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Author: Antonio Villanacci Publisher: Springer Science & Business Media ISBN: 1475736193 Category : Mathematics Languages : en Pages : 495
Book Description
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 .
Author: Antonio Villanacci Publisher: Springer Science & Business Media ISBN: 1475736193 Category : Mathematics Languages : en Pages : 495
Book Description
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 .
Author: Ryō Nagata Publisher: World Scientific ISBN: 9789812794765 Category : Business & Economics Languages : en Pages : 242
Book Description
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.
Author: Gerard Debreu Publisher: Edward Elgar Publishing ISBN: Category : Business & Economics Languages : en Pages : 584
Book Description
This three-volume work provides a collection of essays on general equilibrium theory, illustrating its role as one of the major theoretical developments in economics since 1945. The aim is to improve access to the literature on this subject, which is not always readily available.
Author: Ryo Nagata Publisher: World Scientific ISBN: 981448265X Category : Business & Economics Languages : en Pages : 235
Book Description
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.
Author: Ross M. Starr Publisher: Cambridge University Press ISBN: 1139496735 Category : Business & Economics Languages : en Pages : 379
Book Description
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.
Author: Charalambos D. Aliprantis Publisher: Springer Science & Business Media ISBN: 3662218933 Category : Business & Economics Languages : en Pages : 294
Book Description
This monograph is a systematic exposition of the authors' research on general equi librium models with an infinite number of commodities. It is intended to serve both as a graduate text on aspects of general equilibrium theory and as an introduction, for economists and mathematicians working in mathematical economics, to current research in a frontier area of general equilibrium theory. To this end, we have pro vided two introductory chapters on the basic economic model and the mathematical framework. The exercises at the end of each section complement the main exposition. Chapter one is a concise but substantiative discussion of the questions of exis tence and optimality of competitive equilibria in the Walrasian general equilibrium model of an economy with a finite number of households, firms and commodities. Our extension of this model to economies with an infinite number of commodities constitutes the core material of this book and begins in chapter three. Readers fa miliar with the Walrasian general equilibrium model as exposited in (13], [23] or [52] may treat chapter one as a handy reference for the main economic concepts and notions that are used throughout the book.
Author: Ioannis N. Parasidis Publisher: Springer Nature ISBN: 3030847217 Category : Mathematics Languages : en Pages : 1050
Book Description
This contributed volume provides an extensive account of research and expository papers in a broad domain of mathematical analysis and its various applications to a multitude of fields. Presenting the state-of-the-art knowledge in a wide range of topics, the book will be useful to graduate students and researchers in theoretical and applicable interdisciplinary research. The focus is on several subjects including: optimal control problems, optimal maintenance of communication networks, optimal emergency evacuation with uncertainty, cooperative and noncooperative partial differential systems, variational inequalities and general equilibrium models, anisotropic elasticity and harmonic functions, nonlinear stochastic differential equations, operator equations, max-product operators of Kantorovich type, perturbations of operators, integral operators, dynamical systems involving maximal monotone operators, the three-body problem, deceptive systems, hyperbolic equations, strongly generalized preinvex functions, Dirichlet characters, probability distribution functions, applied statistics, integral inequalities, generalized convexity, global hyperbolicity of spacetimes, Douglas-Rachford methods, fixed point problems, the general Rodrigues problem, Banach algebras, affine group, Gibbs semigroup, relator spaces, sparse data representation, Meier-Keeler sequential contractions, hybrid contractions, and polynomial equations. Some of the works published within this volume provide as well guidelines for further research and proposals for new directions and open problems.