Funkcja użyteczności — krytyka

The utility function has long been the main tool used by many economists due to the mathematization of economics. Some textbooks on mathematical economics state that the application of mathematics in economics imposes greater rigor, precision, and transparency of assumptions, not significantly different from the non-mathematical method. When analyzing utility function, it can be noticed that its application influences the economic analysis by imposing certain behaviors on people and giving them a mechanical character, primarily by introducing a constant relationship between the goods or goals considered by the person. For this reason, it is almost impossible to take into account the real uncertainty in theoretical research, which overly mechanizes the description of decision-making and economic processes.

Turnpike Properties for Dynamical Systems Determined by Differential Inclusions

In this paper, we study the turnpike phenomenon for trajectories of continuous-time dynamical systems generated by differential inclusions, which have a prototype in mathematical economics. In particular, we show that, if the differential inclusion has a certain symmetric property, the turnpike possesses the corresponding symmetric property. If we know a finite number of approximate trajectories of our system, then we know the turnpike and this information can be useful if we need to find new trajectories of our system or their approximations.

A Strategic Approach to Russian Media System Analysis: Defining Mission, Values and Priorities

Modern media has transformed into a full-fledged industry, embedded in the national economy and inextricably linked with other industries. The strong dependence between the main economic indicators of the media industry and macroeconomic indicators determines the importance of a long-term media strategy. A successful strategy of media system development may improve the national economy and ensure social prosperity in the sense of Aristotelian eudaimonia. The research objective was to develop a new methodology for media strategizing with its mission, values, objectives, and strategic priorities. The study was based on strategy theory, media theory, mathematical economics, econometric methods of strategic media monitoring, and a new method of game-theoretic models of the three-sided market. The object of strategizing was a complex multi-level environment formed by media institutions in their interaction with each other and society, media market, infrastructure, manufacturers, developers, and distributors. The Russian media system was subjected to a primary OTSW analysis, which revealed five priorities. The author developed a quantitative assessment methodology for each priority. The research is a foundation for a separate interdisciplinary discipline “Theory of Media Strategy”.

On Some Aspects of the Examination in Econometrics

Teaching econometrics has been studied by a number of researchers, however, there is little information available on the quality of examination and on simplification of tests for demonstration the high-quality knowledge by students in concrete topics of econometrics or mathematical economics.One can note the following main goals of studying the basics of mathematical economics or econometrics by students: forming the notions of mathematical model and of modeling economic processes and phenomena; understanding a role of using mathematical models for economics research and obtaining scientific results; formatting skills for constructing mathematical models in economics, for solving economics problems by mathematical modeling.The main goal of this paper is to simplify test tasks, is to help to students to demonstrate the high-quality knowledge in certain areas of mathematical economics, and also is to construct a system of testing tasks, in which the emphasis was placed on the knowledge and understanding of an algorithm of solving the problem.In the present paper, to quality examine the student knowledge in the basics of mathematical economics, a certain system of tests was constructed and is considered. The main attention is also given to algorithms and techniques of solving some tasks (problems) of mathematical economics. The following topics of mathematical economics are viewed: constructing mathematical models of linear programming, the input-output model, the Monge-Kantorovich transportation problem, the simplex method of linear programming, the graphic method of linear and nonlinear programming, the method of Lagrange multipliers in mathematical optimization. Some primary basic results of studying linear programming, nonlinear programming, and the input-output model are noted.A new system of tests that satisfies the aim of this paper is modeled. The described tests require less time for solving than usual tasks. Here we do not focus on the repetition of auxiliary mathematical knowledge and arithmetic skills. These tests are simplified versions of standard tasks and help students to demonstrate knowledge in the mentioned topics of mathematical economics. The tasks are focused only on the knowledge of basic formulas, techniques, and connections between mathematical objects, economic systems, and their elements.

