Mathematical Models in Economics
Mathematical Models in Economics
Contributor(s): Laura Ungureanu (Editor)
Subject(s): Economy, National Economy, Supranational / Global Economy, Micro-Economics
Published by: ASERS Publishing
Keywords: modelling; economical dynamics; optimal growth; algorithms in macroeconomic policy; statistical model extension; neural network
Summary/Abstract: Mathematical Models in Economics - has been put together with the purpose of giving an example of the possibilities to use specific modern methods (optimal control, neural networks, data envelopment analysis, wave equations, dynamical systems) that can be put into application on a very large scale, in numerous key-areas of the field of economics. Various analysis regarding the static case are made for a more profound understanding of the correlations that arise between different variables in micro and macroeconomics, and they are made as well taking into account the dynamic case, which brings this paper even closer to reality. Furthermore, another subject rendered by the book is that of economic mechanisms from a stochastic point of view (this is especially explained in the chapters regarding the game theory) which prove once more the random character of economic variables. From the multitude of mathematical models regarding the dynamic of different economic variables, this book includes: allocation models, regional growth, dynamic models of the cycle of commerce, others models concerning the crisis of the Euro zone, decision making models or advertising models. While some may be thoroughly analyzed, others reflect only a summarized matter of the problem.
Series: Mathematica ASERS Collection
- Print-ISBN-13: 978-606-92386-6-0
- Page Count: 197
- Publication Year: 2012
- Language: English
Economic Applications of Optimal Control Theory: Regional Growth and Allocation of Investment
Economic Applications of Optimal Control Theory: Regional Growth and Allocation of Investment
(Economic Applications of Optimal Control Theory: Regional Growth and Allocation of Investment)
- Author(s):Stilianos Alexiadis
- Language:English
- Subject(s):Economy
- Page Range:9-26
- No. of Pages:18
- Keywords:regional growth; optimal control theory; optimal growth
- Summary/Abstract:Optimal growth and allocation of investment across spatial units - that is to say regions, constitute two major applications of the Optimal Control Theory in regional economics and economic geography. This chapter provides a detailed examination of the process through which the path of optimal regional growth and the allocation of investment can be determined within the framework of Optimal Control Theory. This theory describes the process of maximizing a given objective function. When the focus is set upon a spatial economy, the objective function may include a single aim - such as maximizing aggregate growth. Nevertheless, it is possible to detect cases in which the objective function includes two different, even competitive aims: promotion of aggregate growth and interregional equity. This case is also examined in this chapter.
- Price: 25.00 €
Game Complete Analysis of Bertrand Duopoly
Game Complete Analysis of Bertrand Duopoly
(Game Complete Analysis of Bertrand Duopoly)
- Author(s):David CARFI, Emanuele Perrone
- Language:English
- Subject(s):Economy
- Page Range:27-49
- No. of Pages:23
- Keywords:duopoly; normal form games; microeconomic policy; complete study; bargaining solutions
- Summary/Abstract:In this chapter, we have applied the Complete Analysis of Differentiable Games (introduced by David Carfì in 2009 and 2010) and already employed by himself and others in Carfi, and Schilliro,2011; Carfi, and Ricciardello, 2010; Carfi, 2009) to the classic Bertrand Duopoly’s (1883) classic oligopolistic market in which two enterprises are producing the same commodity and selling it in the same market. In this classic model, in a competitive background, the two enterprises employ as possible strategies the unit prices of their product, contrary to the Cournot duopoly, in which the enterprises decide to use the quantities of the commodity produced as strategies. The main solutions proposed in the literature for this kind of duopoly (as in the case of Cournot duopoly) are the Nash equilibrium and the Collusive Optimum, without any subsequent critical exam about these two kinds of solutions. The absence of any critical quantitative analysis is due to the relevant lack of knowledge regarding the set of all possible outcomes of this strategic interaction. On the contrary, by considering the Bertrand Duopoly as a differentiable game (games with differentiable payoff functions) and studying it by the new topological methodologies introduced by David Carfì, we obtain an exhaustive and complete vision of the entire payoff space of the Bertrand game (also in asymmetric cases with the help of computers) and this total view allows us to critically analyze the classic solutions and to find other ways of action to select Pareto strategies. In order to illustrate the application of this topological methodology to the considered infinite game, several compromise pricing-decisions have been considered, and we show how the complete study gives a real and extremely extended comprehension of the classic model.
