Mathematical Economics And The Dynamics Of Capitalism
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| Author | : Peter Flaschel |
| Publisher | : Routledge |
| Total Pages | : 385 |
| Release | : 2016-04-01 |
| Genre | : Business & Economics |
| ISBN | : 1134057571 |
Richard Goodwin was a pioneer in the use of mathematical tools to understand the dynamics of capitalist economies. This book contains contributions which focus on the rigorous extension of Goodwin’s modelling of macro-dynamics and the micro-structures underlying them, and also research with a wider perspective related to Goodwin’s vision of an integrated Marx-Keynes-Schumpeter (M-K-S) system of the dynamics of capitalist economies. The variety of approaches in this book range from detailed business cycle analyses to Schumpeterian processes of creative destruction. They include thorough theoretical analysis of delayed dynamical systems. empirical studies of Goodwin’s classical growth cycle model and the integration of Keynesian aspects of effective demand and of financial mechanisms that impact the real macro-economy. micro-economic structural analysis. expectations driven aspects of micro-founded business cycle modelling
| Author | : Peter Flaschel |
| Publisher | : Routledge |
| Total Pages | : 310 |
| Release | : 2016-04-01 |
| Genre | : Business & Economics |
| ISBN | : 113405758X |
Richard Goodwin was a pioneer in the use of mathematical tools to understand the dynamics of capitalist economies. This book contains contributions which focus on the rigorous extension of Goodwin’s modelling of macro-dynamics and the micro-structures underlying them, and also research with a wider perspective related to Goodwin’s vision of an integrated Marx-Keynes-Schumpeter (M-K-S) system of the dynamics of capitalist economies. The variety of approaches in this book range from detailed business cycle analyses to Schumpeterian processes of creative destruction. They include thorough theoretical analysis of delayed dynamical systems. empirical studies of Goodwin’s classical growth cycle model and the integration of Keynesian aspects of effective demand and of financial mechanisms that impact the real macro-economy. micro-economic structural analysis. expectations driven aspects of micro-founded business cycle modelling
| Author | : Emmanuel D. Farjoun |
| Publisher | : Springer Nature |
| Total Pages | : 155 |
| Release | : 2022-04-12 |
| Genre | : Political Science |
| ISBN | : 3030933210 |
This book presents a probabilistic approach to studying the fundamental role of labor in capitalist economies and develops a non-deterministic theoretical framework for the foundations of political economy. By applying the framework to real-world data, the authors offer new insights into the dynamics of growth, wages, and accumulation in capitalist development around the globe. The book demonstrates that a probabilistic political economy based on labor inputs enables us to describe central organizing principles in modern capitalism. Starting from a few basic assumptions, it shows that the working time of employees is the main regulating variable for determining strict numerical limits on the rate of economic growth, the range of wages, and the pace of accumulation under the present global economic system. This book will appeal to anyone interested in how the capitalist mode of production works and its inherent limitations; in particular, it will be useful to scholars and students of Marxian economics. “Emmanuel Farjoun and Moshé Machover, follow up their pathbreaking work on the application of statistical physics methods to political economy in this book with David Zachariah, in which they develop methods for making educated and structured estimates of stylized facts applicable to capitalist economies. There’s a lot for economists and anyone interested in the political economy of capitalism to learn from their reasoning on these issues, including their novel and challenging suggestion of bounds on the rates of increase of use-value productivity of labor, and on the range of variation of the wage share.” Duncan K. Foley, Leo Model Professor of Economics, New School for Social Research
| Author | : V.L. Makarov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 268 |
| Release | : 2012-12-06 |
| Genre | : Business & Economics |
| ISBN | : 1461298865 |
This book is devoted to the mathematical analysis of models of economic dynamics and equilibria. These models form an important part of mathemati cal economics. Models of economic dynamics describe the motion of an economy through time. The basic concept in the study of these models is that of a trajectory, i.e., a sequence of elements of the phase space that describe admissible (possible) development of the economy. From all trajectories, we select those that are" desirable," i.e., optimal in terms of a certain criterion. The apparatus of point-set maps is the appropriate tool for the analysis of these models. The topological aspects of these maps (particularly, the Kakutani fixed-point theorem) are used to study equilibrium models as well as n-person games. To study dynamic models we use a special class of maps which, in this book, are called superlinear maps. The theory of superlinear point-set maps is, obviously, of interest in its own right. This theory is described in the first chapter. Chapters 2-4 are devoted to models of economic dynamics and present a detailed study of the properties of optimal trajectories. These properties are described in terms of theorems on characteristics (on the existence of dual prices) and turnpike theorems (theorems on asymptotic trajectories). In Chapter 5, we state and study a model of economic equilibrium. The basic idea is to establish a theorem about the existence of an equilibrium state for the Arrow-Debreu model and a certain generalization of it.
| Author | : Edwin Burmeister |
| Publisher | : CUP Archive |
| Total Pages | : 358 |
| Release | : 1980-11-28 |
| Genre | : Business & Economics |
| ISBN | : 9780521228893 |
Capital theory and dynamics are cornerstones for almost every branch of economics. Except in a fictional world where the economies of yesterday, today, and tomorrow are identical, issues of capital formation and dynamic behaviour must always arise. Although the specialist literature is technically demanding, Professor Burmeister shows that its important results can be understood and their economic significance grasped by those who do not possess the "mathematical literacy" required to follow rigorous proofs. Even if future events are known with certainty, they still influence the current economic state. This is the pure role of time. That future events are not known with certainty adds another complexity. This book focuses mainly on the pure role of time.
