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Author: Yves Balasko
Publisher: MIT Press (MA)
ISBN: 9780262026543
Category : Business & Economics
Languages : en
Pages : 225
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Book Description
A leading scholar in the field presents post-1970s developments in the theory ofgeneral equilibrium, unified by the concept of equilibrium manifold.
Author: Yves Balasko
Publisher: MIT Press (MA)
ISBN: 9780262026543
Category : Business & Economics
Languages : en
Pages : 225
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Book Description
A leading scholar in the field presents post-1970s developments in the theory ofgeneral equilibrium, unified by the concept of equilibrium manifold.
Author: Yves Balasko
Publisher: MIT Press
ISBN: 0262262045
Category : Business & Economics
Languages : en
Pages : 245
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Book Description
A leading scholar in the field presents post-1970s developments in the theory of general equilibrium, unified by the concept of equilibrium manifold. In The Equilibrium Manifold, noted economic scholar and major contributor to the theory of general equilibrium Yves Balasko argues that, contrary to what many textbooks want readers to believe, the study of the general equilibrium model did not end with the existence and welfare theorems of the 1950s. These developments, which characterize the modern phase of the theory of general equilibrium, led to what Balasko calls the postmodern phase, marked by the reintroduction of differentiability assumptions and the application of the methods of differential topology to the study of the equilibrium equation. Balasko's rigorous study demonstrates the central role played by the equilibrium manifold in understanding the properties of the Arrow-Debreu model and its extensions. Balasko argues that the tools of differential topology articulated around the concept of equilibrium manifold offer powerful methods for studying economically important issues, from existence and uniqueness to business cycles and economic fluctuations. After an examination of the theory of general equilibrium's evolution in the hundred years between Walras and Arrow-Debreu, Balasko discusses the properties of the equilibrium manifold and the natural projection. He highlights the important role of the set of no-trade equilibria, the structure of which is applied to the global structure of the equilibrium manifold. He also develops a geometric approach to the study of the equilibrium manifold. Applications include stability issues of adjustment dynamics for out-of-equilibrium prices, the introduction of price-dependent preferences, and aspects of time and uncertainty in extensions of the general equilibrium model that account for various forms of market frictions and imperfections. Special effort has been made at reducing the mathematical technicalities without compromising rigor. The Equilibrium Manifold makes clear the ways in which the postmodern” developments of the Arrow-Debreu model improve our understanding of modern market economies.
Author: Yves Balasko
Publisher: Princeton University Press
ISBN: 1400838916
Category : Business & Economics
Languages : en
Pages : 188
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Book Description
The concept of general equilibrium, one of the central components of economic theory, explains the behavior of supply, demand, and prices by showing that supply and demand exist in balance through pricing mechanisms. The mathematical tools and properties for this theory have developed over time to accommodate and incorporate developments in economic theory, from multiple markets and economic agents to theories of production. Yves Balasko offers an extensive, up-to-date look at the standard theory of general equilibrium, to which he has been a major contributor. This book explains how the equilibrium manifold approach can be usefully applied to the general equilibrium model, from basic consumer theory and exchange economies to models with private ownership of production. Balasko examines properties of the standard general equilibrium model that are beyond traditional existence and optimality. He applies the theory of smooth manifolds and mappings to the multiplicity of equilibrium solutions and related discontinuities of market prices. The economic concepts and differential topology methods presented in this book are accessible, clear, and relevant, and no prior knowledge of economic theory is necessary. General Equilibrium Theory of Value offers a comprehensive foundation for the most current models of economic theory and is ideally suited for graduate economics students, advanced undergraduates in mathematics, and researchers in the field.
Author: J. Carr
Publisher: Springer Science & Business Media
ISBN: 1461259290
Category : Mathematics
Languages : en
Pages : 152
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Book Description
These notes are based on a series of lectures given in the Lefschetz Center for Dynamical Systems in the Division of Applied Mathematics at Brown University during the academic year 1978-79. The purpose of the lectures was to give an introduction to the applications of centre manifold theory to differential equations. Most of the material is presented in an informal fashion, by means of worked examples in the hope that this clarifies the use of centre manifold theory. The main application of centre manifold theory given in these notes is to dynamic bifurcation theory. Dynamic bifurcation theory is concerned with topological changes in the nature of the solutions of differential equations as para meters are varied. Such an example is the creation of periodic orbits from an equilibrium point as a parameter crosses a critical value. In certain circumstances, the application of centre manifold theory reduces the dimension of the system under investigation. In this respect the centre manifold theory plays the same role for dynamic problems as the Liapunov-Schmitt procedure plays for the analysis of static solutions. Our use of centre manifold theory in bifurcation problems follows that of Ruelle and Takens [57) and of Marsden and McCracken [51).
