Download or read book Optimality in Infinite Horizon Economies written by Anders Borglin and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern welfare economics as it is known today to economists took its final shape with the emergence of the Arrow-Debreu model. The classical conjectures about the beneficient workings of markets together with the converse statement, that optimal (in the sense of Pareto) allocations may be sustained by prices and markets, has laid a firm foundation for further research in welfare economics. But more than that, it has inspired researchers to take up entirely new topics, notably by closer considerations of situations where the assumptions of the original model may seem overly restrictive. One of these new directions has been connected with generalizing the model so that it takes into account the possibility of infinitely many commodities. On the face of it, the idea of an infinity of commodities may seem a mathematical fancy having no "real" counterpart in economic life. This is not so, however. Quite to the contrary, infinity enters in a very natural way when it is taken into account that economic transactions take place over time. 2 In the Arrow-Debreu formalism, time may be incorporated into the model in a very simple way using dated commodities. Thus two commodities are considered as being different if they are to be delivered at different points of time.

Download or read book Infinite Horizon Optimal Control written by Dean A. Carlson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with various classes of deterministic continuous time optimal control problems wh ich are defined over unbounded time intervala. For these problems, the performance criterion is described by an improper integral and it is possible that, when evaluated at a given admissible element, this criterion is unbounded. To cope with this divergence new optimality concepts; referred to here as "overtaking", "weakly overtaking", "agreeable plans", etc. ; have been proposed. The motivation for studying these problems arisee primarily from the economic and biological aciences where models of this nature arise quite naturally since no natural bound can be placed on the time horizon when one considers the evolution of the state of a given economy or species. The reeponsibility for the introduction of this interesting class of problems rests with the economiste who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey who, in his seminal work on a theory of saving in 1928, considered a dynamic optimization model defined on an infinite time horizon. Briefly, this problem can be described as a "Lagrange problem with unbounded time interval". The advent of modern control theory, particularly the formulation of the famoue Maximum Principle of Pontryagin, has had a considerable impact on the treatment of these models as well as optimization theory in general.

Download or read book Decentralization In Infinite Horizon Economies written by Mukul Majumdar and published by CRC Press. This book was released on 2019-03-07 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book summarizes some issues involved in developing a theory of decentralized resource allocation mechanism in infinite horizon economies. It constitutes a definitive account of cutting-edge research on a topic of continuing importance in price theory. .

Download or read book Turnpike Phenomenon and Infinite Horizon Optimal Control written by Alexander J. Zaslavski and published by Springer. This book was released on 2014-09-04 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of the turnpike phenomenon and describes the existence of solutions for a large variety of infinite horizon optimal control classes of problems. Chapter 1 provides introductory material on turnpike properties. Chapter 2 studies the turnpike phenomenon for discrete-time optimal control problems. The turnpike properties of autonomous problems with extended-value integrands are studied in Chapter 3. Chapter 4 focuses on large classes of infinite horizon optimal control problems without convexity (concavity) assumptions. In Chapter 5, the turnpike results for a class of dynamic discrete-time two-player zero-sum game are proven. This thorough exposition will be very useful for mathematicians working in the fields of optimal control, the calculus of variations, applied functional analysis and infinite horizon optimization. It may also be used as a primary text in a graduate course in optimal control or as supplementary text for a variety of courses in other disciplines. Researchers in other fields such as economics and game theory, where turnpike properties are well known, will also find this Work valuable.

Download or read book Introduction to Modern Economic Growth written by Daron Acemoglu and published by Princeton University Press. This book was released on 2008-12-15 with total page 1009 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Nobel Prize–winning economist Daron Acemoglu, an incisive introduction to economic growth Introduction to Modern Economic Growth is a groundbreaking text from one of today's leading economists. Daron Acemoglu gives graduate students not only the tools to analyze growth and related macroeconomic problems, but also the broad perspective needed to apply those tools to the big-picture questions of growth and divergence. And he introduces the economic and mathematical foundations of modern growth theory and macroeconomics in a rigorous but easy to follow manner. After covering the necessary background on dynamic general equilibrium and dynamic optimization, the book presents the basic workhorse models of growth and takes students to the frontier areas of growth theory, including models of human capital, endogenous technological change, technology transfer, international trade, economic development, and political economy. The book integrates these theories with data and shows how theoretical approaches can lead to better perspectives on the fundamental causes of economic growth and the wealth of nations. Innovative and authoritative, this book is likely to shape how economic growth is taught and learned for years to come. Introduces all the foundations for understanding economic growth and dynamic macroeconomic analysis Focuses on the big-picture questions of economic growth Provides mathematical foundations Presents dynamic general equilibrium Covers models such as basic Solow, neoclassical growth, and overlapping generations, as well as models of endogenous technology and international linkages Addresses frontier research areas such as international linkages, international trade, political economy, and economic development and structural change An accompanying Student Solutions Manual containing the answers to selected exercises is available (978-0-691-14163-3/$24.95). See: https://press.princeton.edu/titles/8970.html For Professors only: To access a complete solutions manual online, email us at: [email protected]