| Author | : A. Simonovits |
| Publisher | : Palgrave Macmillan |
| Total Pages | : 318 |
| Release | : 2000-06-05 |
| Genre | : Business & Economics |
| ISBN | : 9780333778180 |
This book contains a concise description of important mathematical methods of dynamics and suitable economic models. It covers discrete as well as continuous-time systems, linear and nonlinear models. Mixing traditional and modern materials, the study covers dynamics with and without optimization, naive and rational expectations, respectively. In addition to standard models of growth and cycles, the book also contains original studies on control of a multisector economy and expectations-driven multicohort economy. Numerous examples, problems (with solutions) and figures complete the book.
| Author | : E. Roy Weintraub |
| Publisher | : Duke University Press |
| Total Pages | : 329 |
| Release | : 2002-05-28 |
| Genre | : Business & Economics |
| ISBN | : 0822383802 |
In How Economics Became a Mathematical Science E. Roy Weintraub traces the history of economics through the prism of the history of mathematics in the twentieth century. As mathematics has evolved, so has the image of mathematics, explains Weintraub, such as ideas about the standards for accepting proof, the meaning of rigor, and the nature of the mathematical enterprise itself. He also shows how economics itself has been shaped by economists’ changing images of mathematics. Whereas others have viewed economics as autonomous, Weintraub presents a different picture, one in which changes in mathematics—both within the body of knowledge that constitutes mathematics and in how it is thought of as a discipline and as a type of knowledge—have been intertwined with the evolution of economic thought. Weintraub begins his account with Cambridge University, the intellectual birthplace of modern economics, and examines specifically Alfred Marshall and the Mathematical Tripos examinations—tests in mathematics that were required of all who wished to study economics at Cambridge. He proceeds to interrogate the idea of a rigorous mathematical economics through the connections between particular mathematical economists and mathematicians in each of the decades of the first half of the twentieth century, and thus describes how the mathematical issues of formalism and axiomatization have shaped economics. Finally, How Economics Became a Mathematical Science reconstructs the career of the economist Sidney Weintraub, whose relationship to mathematics is viewed through his relationships with his mathematician brother, Hal, and his mathematician-economist son, the book’s author.
| Author | : Venkat Venkatasubramanian |
| Publisher | : Columbia University Press |
| Total Pages | : 410 |
| Release | : 2017-08-08 |
| Genre | : Business & Economics |
| ISBN | : 0231543220 |
Many in the United States feel that the nation’s current level of economic inequality is unfair and that capitalism is not working for 90% of the population. Yet some inequality is inevitable. The question is: What level of inequality is fair? Mainstream economics has offered little guidance on fairness and the ideal distribution of income. Political philosophy, meanwhile, has much to say about fairness yet relies on qualitative theories that cannot be verified by empirical data. To address inequality, we need to know what the goal is—and for this, we need a quantitative, testable theory of fairness for free-market capitalism. How Much Inequality Is Fair? synthesizes concepts from economics, political philosophy, game theory, information theory, statistical mechanics, and systems engineering into a mathematical framework for a fair free-market society. The key to this framework is the insight that maximizing fairness means maximizing entropy, which makes it possible to determine the fairest possible level of pay inequality. The framework therefore provides a moral justification for capitalism in mathematical terms. Venkat Venkatasubramanian also compares his theory’s predictions to actual inequality data from various countries—showing, for instance, that Scandinavia has near-ideal fairness, while the United States is markedly unfair—and discusses the theory’s implications for tax policy, social programs, and executive compensation.
| Author | : Kamran Dadkhah |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 547 |
| Release | : 2011-01-11 |
| Genre | : Business & Economics |
| ISBN | : 3642137482 |
This is a book on the basics of mathematics and computation and their uses in economics for modern day students and practitioners. The reader is introduced to the basics of numerical analysis as well as the use of computer programs such as Matlab and Excel in carrying out involved computations. Sections are devoted to the use of Maple in mathematical analysis. Examples drawn from recent contributions to economic theory and econometrics as well as a variety of end of chapter exercises help to illustrate and apply the presented concepts.
| Author | : Sten A. Thore |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 207 |
| Release | : 2012-12-06 |
| Genre | : Business & Economics |
| ISBN | : 9401106592 |
In his book "Jurassic Park" (and in the movie based on the book), Michael Crichton describes a crazed professor who through techniques of genetic engineering manages to recreate the dinosaurs and giant ferns of 65 million years past. Once the giant Tyrannosaurus Rex is brought to life. a powerful dynamics sets in: evolution. The prehistoric world embarks on a collision course with man. Researching his book, Crichton had been reading up on paleontology and on the mathematical theory of evolution, catastrophes, and chaos. Crichton explains some of the twists of nonlinear mathematics that are rewriting not only thermodynamics, physics, and chemistry (that all grapple with evolving and turbulent processes) but also paleontology, genetics, medicine and even anthropology. Collapse and chaos is not limited to prehistoric animal kingdoms and ancient civilizations. The collapse of the Soviet Union and the political and economic chaos in its aftermath demonstrate that modern civilizations are just as vulnerable. This book aims at reexamining some main portions of the discipline of economics from the point of view of economic change and creativity. There are two aspects to this perspective. First, diversity and complexity. The range of different kinds of high technology products available to consumers and producers increases rapidly. Each product is the result of a long and complex production hierarchy. As these hierarchies grow, they deliver ever more diversified and complex high tech goods. Other hierarchies fall by the wayside.