Foundations of Contemporary Economics: Harold Hotelling on Location and Exhaustible Resources

Harold Hotelling is an influential statistician working in the field of economic theory at the beginning of the 20th century. His contributions to economics are trailblazing and open new topics for economic and business analysis. His best-known work is his solution to the problem of exhaustible resources. He also triggered the exploration of spatial economics and the analysis of product differentiation through his solution of the optimal location of producers in a duopoly. Less known, but important, are his contributions to the development of modern neoclassical microeconomic theory. Hotelling is also one of the scientists who initiated the turn towards mathematical economics in the 1950s. In this paper we provide an introduction of his groundbreaking work on economic theory.

Solution of the system of nonlinear PDEs characterizing CES property under quasi-homogeneity conditions

The constant elasticity of substitution (CES for short) is a basic property widely used in some areas of economics that involves a system of second-order nonlinear partial differential equations. One of the most remarkable results in mathematical economics states that under homogeneity condition i.e. the production function is a homogeneous function of a certain degree, there are no other production models with the CES property apart from the famous Cobb–Douglas and Arrow–Chenery–Minhas–Solow production functions. In this paper we generalize this classification result to a much wider framework of production functions under quasi-homogeneity conditions, showing in particular the existence of three new classes of production models with the CES property.

A Weak Turnpike Property for Perturbed Dynamical Systems with a Lyapunov Function

In this work, we obtain a weak version of the turnpike property of trajectories of perturbed discrete disperse dynamical systems, which have a prototype in mathematical economics.

Strict Rules of Free Competition (about The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2020)

Studying the research results by Nobel prize-winning economists is a fundamentally important task for determining the most promising areas of development of Russian economic science. The author traces the connections between all these works and their predecessors’ work, many of whom were also awarded the Nobel prize in economics. Three lines of development of the predecessors’ achievements are identifid: information asymmetry, limited rationality, the design of market mechanism and new institutionalism. The article does not address the problems of auction theory related to its formal justifiation, which is part of mathematical economics and game theory. However, it is noted that this is an essential part of the laureates’ achievements. The article’s main conclusions are that the prize received for “improving the theory of auctions” fis into the broader economic research context. The winners solved the problems of maintaining free competition and reducing the market’s likelihood of monopolization. The author pays special attention to the results of the empirical analysis of actually implemented auctions. This analysis is divided into three parts, corresponding to the three stages of each auction: starting problems (distrust, the reputation of participants, etc.), the course of the auction (behaviour of participants and results, in particular, the “winner’s curse”.

El rechazo de Carl Menger a la economía matemática. Una aproximación

This article tries, on the one hand, to analyse why Carl Menger, the Austrian School of Economics founder, rejected the use of mathematics as a tool for economic theory and the scope of his opposition. On the other hand, the article considers the advances in mathematical science in order to question at what point Menger’s methodology is still sounding, or on the contrary, if these new developments allow a wider use of mathematical economics maintaining, at the same time, the Austrian methodological assumptions. Nowadays, the Multicriteria Decision Theory has emerged as a powerful tool to assist in the process of searching for decisions, which best satisfy a multitude of conflicting objectives.These advancements may question the persistent opposition to mathematical economics not so much from Carl Menger but from his successors. Key words: Economic methodology, Austrian School of Economics, Carl Menger, mathematical economics, Multicriteria Decision Theory. JEL Classification: B1, B2, B4, C6, C8. Resumen: El objetivo de este documento de trabajo es, por un lado, analizar los motivos que llevaron al fundador de la Escuela Austriaca, Carl Menger, a rechazar el empleo de las matemáticas como herramienta de la teoría económica y el alcance de esta oposición. Por otra parte, se trata de considerar si actualmente esta postura metodológica sigue siendo válida o, por el contrario, los avances en la matemática permiten un empleo más amplio en la teoría económica manteniendo los postulados mengerianos. Hoy en día, la matemática también ha evolucionado y han aparecido disciplinas como la Teoría de la Decisión Multicriterio que intenta solucionar los problemas que afloran en la toma de decisiones cuando existen objetivos múltiples y, a menudo, conflictivos entre sí. Estos avances ponen sobre la mesa el recalcitrante rechazo hacia las matemáticas, no tanto de Menger, como de sus seguidores. Palabras clave: Metodología de la economía, Escuela Austriaca de Economía, Carl Menger, economía matemática, Teoría de la Decisión Multicriterio.