Convex Structures And Economic Theory
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| Author | : Hukukane Nikaido |
| Publisher | : Elsevier |
| Total Pages | : 422 |
| Release | : 2016-06-03 |
| Genre | : Mathematics |
| ISBN | : 1483266680 |
Mathematics in Science and Engineering, Volume 51: Convex Structures and Economic Theory consists of an account of the theory of convex sets and its application to several basic problems that originate in economic theory and adjacent subject matter. This volume includes examples of problems pertaining to interesting static and dynamic phenomena in linear and nonlinear economic systems, as well as models initiated by Leontief, von Neumann, and Walras. The topics covered are the mathematical theorems on convexity, simple multisector linear systems, balanced growth in nonlinear systems, and efficient allocation and growth. The working of Walrasian competitive economies, special features of competitive economies, and Jacobian matrix and global univalence are also covered. This publication is suitable for advanced students of mathematical economics and related fields, but is also beneficial for anyone who wishes to become familiar with the basic ideas, methods, and results in the mathematical treatment in economic theory through a detailed exposition of a number of typical representative problems.
| Author | : Ken Urai |
| Publisher | : World Scientific |
| Total Pages | : 311 |
| Release | : 2010 |
| Genre | : Business & Economics |
| ISBN | : 9812837191 |
1. Introduction. 1.1. Mathematics is language. 1.2. Notes on some mathematical tools in this book. 1.3. Basic mathematical concepts and definitions -- 2. Fixed-point theorems. 2.1. Classical results and basic extensions. 2.2. Convexity and duality for general spaces. 2.3. Extension of classical results to general spaces -- 3. Nash equilibrium and abstract economy. 3.1. Multi-agent product settings for games. 3.2. Nash equilibrium. 3.3. Abstract economy -- 4. Gale-Nikaido-Debreu's theorem. 4.1. Gale-Nikaido-Debreu's theorem. 4.2. Market equilibria in general vector spaces. 4.3. Demand-supply coincidence in general spaces -- 5. General economic equilibrium. 5.1. General preferences and basic existence theorems. 5.2. Pareto optimal allocations. 5.3. Existence of general equilibrium -- 6. The C̮ech type homology theory and fixed points. 6.1. Basic concepts in algebraic topology. 6.2. Vietoris-Begle mapping and local connectedness. 6.3. Nikaido's analogue of Sperner's lemma. 6.4. Eilenberg-Montgomery's theorem -- 7. Convex structure and fixed-point index. 7.1. Lefschetz's fixed-point theorem and its extensions. 7.2. Cohomology theory for general spaces. 7.3. Dual-system structure and differentiability. 7.4. Linear Approximation for Isolated Fixed Points. 7.5. Indices for compact set of fixed points -- 8. Applications to related topics. 8.1. KKM, KKMS, and core existence. 8.2. Eaves' theorem. 8.3. Fan-Browder's coincidence theorem. 8.4. L-majorized mappings. 8.5. Variational inequality problem. 8.6. Equilibrium with cooperative concepts. 8.7. System of inequalities and affine transformations -- 9. Mathematics and social science. 9.1. Basic concepts in axiomatic set theory. 9.2. Individuals and rationality. 9.3. Society and values -- 10. Concluding discussions. 10.1. Fixed points and economic equilibria. 10.2. Rationality and fixed-point views of the world
| Author | : Peter Nijkamp |
| Publisher | : Elsevier |
| Total Pages | : 648 |
| Release | : 1986 |
| Genre | : Business & Economics |
| ISBN | : 9780444879707 |
This second volume of the Handbook presents professional surveys of all the important topics in urban economics. The first section contains 6 surveys on locational analysis, the second, 5 surveys of specific urban markets, and the third part presents 5 surveys of government policy issues. The book brings together exhaustive research by distinguished scholars from many countries. It is the only complete survey volume of urban economics and should serve as a reference volume to scholars and graduate students for many years. For more information on the Handbooks in Economics series, please see our home page on http://www.elsevier.nl/locate/hes
| Author | : Akira Takayama |
| Publisher | : Cambridge University Press |
| Total Pages | : 770 |
| Release | : 1985-08-30 |
| Genre | : Business & Economics |
| ISBN | : 9780521314985 |
This systematic exposition and survey of mathematical economics emphasizes the unifying structures of economic theory.
