Multisector dynamic linear systems and the turnpike theorem.

  • 70 Pages
  • 3.43 MB
  • English
Inst. f. Höhere Studien) , (Wien
Economic development -- Linear programming., Economics -- Linear program
SeriesInstitut für Höhere Studien und Wissenschaftliche Forschung, Wien. Research memorandum, no. 59, Research memorandum (Institut für Höhere Studien und Wissenschaftliche Forschung (Vienna, Austria)) ;, no. 59.
LC ClassificationsHD82 .L86
The Physical Object
Pagination54 l., l. 55-56 diagrs., 67-70 l.
ID Numbers
Open LibraryOL5453624M
LC Control Number73155760

Multisector dynamic linear systems and the turnpike theorem. the subject of this study is an analysis of two of the basic linear systems; leontief's system and von neumann's model. the properties of the dual prices in a turnpike example are examined.

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the chapters in this study are organized as follows: chapter i furnishes the mathematical Author: Mikulas Luptacik. Turnpike theorems for the general multisector model with a Ramsey objective and a von Neumann technology were first proved by Gale and McKenzie.

Their order of proof does not differ from that of Atsumi, which is, in turn, parallel to the proof used by Radner in. 2.A history of Turnpikes. The turnpike theory is originated in two famous papers.

One is the paper by John von Neumann () titled “A Model of General Economic Equilibrium”, and the other is the one by Frank Ramsey () titled “A Mathematical Theory of Saving”. 9. Other Linear Systems Chapter III. Balanced Growth in Nonlinear Systems The Solow-Samuelson-Type Relative Stability Theorems Income Propagation Under Autonomous Spending Chapter IV.

Efficient Allocation and Growth Production Technology Sets Theorems on Self-Sustained Efficient Growth A Consumption Turnpike Theorem Chapter Edition: 1. Yano, M., b, The turnpike of dynamic general equilibrium paths and its insensitivity to initial conditions, Journal of Mathemath:al Econom Yano, M., c, Competitive equilibria and turnpikes in a McKenzie economy, I: A neighborhood turnpike theorem, International Economic Rev Cited by: 1.

Multisector growth models are basic building blocks not only for Multisector dynamic linear systems and the turnpike theorem. book planning models (Majumdar ; McKenzie ) but also for recursive general equilibrium models (McKenzie ; Stokey and Lucas ), and for econometrically tractable models for business cycle research (Cooley ) and general macroeconomics (Sargent ).Majumdar has already covered some basic theory, some.

The dynamic systems of Walrasian multi-sector economies and the family of solutions (time paths) for steady-state and persistent growth per capita are parametrically characterized. Journal of Economic Dynamics and Control 18 () North-Holland Turnpike theory Some new results on the saddle point property of equilibria and on the existence of endogenous cycles Pierre Cartigny and Alain Venditti* Laboratoire G.R.E.Q.E., Universitd'Aix-Marsei Marseille, France Received Julyfinal version received February This paper discusses the.

the linear system included in the non-linear system, it is possible to analyze the dynamics of the. Thus, the matter of whether a turnpike theorem is established or convergence occurs upon. This is done by surveying both unpublished and published work by Uzawa, Cass, Koopmans, and McKenzie regarding growth and the turnpike, the cross-fertilization between them, and how this brought about the conflation of optimality and the turnpike, and the metamorphosis of the notion of the turnpike, from that of Dorfman–Samuelson Solow, to the Koopmans–McKenzie “amalgam” of models.

Downloadable. In Section 1, we explain the neoclassical optimal growth model, which includes multi capital goods, and is derived from neoclassical production functions; the transformations to the reduced model are also explained. Section 2 pertains to the explanation of the methods for proving the consumption turnpike theorem demonstrated by Scheinkman () and McKenzie ().

Montrucchio, Luigi, "A New Turnpike Theorem for Discounted Programs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages, W. & Majumdar, M., "Global asymptotic stability results for multisector models of optimal growth under uncertainty when future utilities are discounted," Journal of Economic Theory, Elsevier.

Dual Linear Relations and Gale-Nikaido Theorems The von Neumann Economic System and Maximal Paths Kuhn-Tucker Theorems, Concave and Quasi-Concave Programming Duality in Linear Programming, the Morishima Turnpike Theorem, and Other Related Problems Exercises References and Further Reading.

Contact Information. Mukul Majumdar Professor Uris Hall Cornell University Ithaca, NY E-mail: [email protected] Phone: () Fax: () Allen contains an excellent coverage (Chapters 1 through 9) of single-sector economic models with complex dynamic specifications, as contrasted with the models of this book, which are multisector with simple dynamic specifications.

The coverage of linear methods is broad, but the exposition is not in the most desirable form. Dynamic Zero-Sum Games with Linear Constraints. Turnpike Theory of Continuous-Time Linear Optimal Control Problems, () Turnpike Theorem for an Infinite Horizon Optimal Control Problem with Time Delay.

