states with given characteristics. The latter can specify states accepted from the viewpoint of functioning efficiency. For economies, it is important to determine the most efficient equilibrium state (or close to it) and to show one the way to reach it. Within the framework of this approach, problems can be considered in which the conditions of the absence of arbitration in economies [1] are investigated, namely, in the case of equilibria of the Walrasian type [2]. The amount of information obtained as a result of such an investigation will be sufficient to analyze the behavior of economies and to find out how to avoid or compensate the effect of the destabilizing factors on the processes running in an economy. The presence of monopolies can be considered as a destabilizing factor in an economy. This article considers the possibility of control of an economy with the help of the choice of a taxation strategy to compensate negative manifestations of monopolism. The influence of the dependence of coefficients of goods consumption by the subjects of an economy on the vector of prices for the realization of possible equilibrium states of the economy is investigated. The factor of this dependence can exert an appreciable influence on pricing in an economy, and the price vector is one of the main characteristics of an equilibrium state. Goods consumption coefficients must reflect consumer’s preferences in choosing between goods. Acceptable results of the analysis of possible scenarios of developing economies with allowance for an approximation of unfailing interests of consumers are obtained in [1, 3]. In this approximation, goods consu
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