| Author | : Giorgio P. Szegö |
| Publisher | : Academic Press |
| Total Pages | : 336 |
| Release | : 2014-05-10 |
| Genre | : Business & Economics |
| ISBN | : 1483273466 |
Economic Theory, Econometrics, and Mathematical Economics: New Quantitative Techniques for Economic Analysis provides a critical appraisal of the results, the limits, and the developments of well-established quantitative techniques. This book presents a detailed analysis of the quantitative techniques for economic analysis. Organized into four parts encompassing 16 chapters, this book begins with an overview of the general questions concerning models and model making. This text then provides the main results and various interesting economic applications of some quantitative techniques that have not been widely used in the economic field. Other chapters consider the principle of optimality in dynamic programing wherein the infinite sequence of consumption-saving decisions can be reduced to one decision. This book discusses as well the methods for online control and management of large-scale systems. The final chapter deals with special problems. This book is a valuable resource for economists, social scientists, epistemologists, economic historians, and research workers.
| Author | : Michael G. Allingham |
| Publisher | : Springer |
| Total Pages | : 129 |
| Release | : 1989-06-18 |
| Genre | : Business & Economics |
| ISBN | : 1349102652 |
Aimed at students of economic theory and finance, this book examines the relation between the prices prevailing in the markets and the characteristics of the various market participants. It demonstrates how prices are formed, how they change and other properties of markets.
| Author | : V.L. Makarov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 268 |
| Release | : 2012-12-06 |
| Genre | : Business & Economics |
| ISBN | : 1461298865 |
This book is devoted to the mathematical analysis of models of economic dynamics and equilibria. These models form an important part of mathemati cal economics. Models of economic dynamics describe the motion of an economy through time. The basic concept in the study of these models is that of a trajectory, i.e., a sequence of elements of the phase space that describe admissible (possible) development of the economy. From all trajectories, we select those that are" desirable," i.e., optimal in terms of a certain criterion. The apparatus of point-set maps is the appropriate tool for the analysis of these models. The topological aspects of these maps (particularly, the Kakutani fixed-point theorem) are used to study equilibrium models as well as n-person games. To study dynamic models we use a special class of maps which, in this book, are called superlinear maps. The theory of superlinear point-set maps is, obviously, of interest in its own right. This theory is described in the first chapter. Chapters 2-4 are devoted to models of economic dynamics and present a detailed study of the properties of optimal trajectories. These properties are described in terms of theorems on characteristics (on the existence of dual prices) and turnpike theorems (theorems on asymptotic trajectories). In Chapter 5, we state and study a model of economic equilibrium. The basic idea is to establish a theorem about the existence of an equilibrium state for the Arrow-Debreu model and a certain generalization of it.
| Author | : Yasuhiro Sakai |
| Publisher | : Springer Nature |
| Total Pages | : 238 |
| Release | : |
| Genre | : |
| ISBN | : 9819952859 |
| Author | : Noritsugu Nakanishi |
| Publisher | : World Scientific |
| Total Pages | : 289 |
| Release | : 2018-10-29 |
| Genre | : Business & Economics |
| ISBN | : 9813274409 |
This textbook aims to explain the principles in international trade theory and show how some useful trade models work. The book concentrates on two fundamental issues in international trade, that is, the 'determinants of trade patterns' and the 'welfare gains from trade' in various economic environments. Chapters 1 through 3 assume perfect competition and explore the workings of the Ricardian model, the Heckscher-Ohlin-Samuelson model, the Specific Factors model and more recent development of the Eaton-Kortum model. Chapter 4 examines various welfare criteria and their relation to the 'social utility function' and, then, proves the basic gains-from-trade proposition. Chapters 5 and 6 examine the implications of imperfect competition using a unified oligopolistic model and variations of the monopolistically competitive model. The roles of the strategic interaction among firms, the economies of scale, product differentiation, the heterogeneity of firms, and the geographic distribution of agents will be highlighted. Chapter 7 deals with some trade policy issues such as the effects of tariffs, the relation of tariffs to other policy measures, and the so-called strategic trade policies.
| Author | : Ross M. Starr |
| Publisher | : Cambridge University Press |
| Total Pages | : 280 |
| Release | : 1997-07-13 |
| Genre | : Business & Economics |
| ISBN | : 9780521564731 |
General Equilibrium Theory: An Introduction treats the classic Arrow-Debreu general equilibrium model in a form accessible to graduate students and advanced undergraduates in economics and mathematics. Topics covered include mathematical preliminaries, households and firms, existence of general equilibrium, Pareto efficiency of general equilibrium, the First and Second Fundamental Theorems of Welfare Economics, the core and core convergences, future markets over time and contingent commodity markets under uncertainty. Demand, supply, and excess demand appear first as (point-valued) functions, then optionally as (set-valued) correspondences. The mathematics presented (with elementary proofs of the theorems) includes a real analysis, the Brouwer fixed point theorem, and separating and supporting hyperplane theorems. Optional chapters introduce the existence of equilibrium with set-valued supply and demand, the mathematics of upper and lower hemicontinuous correspondences, and the Kakutani fixed point theorem. The treatment emphasizes clarity and accessibility to the student through use of examples and intuition.