Download or read book Foundations of Dynamic Economic Analysis written by Michael Ralph Caputo and published by Cambridge University Press. This book was released on 2005-01-17 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Dynamic Economic Analysis presents a modern and thorough exposition of the fundamental mathematical formalism used to study optimal control theory, i.e., continuous time dynamic economic processes, and to interpret dynamic economic behavior. The style of presentation, with its continual emphasis on the economic interpretation of mathematics and models, distinguishes it from several other excellent texts on the subject. This approach is aided dramatically by introducing the dynamic envelope theorem and the method of comparative dynamics early in the exposition. Accordingly, motivated and economically revealing proofs of the transversality conditions come about by use of the dynamic envelope theorem. Furthermore, such sequencing of the material naturally leads to the development of the primal-dual method of comparative dynamics and dynamic duality theory, two modern approaches used to tease out the empirical content of optimal control models. The stylistic approach ultimately draws attention to the empirical richness of optimal control theory, a feature missing in virtually all other textbooks of this type.

Download or read book Optimal Control Problems Arising in Mathematical Economics written by Alexander J. Zaslavski and published by Springer Nature. This book was released on 2022-06-28 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of two large classes of discrete-time optimal control problems arising in mathematical economics. Nonautonomous optimal control problems of the first class are determined by a sequence of objective functions and sequence of constraint maps. They correspond to a general model of economic growth. We are interested in turnpike properties of approximate solutions and in the stability of the turnpike phenomenon under small perturbations of objective functions and constraint maps. The second class of autonomous optimal control problems corresponds to another general class of models of economic dynamics which includes the Robinson–Solow–Srinivasan model as a particular case. In Chap. 1 we discuss turnpike properties for a large class of discrete-time optimal control problems studied in the literature and for the Robinson–Solow–Srinivasan model. In Chap. 2 we introduce the first class of optimal control problems and study its turnpike property. This class of problems is also discussed in Chaps. 3–6. In Chap. 3 we study the stability of the turnpike phenomenon under small perturbations of the objective functions. Analogous results for problems with discounting are considered in Chap. 4. In Chap. 5 we study the stability of the turnpike phenomenon under small perturbations of the objective functions and the constraint maps. Analogous results for problems with discounting are established in Chap. 6. The results of Chaps. 5 and 6 are new. The second class of problems is studied in Chaps. 7–9. In Chap. 7 we study the turnpike properties. The stability of the turnpike phenomenon under small perturbations of the objective functions is established in Chap. 8. In Chap. 9 we establish the stability of the turnpike phenomenon under small perturbations of the objective functions and the constraint maps. The results of Chaps. 8 and 9 are new. In Chap. 10 we study optimal control problems related to a model of knowledge-based endogenous economic growth and show the existence of trajectories of unbounded economic growth and provide estimates for the growth rate.

Download or read book Sufficient Conditions for Optimality in Infinite Horizon Linear Economic Models written by David Stephen Prince Hopkins and published by . This book was released on 1969 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report contains some results concerning the numerical computation of optimal solutions to infinite-horizon dynamic linear programs. Models of this type arise in several contexts in the economics literature. Two sets of sufficient conditions for optimality are formulated. These refer to a general dynamic structure in which the constraints for any period, t, do not include any variable whose time subscript is greater than t. The sufficiency theorems proved in Chapter 3 ensure that a given solution which meets one of these sets of conditions is infinite-horizon optimal. The remainder of the work is concerned with demonstrating how one might construct an infinite-horizon optimal solution in practice. For this purpose, two economic applications are considered - a model for equipment replacement and capacity expansion, and a development planning model. (Author).

Download or read book Modern Optimal Control written by E. O. Roxin and published by CRC Press. This book was released on 1989-07-28 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advances in Mathematical Economics written by Toru Maruyama and published by Springer Nature. This book was released on 2020-02-20 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories.

Download or read book Optimal Control Problems Arising in Forest Management written by Alexander J. Zaslavski and published by Springer. This book was released on 2019-08-16 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of optimal control problems arising in forest management, an important and fascinating topic in mathematical economics studied by many researchers over the years. The volume studies the forest management problem by analyzing a class of optimal control problems that contains it and showing the existence of optimal solutions over infinite horizon. It also studies the structure of approximate solutions on finite intervals and their turnpike properties, as well as the stability of the turnpike phenomenon and the structure of approximate solutions on finite intervals in the regions close to the end points. The book is intended for mathematicians interested in the optimization theory, optimal control and their applications to the economic theory.

Download or read book Optimal Control Theory written by Suresh P. Sethi and published by Springer Nature. This book was released on 2022-01-03 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers’ understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields.

Download or read book Handbook on Optimal Growth 1 written by Rose-Anne Dana and published by Springer Science & Business Media. This book was released on 2006-07-01 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of efficient or optimal allocation of resources is a fundamental concern of economic analysis. This book provides surveys of significant results of the theory of optimal growth, as well as the techniques of dynamic optimization theory on which they are based. Armed with the results and methods of this theory, a researcher will be in an advantageous position to apply these versatile methods of analysis to new issues in the area of dynamic economics.

