Optimal Control And System Theory In Dynamic Economic Analysis

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.

New Trends in Dynamic System Theory and Economics contains selected papers presented at a two-week seminar on New Trends in Dynamic System Theory and Economics held at the International Center for Mechanical Sciences in Udine, Italy, on September 12-23, 1977. Contributors discuss recent trends in the application of dynamic system theory in economic analysis, paying particular attention to information patterns and uncertainty, optimal control theory and its application, and disequilibrium analysis. This book is divided into three sections and consists of 20 chapters. Decision problems of agents with different or imperfect information or under uncertainty are first discussed. This section gives a detailed analysis of the properties of Nash and Stackelberg equilibria in dynamic games under several different information patterns. Consideration is also given to microdecision problems of individual agents, macroeconomic stabilization of an uncertain dynamic economy, and the uncertainty of parameter values. The chapters that follow focus on recent advances in optimal control theory and application of control theory. Disequilibrium analysis of a macroeconomic model is presented, along with the dynamics of disequilibria of a macroeconomic model with flexible wages and prices. A generalization of Pareto optimality is used to discuss the connection between the optimality and stability problems in a general setting. The last three chapters explore ""modern"" approaches to tâtonnement processes. This book will be of interest to students and practitioners of applied mathematics and econometrics.

This book deals with the stabilisation and control of centralised policy-making and its economic implications.

Giovanni Castellani Rector of the University of Venice This book contains the Proceedings of the Conference on "Economic Policy and Control Theory" which was held at the University of Venice (Italy) on 27 January-l February 1985. The goal of the Conference was to survey the main developments of control theory in economics, by emphasizing particularly new achievements in the analysis of dynamic economic models by con trol methods. The development of control theory is strictly related to the development of science and technology in the last forty years. Control theory was indeed applied mainly in engineering, and only in the sixties economists started using control methods for analys ing economic problems, even if some preliminary economic applica tions of calculus of variations, from which control theory was then developed, date back to the twenties. Applications of control theory in economics also had to solve new, complicated, problems, like those encountered in optimal growth models, or like the determination of the appropriate inter temporal social welfare function, of the policy horizon and the relative final state of the system, of the appropriate discount factor. Furthermore, the uncertainty characterizing economic models had to be taken into account, thus giving rise to the development of stochastic control theory in economics.

Optimal Control theory has been increasingly used in Economi- and Management Science in the last fifteen years or so. It is now commonplace, even at textbook level. It has been applied to a great many areas of Economics and Management Science, such as Optimal Growth, Optimal Population, Pollution control, Natural Resources, Bioeconomics, Education, International Trade, Monopoly, Oligopoly and Duopoly, Urban and Regional Economics, Arms Race control, Business Finance, Inventory Planning, Marketing, Maintenance and Replacement policy and many others. It is a powerful tool of dynamic optimization. There is no doubt social sciences students should be familiar with this tool, if not for their own research, at least for reading the literature. These Lecture Notes attempt to provide a plain exposition of Optimal Control Theory, with a number of economic examples and applications designed mainly to illustrate the various techniques and point out the wide range of possible applications rather than to treat exhaustively any area of economic theory or policy. Chapters 2,3 and 4 are devoted to the Calculus of Variations, Chapter 5 develops Optimal Control theory from the Variational approach, Chapter 6 deals with the problems of constrained state and control variables , Chapter 7, with Linear Control models and Chapter 8, with stabilization models. Discrete systems are discussed in Chapter 9 and Sensitivity analysis in Chapter 10. Chapter 11 presents a wide range of Economics and Management Science applications.