Author: Yves Balasko
Publisher: World Scientific
ISBN: 9814651729
Category : Business & Economics
Languages : en
Pages : 281
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Book Description
The economic theory of general equilibrium underpins the most important models used in economic theory in general and in its more specialized areas such as macroeconomics, international trade, environmental economics, growth theory, and developmental economics. In Foundations of the Theory of General Equilibrium, leading academic scholar, Yves Balasko offers a good introduction to the economic theory of general equilibrium and makes use of various mathematical tools as intuitive and easy as possible. The second half of the book addresses properties of the general equilibrium model that are still at the frontier of current research. These properties deal with the characterization of economies with a unique equilibrium and, more generally, with the relationships between the number of equilibria and the fundamentals of an economy.
Author: Andreu Mas-Colell
Publisher: Cambridge University Press
ISBN: 9780521388702
Category : Business & Economics
Languages : en
Pages : 396
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Book Description
This book brings together the author's pioneering work, written over the last twenty years, on the use of differential methods in general equilibrium theory.
Author: Rida Laraki
Publisher: Springer Nature
ISBN: 303026646X
Category : Mathematics
Languages : en
Pages : 240
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Book Description
This book gives a concise presentation of the mathematical foundations of Game Theory, with an emphasis on strategic analysis linked to information and dynamics. It is largely self-contained, with all of the key tools and concepts defined in the text. Combining the basics of Game Theory, such as value existence theorems in zero-sum games and equilibrium existence theorems for non-zero-sum games, with a selection of important and more recent topics such as the equilibrium manifold and learning dynamics, the book quickly takes the reader close to the state of the art. Applications to economics, biology, and learning are included, and the exercises, which often contain noteworthy results, provide an important complement to the text. Based on lectures given in Paris over several years, this textbook will be useful for rigorous, up-to-date courses on the subject. Apart from an interest in strategic thinking and a taste for mathematical formalism, the only prerequisite for reading the book is a solid knowledge of mathematics at the undergraduate level, including basic analysis, linear algebra, and probability.
Author: James A. Michener
Publisher: Dial Press
ISBN: 0804151415
Category : Fiction
Languages : en
Pages : 1474
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Book Description
Spanning four and a half centuries, James A. Michener’s monumental saga chronicles the epic history of Texas, from its Spanish roots in the age of the conquistadors to its current reputation as one of America’s most affluent, diverse, and provocative states. Among his finely drawn cast of characters, emotional and political alliances are made and broken, as the loyalties established over the course of each turbulent age inevitably collapse under the weight of wealth and industry. With Michener as our guide, Texas is a tale of patriotism and statesmanship, growth and development, violence and betrayal—a stunning achievement by a literary master. BONUS: This edition includes an excerpt from James A. Michener's Hawaii. Praise for Texas “Fascinating.”—Time “A book about oil and water, rangers and outlaws, frontier and settlement, money and power . . . [James A. Michener] manages to make history vivid.”—The Boston Globe “A sweeping panorama . . . [Michener] grapples earnestly with the Texas character in a way that Texas’s own writers often don’t.”—The Washington Post Book World “Vast, sprawling, and eclectic in population and geography, the state has just the sort of larger-than-life history that lends itself to Mr. Michener’s taste for multigenerational epics.”—The New York Times
Author: Taeyoung Lee
Publisher: Springer
ISBN: 3319569538
Category : Mathematics
Languages : en
Pages : 561
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Book Description
This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.
Author: Yves Balasko
Publisher:
ISBN: 9781788210409
Category : Equilibrium (Economics).
Languages : en
Pages : 0
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Book Description
Written by one of the key pioneers in the field, this book offers an accessible introduction to general equilibrium theory. Written for undergraduates taking courses in economic theory and modelling who have limited mathematical proficiency, the book fills a gap between forbidding technical expositions and the less rigorous elementary ones.
