The Power Theory of Exchange and Money (PTEM) refines the economic neoclassical two-equation model of exchange. PTEM replaces the statistical average condition of exchange, which represents the equality of supply and demand for all transactions in the market, with a more specific equation of the equality of the generalized power of the parties in relation to their objects of exchange. The purpose of the article is to show the application of PTEM for the study of various social phenomena. Along with a brief summary of the main statements of this theory, its integration into the existing corpus of theories and ideas in economics and sociology is considered. The conclusions of power theory are then applied to consider the following topics: the objective motivation of exchange by the desire to increase power, the power nature of market equilibrium, the power nature of money, the accumulation of power through profit, the creation of money as a power act, the role of the state in the creation of money, the measure of power as a possible tool for social and political research.

Modern exchange theories model a large market, but do not explain single exchange. The paper considers the phenomenon of single exchange and formulates the general exchange problem in the form of a system of two equations, subjective and objective. Subjective equilibrium is given by the Walras-Jevons marginal utility equation. Objective equilibrium equations by Walras and Jevons are averaged over all transactions in the market and can only give a rough general picture without explaining the specific price of an individual exchange. An exchange micro-condition must be found that, when averaged, will give the Walras market equilibrium macro-condition. The study of the internal structure of exchange leads to the need to consider power. The concept of generalized power is introduced. It is generalized power that serves as the primary comparable and measurable objective basis of exchange. The power theory of exchange provides the objective price-equation. It is demonstrated that money is a measure of generalized power in exchange and a certification of generalized power in subsequent exchanges. The proposed theory is able to uniformly explain any exchange, including a single one, which is impossible with the existing theories of exchange.

Arguments of Mises and Hayek, who opposed the planned economy (PE), are used in the paper as a starting point for establishing the objective area of effective application of the PE. The abstract model of PE, based on the definitions of Mises and Hayek, leads to the conclusion that for the effective use of PE, it must be a part of mixed economy and it must produce a limited amount of essential goods of irreducible demand. These goods must be distributed among all members of society free of charge, evenly, without competition. Examples of a mixed economy are given that meet this requirement. Calculations of the personal benefit in the transition to a mixed model of the economy have been carried out. The positive and negative qualities of the planned and market methods of organization are considered. Mixed economy model combines these qualities in optimal construction. An analytical framework has been introduced for the construction of product characterization curves. Such curves provide criteria for determining the efficiency of manufacturing of this product in a planned economy. The general economic prerequisites for the usability of the PE are clarified. The applicability and advantages of the PE for the organization of the universal basic income (UBI) system are demonstrated. The possibility of using PE to solve the problem of guaranteed employment is mentioned.