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Two central problems in the pure theory of economic growth are analysed in this monograph: 1) the dynamic laws governing the economic growth processes, 2) the kinematic and geometric properties of the set of solutions to the dynamic systems. With allegiance to rigor and the emphasis on the theoretical fundamentals of prototype mathematical growth models, the treatise is written in the theorem-proof style. To keep the exposition orderly and as smooth as possible, the economic analysis has been separated from the purely mathematical issues, and hence the monograph is organized in two books. Regarding the scope and content of the two books, an "Introduction and Over view" has been prepared to offer both motivation and a brief account. The introduc tion is especially designed to give a recapitulation of the mathematical theory and results presented in Book II, which are used as the unifying mathematical framework in the analysis and exposition of the different economic growth models in Book I. Economists would probably prefer to go directly to Book I and proceed by consult ing the mathematical theorems of Book II in confirming the economic theorems in Book I. Thereby, both the independence and interdependence of the economic and mathematical argumentations are respected.
Consists of David Cass' early work from his time in graduate school at Stanford University, studying under Hirofumi Uzawa, and as an assistant professor at Yale's Cowles Commission, and his tenure at Carnegie Mellon University's Graduate School of Industrial Administration.
Volume I of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. The chapters are thematically organized into the following main areas: cellular biophysics, regulatory networks, developmental biology, biomedical applications, data analysis and model validation. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Virtually all of contemporary macroeconomics is underpinned by a Phillips curve of one variety or another; yet most of this literature displays a curious neglect of the theoretical dynamic stabilisation perspective provided by A. W. H. Phillips. This 2000 volume collected for the first time the major work of one of the great economists, integrating Phillips's empirical work with his theoretical contribution. In addition to twelve substantive chapters, twenty-nine economists including Lawrence Klein, James Meade, Thomas Sargent, Peter Phillips, David Hendry, William Baumol, Richard Lipsey and Geoffrey Harcourt highlight and interpret Phillips's ongoing influence. This volume also contains six of Phillips's previously unpublished essays, four of which were thought to have been lost. The fifth such essay (Phillips's second empirical Phillips curve) was previously an informal working paper of which few copies circulated, and the sixth essay is a forerunner of the Lucas Critique written by Phillips shortly before his death.
This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses). At the present time the qualitative theory of such equations is under rapid development. After a presentation of the fundamental theory of existence, uniqueness and continuability of solutions, a systematic development of stability theory for that class of problems is given which makes the book unique. It addresses to a wide audience such as mathematicians, applied researches and practitioners.
Graduate-level text provides complete and rigorous expositions of economic models analyzed primarily from the point of view of their mathematical properties, followed by relevant mathematical reviews. Part I covers optimizing theory; Parts II and III survey static and dynamic economic models; and Part IV contains the mathematical reviews, which range fromn linear algebra to point-to-set mappings.
This book provides an introduction to advanced macrodynamics, viewed as a di- quilibriumtheoryof?uctuatinggrowth. Itbuildsonanearlierattempttoreformulate 1 the foundations of macroeconomics from the perspective of real markets diseq- librium and the con?ict over income distribution between capital and labor. It does so, not because it wants to support the view that this class con?ict is inevitable, but with the perspective that an understanding of this con?ict may help to formulate socio-economic principles and policies that can help to overcome class con?ict at least in its cruder forms or that can even lead to rationally understandable proce- 2 dures and rules that turn this con?ict into a consensus-driven interaction between 3 capitalists or their representatives and the employable workforce. The book starts from established theories of temporary equilibrium positions, the forces of real growth, and the con?ict over income distribution, represented by basic modeling approaches, which it considers in detail in its Part I in order to prepare the ground for their integration in Part II of the book. In this way we inspect what types of models of disequilibrium, income distribution, and real growth we have at our disposal, as models that have proved to be of real interest and sound from a rigorous modeling perspective.
A classic account of mathematical programming and control techniques and their applications to static and dynamic problems in economics.
An updated edition of a widely used textbook, offering a clear and comprehensive presentation of mathematics for undergraduate economics students. This text offers a clear and comprehensive presentation of the mathematics required to tackle problems in economic analyses, providing not only straightforward exposition of mathematical methods for economics students at the intermediate and advanced undergraduate levels but also a large collection of problem sets. This updated and expanded fourth edition contains numerous worked examples drawn from a range of important areas, including economic theory, environmental economics, financial economics, public economics, industrial organization, and the history of economic thought. These help students develop modeling skills by showing how the same basic mathematical methods can be applied to a variety of interesting and important issues. The five parts of the text cover fundamentals, calculus, linear algebra, optimization, and dynamics. The only prerequisite is high school algebra; the book presents all the mathematics needed for undergraduate economics. New to this edition are “Reader Assignments,” short questions designed to test students’ understanding before they move on to the next concept. The book’s website offers additional material, including more worked examples (as well as examples from the previous edition). Separate solutions manuals for students and instructors are also available.