Power Theory of Exchange and Money

Modern exchange theories model a large market, but do not explain single exchanges. This 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. This methodology is based on an interdisciplinary analysis of an abstract exchange model in the form of a system of equations. The proposed theory is able to uniformly explain any exchange, including a single one, which is impossible with the existing theories of exchange.

The Shared Economy

The theory of marginal utility describes how consumers choose between goods. However, marginal utility has also found application in a wide range of weightier subjects. For example, marginal utility can be used in the allocation of resources in healthcare programmes. This paper posits that marginal utility is also applicable in the allocation of the national income among corporations, government, and households. Using data from the UK Office for National Statistics, this paper finds that for the most part of the decade, from 2009 to 2018, household disposable income fell short of what might be considered an optimal share of the national income.

Power Theory of Exchange and Money

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.

Power Theory of Exchange and Money

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.

Accounting for Inequality Aversion Can Justify the 2◦ C Goal

Impact assessment models are a tool largely used to investigate the benefit of reducing polluting emissions and limiting the anthropogenic mean temperature rise. However, they have been often criticised for suggesting low levels of abatement. Countries and regions, that are generally the actors in these models, are usually depicted as having standard concave utility functions in consumption. This, however, disregards a potentially important aspect of environmental negotiations, namely its distributive implications. The present paper tries to fill this gap assuming that countries\regions have Fehr and Schmidt (1999) (F&S) utility functions, specifically tailored for including inequality aversion. Thereby, we propose a new method for the empirical estimation of the inequality aversion parameters by establishing a link between the well known concept of elasticity of marginal utility of consumption and the F&S utility functions, accounting for heterogeneity of countries/regions. By adopting the RICE model, we compare its standard results with the ones obtained introducing F&S utility functions, showing that, under optimal cooperation, the level of temperature rise is significantly lower in the last scenario. In particular, in the last year of the simulation, the optimal temperature rise is 2.1 ◦ C. Furthermore, it is shown that stable coalitions are easier to be achieved when F&S preferences are assumed, even if the advantageous inequality aversion parameter (altruism) is assumed to have a very low value. However, self–sustaining coalitions are far from reaching the environmental target of limiting the mean temperature rise below 2 ◦ C despite the adoption of F&S utility functions.

St. Petersburg paradox: adoption of decisions on the basis of data mining and development of software in the sphere of business analytics

This article is devoted to analysis of models of St. Petersburg paradox, as well as development of software in the sphere of business analysis. This work is based on mathematical models using theories of probability and games as well as expert survey method. It is demonstrated that the St. Petersburg paradox is a mathematical problem of probability theory with artificial conditions. The influence of this problem on economical theory is exemplified by such provisions as the principle of diminishing marginal utility, the use of expected utility as criterion of decision adoption in uncertain environment, as well as foundations of microeconomics of insurance and risk management, theory of games and some approaches to financial simulation. Adoption of decisions on the basis of the St. Petersburg paradox is analyzed. Review of main decisions of the St. Petersburg paradox and their influence for economic theory has confirmed that the St. Petersburg paradox as a mathematical problem can be used as mathematical model upon implementation of financial simulation. Comparative analysis of available BI solutions has confirmed that most of them propose all major functions, and significant differences can be revealed in penetration of expanded functions.

On the Identifiability of Hierarchical Decision Models

Interpretability is a desirable property for machine learning and decision models, particularly in the context of safety-critical applications. Another most desirable property of the sought model is to be unique or {\em identifiable} in the considered class of models: the fact that the same functional dependency can be represented by a number of syntactically different models adversely affects the model interpretability, and prevents the expert from easily checking their validity. This paper focuses on the Choquet integral (CI) models and their hierarchical extensions (HCI). HCIs aim to support expert decision making, by gradually aggregating preferences based on criteria; they are widely used in multi-criteria decision aiding {and are receiving interest from the} Machine Learning {community}, as they preserve the high readability of CIs while efficiently scaling up w.r.t. the number of criteria. The main contribution is to establish the identifiability property of HCI under mild conditions: two HCIs implementing the same aggregation function on the criteria space necessarily have the same hierarchical structure and aggregation parameters. The identifiability property holds even when the marginal utility functions are learned from the data. This makes the class of HCI models a most appropriate choice in domains where the model interpretability and reliability are of primary concern.

Rediscovering Use Value

This chapter rediscovers use value as an essential category for understanding commodification and capitalism more generally. The distinction between use value and exchange value goes back to ancient Greek philosophy and it played an important role in classical political economy. However, with the invention of marginal utility in the late nineteenth century, use value moved from the center to the fringes of economic thinking. Even where it survived, such as in Marxist scholarship, there was considerable disagreement about the role of use value in a critical political economy. The chapter, furthermore, explores the value of nature and by doing so unveils the shortcomings of the concept of marginal utility. One problem is that marginal utility denies the existence of collective value. Following Polanyi, the chapter argues that products not only have individual value, but also have a social and ecological utility. And social and ecological utility can differ considerably from individual valuation.