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Author: Yasuo Murata
Publisher: Academic Press
ISBN: 1483271293
Category : Business & Economics
Languages : en
Pages : 439
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Book Description
Economic Theory and Mathematical Economics: Mathematics for Stability and Optimization of Economic Systems provides information pertinent to the stability aspects and optimization methods relevant to various economic systems. This book presents relevant mathematical theorems sufficient to develop important economic systems, including Leontief input–output systems, Keynesian dynamic models, the Ramsey optimal accumulation systems, and von Neumann expanding economic systems. Organized into two parts encompassing nine chapters, this book begins with an overview of useful theorems on matrices, eigenvalue problems, and matrices with dominant diagonals and P-matrices. This text then explores the linear transformations on vector spaces. Other chapters consider the Hawkins–Simon theorem concerning non-negative linear systems. This book discusses as well the dual linear relations and optimization methods applicable to inequality economic systems. The final chapter deals with powerful optimal control method for dynamical systems. This book is a valuable resource for mathematicians, economists, research workers, and graduate students.
Author: Yasuo Murata
Publisher: Academic Press
ISBN: 1483271293
Category : Business & Economics
Languages : en
Pages : 439
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Book Description
Economic Theory and Mathematical Economics: Mathematics for Stability and Optimization of Economic Systems provides information pertinent to the stability aspects and optimization methods relevant to various economic systems. This book presents relevant mathematical theorems sufficient to develop important economic systems, including Leontief input–output systems, Keynesian dynamic models, the Ramsey optimal accumulation systems, and von Neumann expanding economic systems. Organized into two parts encompassing nine chapters, this book begins with an overview of useful theorems on matrices, eigenvalue problems, and matrices with dominant diagonals and P-matrices. This text then explores the linear transformations on vector spaces. Other chapters consider the Hawkins–Simon theorem concerning non-negative linear systems. This book discusses as well the dual linear relations and optimization methods applicable to inequality economic systems. The final chapter deals with powerful optimal control method for dynamical systems. This book is a valuable resource for mathematicians, economists, research workers, and graduate students.
Author: Brian Beavis
Publisher: Cambridge University Press
ISBN: 9780521336055
Category : Economics, Mathematical
Languages : en
Pages : 440
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Book Description
This book presents a coherent and systematic exposition of the mathematical theory of the problems of optimization and stability. Both of these are topics central to economic analysis since the latter is so much concerned with the optimizing behaviour of economic agents and the stability of the interaction processes to which this gives rise. The topics covered include convexity, mathematical programming, fixed point theorems, comparative static analysis and duality, the stability of dynamic systems, the calculus of variations and optimal control theory. The authors present a more detailed and wide-ranging discussion of these topics than is to be found in the few books which attempt a similar coverage. Although the text deals with fairly advanced material, the mathematical prerequisites are minimised by the inclusion of an integrated mathematical review designed to make the text self-contained and accessible to the reader with only an elementary knowledge of calculus and linear algebra. A novel feature of the book is that it provides the reader with an understanding and feel for the kinds of mathematical techniques most useful for dealing with particular economic problems. This is achieved through an extensive use of a broad range of economic examples (rather than the numerical/algebraic examples so often found). This is suitable for use in advanced undergraduate and postgraduate courses in economic analysis and should in addition prove a useful reference work for practising economists.
Author: Morton I. Kamien
Publisher: Courier Corporation
ISBN: 0486310280
Category : Mathematics
Languages : en
Pages : 402
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Book Description
Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.
Author: Giancarlo Gandolfo
Publisher: Springer Science & Business Media
ISBN: 9783540627609
Category : Business & Economics
Languages : en
Pages : 712
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Book Description
Treating the mathematical methods used in the economic dynamics, this book shows how they are utilised to build and analyse dynamical models. Accordingly, the focus is on the methods, and every new mathematical technique introduced is followed by its application to select economic models. The mathematical methods coveredc range from elementary linear difference and differential equations and simultaneous systems to the qualitative analysis of non-linear dynamical systems. Stability considerations are stressed throughout, including many advanced topics. Bifurcation and chaos theory are also dealt with. The reader is guided through a step-by-step analysis of each topic, be it a mathematical method or an economic model. The Study Edition also provides the reader with solutions to the numerous exercises.
