Mathematical Economics Research Articles

Envy-free division via configuration spaces

The classical approach to envy-free division and equilibrium problems arising in mathematical economics typically relies on Knaster-Kuratowski-Mazurkiewicz theorem, Sperner's lemma or some extension involving mapping degree. We propose a different and relatively novel approach where the emphasis is on configuration spaces and equivariant topology, originally developed for applications in discrete and computational geometry (Tverberg type problems, necklace splitting problem, etc.). We illustrate the method by proving several counterparts and extensions of the classical envy-free division theorem of David Gale, where the emphasis is on preferences allowing the players to choose degenerate pieces of the cake.

The Weak Hybrid Equilibria of an Exchange Economy with a Continuum of Agents and Externalities

Abstract Inspired by Zhao, J. 1996. “The Hybrid Equilibria and Core Selection in Exchange Economies with Externalities.” Journal of Mathematical Economics 26 (4): 387–407, Askoura, Y. 2011. “The Weak-Core of a Game in Normal Form with a Continuum of Players.” Journal of Mathematical Economics 47: 43–7, Askoura, Y. 2017. “On the Core of Normal Form Games with a Continuum of Players.” Mathematical Social Sciences 89: 32–42, Yang, Z. 2020. “The Weak α-core of Exchange Economies with a Continuum of Players and Pseudo-utilities.” Journal of Mathematical Economies 91: 43–50 and Yang, Z., and X. Zhang. 2021. “A Weak α-core Existence Theorem of Games with Nonordered Preferences and a Continuum of Agents.” Journal of Mathematical Economics 94: 102464, we establish an exchange economy with externalities and a continuum of agents. We define the weak hybrid equilibrium in this model and prove the existence theorem under the regular conditions. Furthermore, we analyze the relation between the set of hybrid equilibria and the set of competitive equilibria in an exchange economy without externalities and with a continuum of agents.

Utility Maximization Analysis of an Organization: A Mathematical Economic Procedure

In the society utility is the vital concept, especially in mathematical economics. It is considered as the tendency of an object or action that increases or decreases overall happiness. In social sciences, the property of a commodity that enables to satisfy human wants is called utility. This paper has tried to operate utility maximization policy of an organization by considering two constraints: budget constraint and coupon constraint. To develop the maximization policy of utility function, the techniques of multivariate calculus are used. In this study four commodity variables are used to operate the mathematical analysis efficiently. In this article Lagrange multiplier technique is applied to achieve optimal result throughout the study.

Socio-Economic Analysis of Household Energy Security: Evidence from 3D Energy Losses Surface Maps (ELSMs) of a Town Using Conjuncture of Factors Matrix, Digital and Mathematical Analysis

Pakistan is facing perpetual and worsening energy crisis. For vision 2025, the most important litmus test is to overcome energy crisis and ensure energy security by imaginative and innovative energy alternatives. In the same context, scientists, experts and researchers have been focusing on renewables and non-renewable energy generation alternatives, but have largely ignored the flip side. The extravagant use of energy, unlawful connections and losses in distribution system are contributors to ongoing energy crisis. For energy security in a developing country like Pakistan, elimination of energy losses seems a viable option, alongside generation of energy. Therefore, there is a need to have socio-economic analysis of energy losses. In this paper, energy losses for electricity were estimated for Lali Bagh Town of Peshawar, Khyber Pakhtunkhwa Province using a versatile and innovative socio-economic framework. This framework was based on factors matrix comprising socio-economic, environmental and energy factors pertaining to households. Within the factors matrix approach, three methods were used for analysis of energy losses; the statistical analysis to obtain trend and ratings of electricity losses, digital analysis of the data by computer assisted qualitative data analysis software (CAQDAS) to get the digitally iterated and attenuated models along with representative equations and mathematical analysis of equations by Newton-Leibniz integration process to obtain numerical value of the ratings. Based on the results obtained, three dimensional energy losses surface maps (ELSMs) were prepared for Lali Bagh Town of Peshawar, Khyber Pakhtunkhwa Province. At the end, policy recommendations have been given in the context of vision 2025. Paper is a unique combination of theoretical, mathematical and digital cum spatial economics. JEL Classification: O22, Q21, Q31, Q41. Keywords: Socio-economic, Analysis, Energy, Security, Electricity, Losses, Factors, Matrix, Digital, Maps.

Posteriors in Limited Time

This paper obtains a measure-theoretic restriction that must be satisfied by a prior probability measure for posteriors to be computed in limited time. Specifically, it is shown that the prior must be factorizable. Factorizability is a set of independence conditions for events in the sample space that allows agents to calculate posteriors using only a subset of the dataset. The result has important implications for models in mathematical economics and finance that rely on a common prior. If one introduces the limited time restriction to Aumann’s famous Agreeing to Disagree setup, one sees that checking for factorizability requires agents to have access to every event in the measure space, thus severely limiting the scope of the agreement result.

