Differential Topology and General Equilibrium with Complete and Incomplete Markets

Author: Antonio Villanacci,Laura Carosi,Pierluigi Benevieri,Andrea Battinelli

Publisher: Springer Science & Business Media

ISBN: 1475736193

Category: Mathematics

Page: 474

View: 2614

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General equilibrium In this book we try to cope with the challenging task of reviewing the so called general equilibrium model and of discussing one specific aspect of the approach underlying it, namely, market completeness. With the denomination "general equilibrium" (from now on in short GE) we shall mainly refer to two different things. On one hand, in particular when using the expression "GE approach", we shall refer to a long established methodolog ical tradition in building and developing economic models, which includes, as of today, an enormous amount of contributions, ranging in number by several 1 thousands • On the other hand, in particular when using the expression "stan dard differentiable GE model", we refer to a very specific version of economic model of exchange and production, to be presented in Chapters 8 and 9, and to be modified in Chapters 10 to 15. Such a version is certainly formulated within the GE approach, but it is generated by making several quite restrictive 2 assumptions • Even to list and review very shortly all the collective work which can be ascribed to the GE approach would be a formidable task for several coauthors in a lifetime perspective. The book instead intends to address just a single issue. Before providing an illustration of its main topic, we feel the obligation to say a word on the controversial character of GE. First of all, we should say that we identify the GE approach as being based 3 on three principles .

Theory of Regular Economies

Author: Ryō Nagata

Publisher: World Scientific

ISBN: 9789812794765

Category: Business & Economics

Page: 236

View: 7262

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This book presents a comprehensive treatment of the theory of regular economies, which is one of the most advanced topics in modern general equilibrium theory, emphasizing the basic ideas, the tools and the important applications. Although many notions and tools of differential topology are required to understand the theory, the author chooses a minimum of them and heuristically arranges them; that is, instead of lumping together all the necessary mathematics, the author puts at the beginning of each chapter the minimum mathematics required for the economic analysis of the chapter, so that the reader will not only save much effort on the mathematics but also directly understand how successfully the mathematics is used for the economic issues. Contents: Foundations of Regular Economies: What Is a Regular Economy?; Regular Economies and Genericity; Formalization of Regular Economies; The Number of Equilibria in Regular Economies; Stability of Equilibria in Regular Economies; Transversality and Regular Economies: Space of Utility Functions; Transversality and Regular Economies; Transversality Theorems and Regular Economies; The Number of Extended Equilibria in Regular Economies; Developments of Regular Economies: Production Economy with Linear Activities; Incomplete Markets I; Incomplete Markets II. Readership: Upper level undergraduates, graduate students and researchers involved with the application of mathematics to economic analysis.

Business Horizons

The Journal of the Kelley School of Business, Indiana University

Author: Graduate School of Business (Bloomington, IN),Kelley School of Business (Bloomington, IN)

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

View: 9317

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General Equilibrium

Problems and Prospects

Author: Frank Hahn,Professor of Economics Frank Hahn,Fabio Petri

Publisher: Routledge

ISBN: 113443362X

Category: Business & Economics

Page: 544

View: 6380

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In recent years certain leading figures in the world of economics have called the usefulness of general equilibrium theory into question. This superb new book brings together leading economic theorists with important contributions to the ongoing debate. General equilibrium theorists including Michio Morishima, Michael Magill and Martine Quinzii debate strengths, weaknesses and possible futures with leading thinkers such as Herb Gintis, Pierangelo Garegnani and Duncan Foley, who seek to explain the rejection of general equilibrium. Uniquely, none of the contributors portray general equilibrium theory as the perfect guide to market economies actual behaviour, but rather illustrate that there is insufficient acquaintance with existing alternatives and that general equilibrium theory is often used as an ideal 'benchmark'.

Managerial Economics

A Problem-Solving Approach

Author: Nick Wilkinson

Publisher: Cambridge University Press

ISBN: 1139443585

Category: Business & Economics

Page: 556

View: 6520

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Managerial economics, meaning the application of economic methods in the managerial decision-making process, is a fundamental part of any business or management course. This textbook covers all the main aspects of managerial economics: the theory of the firm; demand theory and estimation; production and cost theory and estimation; market structure and pricing; game theory; investment analysis and government policy. It includes numerous and extensive case studies, as well as review questions and problem-solving sections at the end of each chapter. Nick Wilkinson adopts a user-friendly problem-solving approach which takes the reader in gradual steps from simple problems through increasingly difficult material to complex case studies, providing an understanding of how the relevant principles can be applied to real-life situations involving managerial decision-making. This book will be invaluable to business and economics students at both undergraduate and graduate levels who have a basic training in calculus and quantitative methods.

Statistical Physics and Economics

Concepts, Tools, and Applications

Author: Michael Schulz

Publisher: Springer

ISBN: 0387217134

Category: Mathematics

Page: 246

View: 7667

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This systematic book covers in simple language the physical foundations of evolution equations, stochastic processes and generalized Master equations applied on complex economic systems, helping to understand the large variability of financial markets, trading and communications networks.