Download or read book Studies in Austrian Capital Theory Investment and Time written by Malte Faber and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The neglect of time in general and of the time structure of production in particular in mainstream economics led to the rebirth of the Austrian tradition in the seventies. The names of BERNHCLZ, HICKS, KIRZNER and VON WEIZSACKER are representative of different approaches. In 1979 my "Introduction to Modern Austrian Capital Theory" appeared, in which I unified various papers BERNHOLZ and I had written. I also linked our approach to those of VON NEUMANN, of HICKS and of neoclassical capital theory. These "Studies" supplement and continue my "Introduction" in various ways. With all the authors of the present volume I have cooperated for several years. This volume is subdivided into five parts. The first one, Historical Perspectives, gives first an outline on the development of Austrian capital theory from its origins to the present. Next it relates Modern Austrian Capital Theory to SRAFFA's theory and to the Austrian subjectivists' pure time preference theory of interest. The latter theory is represented in its opposition to the traditional productivity-cum-time preference explanation of interest, which is. common t9 neoclassical and BOHM-BAWERKian capital theory alike. The Austrian subjectivist pure time preference theory has been misinterpreted in its recent presentation, which has led to misunderstandings. It is shown that there is no real contradiction between the two appoaches.

Download or read book Optimal Control Problems Related to the Robinson Solow Srinivasan Model written by Alexander J. Zaslavski and published by Springer Nature. This book was released on 2021-08-07 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of classes of optimal control problems arising in economic growth theory, related to the Robinson–Solow–Srinivasan (RSS) model. The model was introduced in the 1960s by economists Joan Robinson, Robert Solow, and Thirukodikaval Nilakanta Srinivasan and was further studied by Robinson, Nobuo Okishio, and Joseph Stiglitz. Since then, the study of the RSS model has become an important element of economic dynamics. In this book, two large general classes of optimal control problems, both of them containing the RSS model as a particular case, are presented for study. For these two classes, a turnpike theory is developed and the existence of solutions to the corresponding infinite horizon optimal control problems is established. The book contains 9 chapters. Chapter 1 discusses turnpike properties for some optimal control problems that are known in the literature, including problems corresponding to the RSS model. The first class of optimal control problems is studied in Chaps. 2–6. In Chap. 2, infinite horizon optimal control problems with nonautonomous optimality criteria are considered. The utility functions, which determine the optimality criterion, are nonconcave. This class of models contains the RSS model as a particular case. The stability of the turnpike phenomenon of the one-dimensional nonautonomous concave RSS model is analyzed in Chap. 3. The following chapter takes up the study of a class of autonomous nonconcave optimal control problems, a subclass of problems considered in Chap. 2. The equivalence of the turnpike property and the asymptotic turnpike property, as well as the stability of the turnpike phenomenon, is established. Turnpike conditions and the stability of the turnpike phenomenon for nonautonomous problems are examined in Chap. 5, with Chap. 6 devoted to the study of the turnpike properties for the one-dimensional nonautonomous nonconcave RSS model. The utility functions, which determine the optimality criterion, are nonconcave. The class of RSS models is identified with a complete metric space of utility functions. Using the Baire category approach, the turnpike phenomenon is shown to hold for most of the models. Chapter 7 begins the study of the second large class of autonomous optimal control problems, and turnpike conditions are established. The stability of the turnpike phenomenon for this class of problems is investigated further in Chaps. 8 and 9.

Download or read book Dynamic Systems Economic Growth and the Environment written by Jesús Crespo Cuaresma and published by Springer Science & Business Media. This book was released on 2009-10-20 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: The major goal of the book is to create an environment for matching different d- ciplinary approaches to studying economic growth. This goal is implemented on the basis of results of the Symposium “Applications of Dynamic Systems to E- nomic Growth with Environment” which was held at the International Institute for Applied Systems Analysis (IIASA) on the 7th–8th of November, 2008, within the IIASA Project “Driving Forces of Economic Growth” (ECG). The symposium was organized by coordinators of the ECG project: Jesus Crespo-Cuaresma from IIASA World Population Program, and Tapio Palokangas and Alexander Tarasyev from IIASA Dynamic Systems Program. The book addresses the issues of sustainability of economic growth in a cha- ing environment, global warming and exhausting energy resources, technological change, and also focuses on explanations of signi?cant ?uctuations in countries’ growth rates. The chapters focus on the analysis of historical economic growth - periences in relation to environmental policy, technological change, development of transport infrastructure, population issues and environmental mortality. The book is written in a popular-science style, accessible to any intelligent lay reader. The prime audience for the book is economists, mathematicians and en- neersworkingonproblemsofeconomicgrowthandenvironment.Themathematical part of the book is presented in a rigorous manner, and the detailed analysis is - pected to be of interest to specialists in optimal control and applications to economic modeling. The book consists of four interrelated parts.

Download or read book Numerical Methods in Economics written by Kenneth L. Judd and published by MIT Press. This book was released on 2023-04-04 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A website contains supplementary material including programs and answers to exercises.