Closedness under addition for families of quasimonotone operators

In the last two decades, several properties of operators that are weaker than monotonicity have received attention by researchers from many areas including mathematical economics, with the goal to develop new tools applicable in convex analysis and related topics. This paper puts in perspective notions that are extensions of monotoniticity but not beyond quasimonotonicity like pseudomonotonicity, semistrict quasimonotonicity, strict quasimonotonicity and proper quasimonotonicity, and discusses systematically when the sum of two operators satisfying one of those properties, inherits the same property. The case of properly quasimonotone operators deserves a special attention since this notion, being stronger than quasimonotonicity, suffices to obtain many results, including the solvability of variational inequality problems. Several examples showing the optimality in some sense of our results, are presented.

Endpoint Functions: Mathematical Apparatus and Economic Applications

Endpoint Functions: Mathematical Apparatus and Economic Applications

Sensitivity Analysis Among Commodities and Coupons During Utility Maximization

In mathematical economics utility is the vital concept. In the society utility is considered as the tendency of an object or action that increases or decreases overall happiness. This study tries to discuss sensitivity analysis during utility maximization investigation. Actually, the method of Lagrange multipliers is a very useful and powerful technique in multivariable calculus. In this paper mathematical formulation of Lagrange multipliers is derived through the optimal devise. This article has taken attempts to find relations among commodities and coupons when the prices of different commodities increase or decrease.

Simulation of disequilibrium and chaos in aggregates of disposable income, wealth, and consumption in EU macroeconomics using nonlinear dynamic analysis

Economic disequilibrium theory (DT) more realistically represents modern macroeconomic systems than general equilibrium theory. DT coupled with applied mathematical economics and nonlinear dynamical analysis generates multi-dimensional phase spaces. Interdependencies of endogenous variables in state space create a flow of different and “parallel economic realities,” which depend on the initial conditions. By modeling variable changes using the nonlinear least squares (NLLS) method, we define the first-order nonlinear ordinary differential equation (NODE) system. The NODE system is impossible to solve analytically. The numerical solution and visualization requires the MATLAB software package, combined with its specialized applications pplane (two-dimensional (2D)) and MATCONT (three-dimensional (3D)). By analyzing the evolution of flow operators, we can predict the future qualitative behavior of the entire system, determine the model-optimal values, and perform inverse modeling for variables. The obtained data advocate better and more stable macroeconomic paths that economic policymakers can pursue. The proposed methodology’s boundaries have strong links to chaos theory. Chaotic behavior can arise after a certain number of periods. We found very high computation accuracy, transformation of discrete variables to continuous functions, and the implementation of high-order polynomial data fitting offset its effects in part and to some reasonable degree.

Turnpike phenomenon for a class of optimal control problems with a Lyapunov function

ABSTRACT In this paper we prove several turnpike results for trajectories of discrete disperse dynamical systems introduced in 1980 by A. M. Rubinov, which have a prototype in mathematical economics.

The Accounting and mathematical methods of the economy in Libya

The paper aims to some economists’ state that accounting and mathematical economics deserve support just like other forms of mathematics, particularly its neighbors in mathematical optimization and mathematical statistics and increasingly in theoretical computer science.

Physical Exercise Effect Evaluation Based on Data Envelopment Analysis

Data envelopment analysis is a new field of interdisciplinary research in operations research management science and mathematical economics. Data envelopment analysis uses mathematical programming to evaluate the relationship between decision-making units with multiple inputs and outputs (abbreviated as DMU). Effectiveness (DEA is effective) is to judge whether DMU is located on the "frontier surface" of the production possibility set. This paper proposes a method for evaluating the effect of physical exercise based on the data envelopment analysis method. First, a multiple logistic regression analysis was performed to examine the relationship between physical exercise effects and physical exercise outcomes. Secondly, the exercise combination efficiency analysis based on data envelopment analysis is used to select the physical exercise time optimally. Then use the historical data for training to obtain the evaluation effect. The results show that the data envelopment analysis method can evaluate the effect of physical exercise well and can also provide decision-making strategies related to sports performance.