This is one chapter from the book “Eseje o teoriich ekonomickeho rustu” (Essays in the Theory of the Economic Growth”, that was published in Czechoslovakia during The main purpose of the book was to fill one of the many gaps in the knowledge of the advanced contemporary economic theory.

These gaps were created in the times of dogmatic Marxism. Recommend & Share. Recommend to Library. Email to a friend. In this paper, the Marx-Sraffa Model is used to investigate the equilibrium of linear multisector system of equations in which only fixed capital is considered as a joint product, and wages are paid in advance.

A unique pair of equilibrium of production prices and activity levels of processes exist, but they are unstable. of dynamic systems ([10]), in which di erent mathematical methods and concepts appear, with many applications in our life.

Suppose we want to control some system modeled by the following state equation: A(y) = f(v) In this case, yis the state vector and vis the control which belongs to the set of admissible controls U ad.

Suppose that A: D(A) ˆY. This book treats stochastic control theory and its applications in management. The main numerical techniques necessary for such applications are presented. Several advanced topics leading to optimal processes are dismissed.

Description Multisector dynamic linear systems and the turnpike theorem. EPUB

The book also considers the theory of some stochastic control processes and several applications to illustrate the ideas. This book describes some general equilibrium models that are dynamic, that have been built to help interpret time-series of observations of economic aggregates and to predict the consequences of alternative government interventions.

The first part of the book describes dynamic programming, search theory, and real dynamic capital pricing models.

These equations together form a complete dynamic system - an equation system defln-ing how its variables evolve over time - for some given F. That is, we know, in principle, what fKt+1g 1 t=0 and fYt;Ct;Itg 1 t=0 will be, given any initial capital value K0.

In order to analyze the dynamics, we now make some assumptions.

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This paper establishes some asymptotic properties of the finite state and action space Markovian decision model. For the discounted case, a turnpike theorem is proven which states that an optimal immediate decision when the planning horizon is sufficiently large is to choose one of the decisions which is optimal when the planning horizon is infinite.

Turnpike theory refers to a set of economic theories about the optimal path of accumulation (often capital accumulation) in a system, depending on the initial and final the context of a macroeconomic exogenous growth model, for example, it says that if an infinite optimal path is calculated, and an economic planner wishes to move an economy from one level of capital to another, as.

SIAM J Control Optim – Zaslavski AJ () The turnpike property for dynamic discrete time zero-sum games. Abstr Appl Anal 4(1)–48 Zaslavski AJ () Turnpike theorem for convex infinite dimensional. J Convex Anal 5(2)– Zaslavski AJ () Turnpike theorem for a class of discrete time optimal control.

Though many books have been written on optimal control in engineering, we see few on discrete-type optimal control. More­ over, since economic models take slightly different forms than do engineer­ ing ones, we need a comprehensive, self-contained treatment of linear optimal control applicable to discrete-time economic systems.

Michio Morishima, Japanese Neo-Walarasian economist, initially at Osaka, and from at the gh never quite abandoning his Neo-Walrasian roots, Morishima remains one of the most enthusiastic proponents of John von Neumann's model of an expanding economy. As a result, Morishima has spent much of his career exploring the von Neumann model and translating existing.

HET. HET Pages: the Paretian System: Equilibrium, Market Failure, Social Welfare, Linear Programming, Revealed Preference Theory, Local Multi-Market Stability, Production Theory: Cost Function, Short-Run and Long-Run, Technical Progress, Classical Ricardian System: the Dynamic Leontief Model, the von Neumann Turnpike, the Non-Substitution Theorem, the Cambridge Capital.

The three volumes of the "Collected Scientific Works of David Cass" are ordered chronologically, which happens to coincide with the development of the three major advances in Cass' research agenda, the development of the neoclassical growth model, the discovery of sunspot equilibria, and the analysis of models of market incompleteness.

This volume consists of Cass' early work from. Michio Morishima (森嶋 通夫, Morishima Michio, J – J ) was a heterodox economist and public intellectual who was the Sir John Hicks Professor of Economics at the London School of Economics from – He was also professor at Osaka University and member of the British he won the Order of Culture (文化勲章, Bunka-kunshō).List of Publications of Fausto Gozzi (see also the MathSciNet site or the Google Scholar site or the Scopus site).

Book. G. Fabbri, F. Gozzi and A. Swiech, Optimal Control in Infinite Dimension: Dynamic Programming and HJB Equations, with a contribution by M.

Fuhrman and G. Tessitore, Probability Theory and Stochastic Modelling, vol. 82, Springer, July Table of Contents 1 Dynamical Systems with Unbounded Time Interval in Engineering, Ecology and Economics.- Introduction.- The regulator problem.- The pest control problem and other problems of optimal control of interacting species.- The optimal economic growth problem.- Definition of optimality on an unbounded time interval.- Uniformly optimal solutions are agreeable.