Author: M.C. Kemp
Publisher: Springer Science & Business Media
ISBN: 146126278X
Category : Business & Economics
Languages : en
Pages : 255
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Book Description
Our objectives may be briefly stated. They are two. First, we have sought to provide a compact and digestible exposition of some sub-branches of mathematics which are of interest to economists but which are underplayed in mathematical texts and dispersed in the journal literature. Second, we have sought to demonstrate the usefulness of the mathematics by providing a systematic account of modern neoclassical economics, that is, of those parts of economics from which jointness in production has been excluded. The book is introductory not in the sense that it can be read by any high-school graduate but in the sense that it provides some of the mathematics needed to appreciate modern general-equilibrium economic theory. It is aimed primarily at first-year graduate students and final-year honors students in economics who have studied mathematics at the university level for two years and who, in particular, have mastered a full-year course in analysis and calculus. The book is the outcome of a long correspondence punctuated by periodic visits by Kimura to the University of New South Wales. Without those visits we would never have finished. They were made possible by generous grants from the Leverhulme Foundation, Nagoya City University, and the University of New South Wales. Equally indispensible were the expert advice and generous encouragement of our friends Martin Beckmann, Takashi Negishi, Ryuzo Sato, and Yasuo Uekawa.
Author: Murray S. Klamkin
Publisher: SIAM
ISBN: 0898712041
Category : Technology & Engineering
Languages : en
Pages : 346
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Book Description
Mathematics of Computing -- Miscellaneous.
Author: Michael Hoy
Publisher: MIT Press
ISBN: 9780262582018
Category : Business & Economics
Languages : en
Pages : 164
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Book Description
This text offers a presentation of the mathematics required to tackle problems in economic analysis. After a review of the fundamentals of sets, numbers, and functions, it covers limits and continuity, the calculus of functions of one variable, linear algebra, multivariate calculus, and dynamics.
Author: Pan-Tai Liu
Publisher: Springer Science & Business Media
ISBN: 1468435728
Category : Science
Languages : en
Pages : 273
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Book Description
As an outgrowth of the advancement in modern control theory during the past 20 years, dynamic modeling and analysis of economic systems has become an important subject in the study of economic theory. Recent developments in dynamic utility, economic planning, and profit optimiza tion, for example, have been greatly influenced by results in optimal control, stabilization, estimation, optimization under conflicts, multi criteria optimization, control of large-scale systems, etc. The great success that has been achieved so far in utilizing modern control theory in economic systems should be attributed to the effort of control theorists as well as economists. Collaboration between the two groups of researchers has proven to be most successful in many instances; nevertheless, the gap between them has existed for some time. Whereas a control theorist frequently sets up a mathematically feasible model to obtain results that permit economic interpretations, an economist is concerned more with the fidelity of the model in representing a real world problem, and results that are obtained (through possibly less mathematical analysis) are due largely to economic insight. The papers appearing in this volume are divided into three parts. In Part I there are five papers on the application of control theory to economic planning. Part II contains five papers on exploration, exploita tion, and pricing of extractive natural resources. Finally, in Part III, some recent advances in large-scale systems and decentralized control appear.
Author: Carlos Daganzo
Publisher: Elsevier
ISBN: 1483299341
Category : Business & Economics
Languages : en
Pages : 239
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Book Description
Multinomial Probit
Author: Toichiro Asada
Publisher: Routledge
ISBN: 1135272328
Category : Business & Economics
Languages : en
Pages : 449
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Book Description
This book investigates the interaction of effective goods demand with the wage-price spiral, and the impact of monetary policy on financial and the real markets from a Keynesian perspective. Endogenous business fluctuations are studied in the context of long-run distributive cycles in an advanced, rigorously formulated and quantitative setup. The material is developed by way of self-contained chapters on three levels of generality, an advanced textbook level, a research-oriented applied level and on a third level that shows how the interaction of real with financial markets has to be modelled from a truly integrative Keynesian perspective. Monetary Macrodynamics shows that the balanced growth path of a capitalist economy is unlikely to be attracting and that the cumulative forces that surround it are controlled in the large by changes in the behavioural factors that drive the wage-price spiral and the financial markets. Such behavioural changes can in fact be observed in actual economies in the interaction of demand-driven business fluctuations with supply-driven wage and price dynamics as they originate from the conflict over income distribution between capital and labour. The book is a detailed critique of US mainstream macroeconomics and uses rigorous dynamic macro-models of a descriptive and applicable nature. It will be of particular relevance to postgraduate students and researchers interested in disequilibrium processes, real wage feedback channels, financial markets and portfolio choice, financial accelerator mechanisms and monetary policy.