Milton Friedman and the Road to Monetarism: A Review Essay

Milton Friedman and the Road to Monetarism: A Review Essay

Arguing with Numbers: The Intersection of Rhetoric and Mathematics

Arguing with Numbers: The Intersection of Rhetoric and Mathematics

The Development of Digital Books Aided Augmented Reality (AR) to Improve Self Efficacy in Favor of Distance Learning

This study aims to create a Digital Book mathematical economics to improve the self-efficacy of students, where Media Powtoon, Augmented Reality (AR) and application Kahoot already present in the design of digital books. To see the feasibility of the book, the attractiveness of the book and the effectiveness of using AR-assisted Economic Mathematics Books to increase student self-efficacy. The research method used in this research is the development of the ADDIE model which has five stages of research implementation, namely Analysis, Design, Develop, Implement, and Evaluate. Through these five stages, researchers will develop an AR-assisted Mathematics Economics book. In this book, several applications will collaborate in providing the presentation of the material in the form of learning videos using the application Powtoon, displaying animations with Augmented Reality (AR) and evaluating learning outcomes using the application Kahoot, so that this book can help the distance lecture process become more interesting. and effective both in presenting the material, the media used to evaluate learning in lectures. The results of this study show that the Digital Book was developed to conclude that it is feasible, interesting and effective to be used as a distance learning medium and helps students in increasing self-efficacy in learning.

New Studies of Modern Economic Though

The article presents the results of research on the latest stage of world economic thought. The views of Nobel laureates in economics are analyzed: R. Mandell, a specialist in world economic relations, B. Holmstrom, a representative of the third generation of neo-institutionalism, P. Romer, a developer of endogenous growth models, E. Duflo, a prominent representative of the modern theory of development, as well as mathematical economists. E. Maskin, R. Myerson, E. Roth, R. Wilson. The views of the influential Japanese economist H. Yoshikawa are interpreted separately.

The Intermediate Value Theorem and Decision-Making in Psychology and Economics: An Expositional Consolidation

On taking the intermediate value theorem (IVT) and its converse as a point of departure, this paper connects the intermediate value property (IVP) to the continuity postulate typically assumed in mathematical economics, and to the solvability axiom typically assumed in mathematical psychology. This connection takes the form of four portmanteau theorems, two for functions and the other two for binary relations, that give a synthetic and novel overview of the subject. In supplementation, the paper also surveys the antecedent literature both on the IVT itself, as well as its applications in economic and decision theory. The work underscores how a humble theorem, when viewed in a broad historical frame, bears the weight of many far-reaching consequences; and testifies to a point of view that the apparently complicated can sometimes be under-girded by a most basic and simple execution.

On group structures of strategic-form games

There are two recognized classes of strategic-form symmetric games, both of which can be conveniently defined through the corresponding player symmetry groups. We investigate the basic properties of these groups and several related concepts. We generalize the notion of coveringness and adapt their results to characterize these player symmetry groups. We study the relationships between the coveringnesses of various symmetry groups. Our results demonstrate that these symmetry groups have rich mathematical structures that are of game theoretical and economic interests.

Where Did John von Neumann's Mathematical Economics Come From?

Abstract This article shows, based on archival material, where and how von Neumann's mathematical economics evolved from the realization around 1932 that there existed a formal analogy between economics and games to the conviction in 1940 that the analogy between homo economicus and homo ludens was more than a formal one. It also shows that von Neumann's application of games to economics echoed in nontrivial ways scholarly discussions of a seminar organized in Fuld Hall at the Institute for Advanced Study in Princeton by von Neumann's historian colleague Edward Mead Earle. In the Earle seminar, an international community of historians and political and social scientists concerned with stability, strategy, and security issues investigated war as a social phenomenon from the perspectives of international relations and military history. In some of their discussions, homo ludens might have appeared as a category that should be taken more seriously in social theory. This article argues that the Earle seminar discussions likely helped convince von Neumann in 1940 that the analogy between economics and games that he had found in 1932 was meaningful in a scholarly way to history, political science, and social science. By putting the von Neumann–Earle seminar connection in the backdrop of Theory of Games and Economic Behavior, this article briefly bridges some interwar, World War II, and Cold War developments related to von Neumann's influence in economics and social science.

Continuity postulates and solvability axioms in economic theory and in mathematical psychology: a consolidation of the theory of individual choice

This paper presents four theorems that connect continuity postulates in mathematical economics to solvability axioms in mathematical psychology, and ranks them under alternative supplementary assumptions. Theorem 1 connects notions of continuity (full, separate, Wold, weak Wold, Archimedean, mixture) with those of solvability (restricted, unrestricted) under the completeness and transitivity of a binary relation. Theorem 2 uses the primitive notion of a separately continuous function to answer the question when an analogous property on a relation is fully continuous. Theorem 3 provides a portmanteau theorem on the equivalence between restricted solvability and various notions of continuity under weak monotonicity. Finally, Theorem 4 presents a variant of Theorem 3 that follows Theorem 1 in dispensing with the dimensionality requirement and in providing partial equivalences between solvability and continuity notions. These theorems are motivated for their potential use in representation theorems.