- Price: 25.00 €
Asymmetric Bertrand Duopoly:Game Complete Analysis by Algebra System Maxima
Asymmetric Bertrand Duopoly:Game Complete Analysis by Algebra System Maxima
(Asymmetric Bertrand Duopoly:Game Complete Analysis by Algebra System Maxima)
- Author(s):David CARFI, Emanuele Perrone
- Language:English
- Subject(s):Economy
- Page Range:50-72
- No. of Pages:13
- Keywords:Asymmetric Bertrand Duopoly; Normal-form Games; Software algorithms in Microeconomic Policy; Complete Analysis of a normal-form complex interaction; Pareto optima; valuation of Nash equilibriums
- Summary/Abstract:In this chapter we apply the Complete Analysis of Differentiable Games (introduced by D. Carfì in 2009 and 2010) and already employed by himself and others in Carfi, and Schiliro, 2011; Carfi, and Ricciardello, 2010 and Carfi, 2009) and some new algorithms employing the software wxMaxima 11.04.0 in order to reach a total knowledge of the classic Bertrand Duopoly (1883), viewed as a complex interaction between two competitive subjects, in a particularly difficult asymmetric case. The software wxMaxima is an interface for the computer algebra system Maxima. Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, systems of linear equations, polynomials, and sets, vectors, matrices. Maxima yields high precision numeric results by using exact fractions, arbitrary precision integers, and variable precision floating point numbers. Maxima can plot functions and data in two and three dimensions. The Bertrand Duopoly is a classic oligopolistic market in which there are two enterprises producing the same commodity and selling it in the same market. In this classic model, in a competitive background, the two enterprises employ as possible strategies the unit prices of their products, contrary to the Cournot duopoly, in which the enterprises decide to use the quantities of the commodity produced as strategies. The main solutions proposed in literature for this kind of duopoly (as in the case of Cournot duopoly) are the Nash equilibrium and the Collusive Optimum, without any subsequent critical exam about these two kinds of solutions. The absence of any critical quantitative analysis is due to the relevant lack of knowledge regarding the set of all possible outcomes of this strategic interaction. On the contrary, by considering the Bertrand Duopoly as a differentiable game (games with differentiable payoff functions) and studying it by the new topological methodologies introduced by D. Carfì, we obtain an exhaustive and complete vision of the entire payoff space of the Bertrand game (this also in asymmetric cases with the help of wxMaxima 11.04.0) and this total view allows us to analyze critically the classic solutions and to find other ways of action to select Pareto strategies, in the asymmetric cases too. In order to illustrate the application of this topological methodology to the considered infinite game, several compromise pricing-decisions are considered, and we show how the complete study gives a real extremely extended comprehension of the classic model.
- Price: 25.00 €
Crisis in the Euro Area: Co-opetitive Game Solutions as New Policy Tools
Crisis in the Euro Area: Co-opetitive Game Solutions as New Policy Tools
(Crisis in the Euro Area: Co-opetitive Game Solutions as New Policy Tools)
- Author(s):David CARFI, Daniele Schiliro
- Language:English
- Subject(s):Economy
- Page Range:73-92
- No. of Pages:20
- Keywords:European Monetary Union; co-opetitive games; macroeconomic policy; bargaining solutions
- Summary/Abstract:The crisis within the euro area has become frequent during 2010. First, it was the Greek economy that faced a default problem of its sovereign debt; in November, it was Ireland that has been in a serious financial situation at the verge of collapse causing difficulties to the euro. In this contribution, we focus on the Greek crisis and we suggest, through a model of co-opetition based on game theory and conceived at a macro level, feasible solutions in a cooperative perspective for the divergent interests which drive the economic policies in Germany and Greece, with the aim of improving the position of Greece, Germany and the whole euro area, also making a contribution to expand the set of macroeconomic policy tools. By means of our general analytical framework of coopetition, we show the strategies that could generate feasible solutions in a cooperative perspective for Germany and Greece, where these feasible solutions aim at offering a win-win outcome for both countries, letting them share the pie fairly within a growth path represented by a non-zero sum game.A remarkable analytical result of our work consists in the determination of the win-win solution by a new selection method on the transferable utility Pareto boundary of the co-opetitive game.
- Price: 25.00 €
Macroeconomics in Wave-Equation Models for Default Probability
Macroeconomics in Wave-Equation Models for Default Probability
(Macroeconomics in Wave-Equation Models for Default Probability)
- Author(s):Han GEURDES
- Language:English
- Subject(s):Economy
- Page Range:93-104
- No. of Pages:12
- Keywords:probability of default; statistical model extension; macroeconomic variables; test for coordinate independence
- Summary/Abstract:This chapter investigates how to adapt existing probability of default (PD) models such as, fore.g. macroeconomic variables and risk variables, and investigate how they can determine together the PD. A difference is made between statistics at default and before default during normal operations. An additional matter is how to test whether or not the probability of default is independent of the chosen reference frame. This translates into the requirement that a phenomenon such as default must preferably be independent of transformations in the macroeconomic and risk variables. Affine coordinate transformations also employed in the theory of special relativity are used to find out if a default in economical variables is relatively independent of its set of coordinates.