Theory of Incomplete Markets

Author: Michael Magill,Martine Quinzii

Publisher: MIT Press

ISBN: 9780262632546

Category: Business & Economics

Page: 558

View: 4634

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Theory of incompl. markets/M. Magill, M. Quinzii. - V.1.

General Equilibrium Theory

An Introduction

Author: Ross M. Starr

Publisher: Cambridge University Press

ISBN: 1139496735

Category: Business & Economics

Page: N.A

View: 8156

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General Equilibrium Theory: An Introduction presents the mathematical economic theory of price determination and resource allocation from elementary to advanced levels, suitable for advanced undergraduates and graduate students of economics. This Arrow–Debreu model (known for two of its most prominent founders, both Nobel Laureates) is the basis of modern price theory and of a wide range of applications. The new edition updates discussion throughout and expands the number and variety of exercises. It offers a revised and extended treatment of core convergence, including the case of non-convex preferences, and introduces the investigation of approximate equilibrium with U-shaped curves and non-convex preferences.

Complex Economics

Individual and Collective Rationality

Author: Alan Kirman

Publisher: Routledge

ISBN: 1136941673

Category: Business & Economics

Page: 272

View: 4752

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The economic crisis is also a crisis for economic theory. Most analyses of the evolution of the crisis invoke three themes, contagion, networks and trust, yet none of these play a major role in standard macroeconomic models. What is needed is a theory in which these aspects are central. The direct interaction between individuals, firms and banks does not simply produce imperfections in the functioning of the economy but is the very basis of the functioning of a modern economy. This book suggests a way of analysing the economy which takes this point of view. The economy should be considered as a complex adaptive system in which the agents constantly react to, influence and are influenced by, the other individuals in the economy. In such systems which are familiar from statistical physics and biology for example, the behaviour of the aggregate cannot be deduced from the behaviour of the average, or "representative" individual. Just as the organised activity of an ants’ nest cannot be understood from the behaviour of a "representative ant" so macroeconomic phenomena should not be assimilated to those associated with the "representative agent". This book provides examples where this can clearly be seen. The examples range from Schelling’s model of segregation, to contributions to public goods, the evolution of buyer seller relations in fish markets, to financial models based on the foraging behaviour of ants. The message of the book is that coordination rather than efficiency is the central problem in economics. How do the myriads of individual choices and decisions come to be coordinated? How does the economy or a market, "self organise" and how does this sometimes result in major upheavals, or to use the phrase from physics, "phase transitions"? The sort of system described in this book is not in equilibrium in the standard sense, it is constantly changing and moving from state to state and its very structure is always being modified. The economy is not a ship sailing on a well-defined trajectory which occasionally gets knocked off course. It is more like the slime described in the book "emergence", constantly reorganising itself so as to slide collectively in directions which are neither understood nor necessarily desired by its components.

Stable Mappings and Their Singularities

Author: M. Golubitsky,V. Guillemin

Publisher: Springer Science & Business Media

ISBN: 146157904X

Category: Mathematics

Page: 209

View: 7604

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This book aims to present to first and second year graduate students a beautiful and relatively accessible field of mathematics-the theory of singu larities of stable differentiable mappings. The study of stable singularities is based on the now classical theories of Hassler Whitney, who determined the generic singularities (or lack of them) of Rn ~ Rm (m ~ 2n - 1) and R2 ~ R2, and Marston Morse, for mappings who studied these singularities for Rn ~ R. It was Rene Thorn who noticed (in the late '50's) that all of these results could be incorporated into one theory. The 1960 Bonn notes of Thom and Harold Levine (reprinted in [42]) gave the first general exposition of this theory. However, these notes preceded the work of Bernard Malgrange [23] on what is now known as the Malgrange Preparation Theorem-which allows the relatively easy computation of normal forms of stable singularities as well as the proof of the main theorem in the subject-and the definitive work of John Mather. More recently, two survey articles have appeared, by Arnold [4] and Wall [53], which have done much to codify the new material; still there is no totally accessible description of this subject for the beginning student. We hope that these notes will partially fill this gap. In writing this manuscript, we have repeatedly cribbed from the sources mentioned above-in particular, the Thom-Levine notes and the six basic papers by Mather.

Mathematical Methods in Economics and Social Choice

Author: norman schofield

Publisher: Springer Science & Business Media

ISBN: 3642398189

Category: Business & Economics

Page: 262

View: 2219

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In recent years, the usual optimization techniques, which have proved so useful in microeconomic theory, have been extended to incorporate more powerful topological and differential methods, and these methods have led to new results on the qualitative behavior of general economic and political systems. These developments have necessarily resulted in an increase in the degree of formalism in the publications in the academic journals. This formalism can often deter graduate students. The progression of ideas presented in this book will familiarize the student with the geometric concepts underlying these topological methods, and, as a result, make mathematical economics, general equilibrium theory, and social choice theory more accessible.

Advanced Microeconomic Theory

Author: Geoffrey Alexander Jehle,Philip J. Reny

Publisher: Prentice Hall

ISBN: 9780273731917

Category: Business & Economics

Page: 672

View: 3469

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Rev. ed. of: Advanced microeconomic theory. 2nd ed. 2001.