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Computation of Economic Equilibria by Path Methods

Computation of Economic Equilibria by Path Methods
Author: Stanford University. Department of Operations Research. Systems Optimization Laboratory
Publisher:
Total Pages: 136
Release: 1977
Genre:
ISBN:

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An introduction to the economic equilibrium model is given and it is demonstrated that a path method can be used to compute equilibria for pure exchange economies in a nonlinear setting. Next, a model is described for an economy in which the utility functions are piecewise linear and the consumption and production sets are polyhedral. It is shown that an equilibrium for this economy is the solution to a system of bilinear equations subject to certain linear inequality and complementarity constraints. Two approaches are discussed for computing equilibria for such economies. The first is the bilinear complementarity algorithm (BCA) and the second is the homotopy retraction algorithm (HRA). Convergence proofs are given for both methods using the general theory for path methods described above. No conclusion could be drawn as to which algorithm was superior, but both performed well enough that it appears that much larger equilibrium problems also can be solved efficiently by these methods.


Fixed Points and Economic Equilibria

Fixed Points and Economic Equilibria
Author: Ken Urai
Publisher: World Scientific
Total Pages: 311
Release: 2010
Genre: Mathematics
ISBN: 9812837183

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Wuthering Heights


Theory of General Economic Equilibrium

Theory of General Economic Equilibrium
Author: Trout Rader
Publisher: Academic Press
Total Pages: 383
Release: 2014-05-10
Genre: Business & Economics
ISBN: 1483268926

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Theory of General Economic Equilibrium provides information pertinent to the general economic equilibrium theory. This book covers a variety of topics, including efficiency, economic systems analysis, welfare economics, and international trade. Organized into three parts encompassing eight chapters, this book begins with an overview of the theory of efficient production and growth where consumer preferences play a subordinate role. This text then examines that for the case where preferences satisfy appropriate conditions, efficiency theory is superseded as normative analysis by optimality theory. Other chapters consider the optimization of consumer preferences that leads to the decline of many families. This book discusses as well the existence of equilibrium, which is of importance to both normative and positive economics. The final chapter deals with the question of the speed with which the economic system attains its equilibrium state, which is assumed to be stationary. This book is a valuable resource for professional economists and advanced graduate students in economics.


Computing Equilibria and Fixed Points

Computing Equilibria and Fixed Points
Author: Zaifu Yang
Publisher: Springer Science & Business Media
Total Pages: 349
Release: 2013-04-17
Genre: Business & Economics
ISBN: 1475748396

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Computing Equilibria and Fixed Points is devoted to the computation of equilibria, fixed points and stationary points. This volume is written with three goals in mind: (i) To give a comprehensive introduction to fixed point methods and to the definition and construction of Gröbner bases; (ii) To discuss several interesting applications of these methods in the fields of general equilibrium theory, game theory, mathematical programming, algebra and symbolic computation; (iii) To introduce several advanced fixed point and stationary point theorems. These methods and topics should be of interest not only to economists and game theorists concerned with the computation and existence of equilibrium outcomes in economic models and cooperative and non-cooperative games, but also to applied mathematicians, computer scientists and engineers dealing with models of highly nonlinear systems of equations (or polynomial equations).


Monograph

Monograph
Author:
Publisher:
Total Pages:
Release: 1975
Genre: Economics
ISBN:

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Economic Equilibrium

Economic Equilibrium
Author: Alan Sussmann Manne
Publisher: North Holland
Total Pages: 280
Release: 1985
Genre: Business & Economics
ISBN:

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Dynamic General Equilibrium Modelling

Dynamic General Equilibrium Modelling
Author: Burkhard Heer
Publisher: Springer Science & Business Media
Total Pages: 548
Release: 2005-12-05
Genre: Business & Economics
ISBN: 3540273123

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Modern business cycle theory and growth theory uses stochastic dynamic general equilibrium models. Many mathematical tools are needed to solve these models. The book presents various methods for computing the dynamics of general equilibrium models. In part I, the representative-agent stochastic growth model is solved with the help of value function iteration, linear and linear quadratic approximation methods, parameterised expectations and projection methods. In order to apply these methods, fundamentals from numerical analysis are reviewed in detail. Part II discusses methods for solving heterogeneous-agent economies. In such economies, the distribution of the individual state variables is endogenous. This part of the book also serves as an introduction to the modern theory of distribution economics. Applications include the dynamics of the income distribution over the business cycle or the overlapping-generations model. Through an accompanying home page to this book, computer codes to all applications can be downloaded.


Dynamic General Equilibrium Modeling

Dynamic General Equilibrium Modeling
Author: Burkhard Heer
Publisher: Springer Science & Business Media
Total Pages: 719
Release: 2011-10-20
Genre: Business & Economics
ISBN: 3540856846

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Modern business cycle theory and growth theory uses stochastic dynamic general equilibrium models. In order to solve these models, economists need to use many mathematical tools. This book presents various methods in order to compute the dynamics of general equilibrium models. In part I, the representative-agent stochastic growth model is solved with the help of value function iteration, linear and linear quadratic approximation methods, parameterised expectations and projection methods. In order to apply these methods, fundamentals from numerical analysis are reviewed in detail. In particular, the book discusses issues that are often neglected in existing work on computational methods, e.g. how to find a good initial value. In part II, the authors discuss methods in order to solve heterogeneous-agent economies. In such economies, the distribution of the individual state variables is endogenous. This part of the book also serves as an introduction to the modern theory of distribution economics. Applications include the dynamics of the income distribution over the business cycle or the overlapping-generations model. In an accompanying home page to this book, computer codes to all applications can be downloaded.