- Price: 25.00 €
Crude Oil Price Modeling: a Multi Scale Wavelet Neural Network Perspective
Crude Oil Price Modeling: a Multi Scale Wavelet Neural Network Perspective
(Crude Oil Price Modeling: a Multi Scale Wavelet Neural Network Perspective)
- Author(s):Rania Jammazi, Chaker Aloui
- Language:English
- Subject(s):Economy
- Page Range:105-131
- No. of Pages:27
- Keywords:Harr à Trous wavelet; neural network; back propagation; crude oil price forecasting; activation function; input-hidden nodes
- Summary/Abstract:Oil price prediction has usually proved to be an intractable task, due to the intrinsic complexity of the oil market mechanism. In addition, the recent oil shock and its consequences re-launch the debate on understanding the behavior underlying the expected oil prices. Combining the dynamic properties of multilayer back propagation neural network and the recent Harr à Trous wavelet decomposition, a Hybrid model HTW-MPNN is implemented to achieve prominent modeling of crude oil price. While recent studies focus on the determination of the best model by comparing various neural architectures or applying several decomposition techniques to the ANN, the new insight of this chapteris to target the issue of the transfer function selection. Based on the work of authors Yonaba H. Anctil F. and Fortin, V., from the year 2010 “Comparing Sigmoid Transfer Functions for Neural Network Multistep Ahead Stream flow forecasting”(published in the Journal of Hydrologic Engineering, April, 275-283), we use three variants of activations function namely sigmoid, bipolar sigmoid and hyperbolic tangent in order to test the model’s flexibility. Furthermore, the forecasting robustness is checked through several levels of input-hidden nodes. Comparatively, simulation results of Hybrid model performs better than the conventional BPNN.
- Price: 25.00 €
The Complexity of Economic Systems. Nonlinear Dynamic Models
The Complexity of Economic Systems. Nonlinear Dynamic Models
(The Complexity of Economic Systems. Nonlinear Dynamic Models)
- Author(s):Laura Ungureanu
- Language:English
- Subject(s):Economy
- Page Range:132-166
- No. of Pages:35
- Keywords:complexity; nonlinear theory; economic evolution; equilibrium; economical dynamics; decision modeling; nonlinear dynamics
- Summary/Abstract:We are witnessing now the beginning of a process of synthesis among the developmental economic theories and the new theory of complexity.Mathematics, the science of spatial forms and quantitative relations, is considered to be the basis of all other sciences. In the analyses dynamics macroeconomic area we can observe a big variety of methods and techniques for research that fluctuates from economy and financial date. Because a lot of economical models were elaborated in the last years, in this chapter we propose to present some nonlinear techniques which can be used in the economic analyses. For example, a complex way to evidence the economic cycles is to determine limits cycles for the dynamical system which model the economic phenomenon.
- Price: 25.00 €
Developing Quality-Driven Production Equilibria
Developing Quality-Driven Production Equilibria
(Developing Quality-Driven Production Equilibria)
- Author(s):Panagiotis D. Zervopoulos, Francisco VARGAS, Gang CHENG
- Language:English
- Subject(s):Economy
- Page Range:167-185
- No. of Pages:19
- Keywords:Data Envelopment Analysis (DEA); context-dependent DEA; effectiveness; efficiency; perceived quality
- Summary/Abstract:Operational effectiveness goes beyond efficiency while it incorporates exogenous variables, non-controllable by the service units. Effectiveness is a fundamental driver for the success of an operational unit within a competitive environment. In this context, we seek to identify the active units that meet both the high or technical efficiency and the perceived high quality criteria. We also aim to develop a roadmap for effectiveness for every operational unit and we consider the feasibility of the results produced by the effectiveness assessment process in the short run. The target values uncovered by comparative optimization techniques (e.g. Data Envelopment Analysis) for efficiency and effectiveness measurement generally have limited managerial implications due to production constraints, available resources, and legal status. This chapter introduces a modified Quality-driven –Efficiency-adjusted Data Envelopment Analysis (MQE-DEA) model to assess effectiveness and provide a step-by-step path to achieve high quality and high efficiency in every operational unit under evaluation. The MQE-DEA model has particular applicability to the effectiveness assessment of homogeneous service units in which an inverse relationship underlies the two dimensions of effectiveness embraced in this study (e.g. bank branches, restaurant chain stores, governmental onestop-shops).
- Price: 25.00 €
