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This book serves not only as an introduction, but also as an advanced text and reference source in the field of deterministic optimal control systems governed by ordinary differential equations. It also includes an introduction to the classical calculus of variations.
An important feature of the book is the inclusion of a large number of examples, in which the theory is applied to a wide variety of economics problems. The presentation of simple models helps illuminate pertinent qualitative and analytic points, useful when confronted with a more complex reality. These models cover: economic growth in both open and closed economies, exploitation of (non-) renewable resources, pollution control, behaviour of firms, and differential games. A great emphasis on precision pervades the book, setting it apart from the bulk of literature in this area. The rigorous techniques presented should help the reader avoid errors which often recur in the application of control theory within economics.
List of contents
Calculus of Variations. Optimal Control Theory Without Restrictions On The State Variables. Extensions. Mixed Constraints. Pure State Constraints. Mixed and Pure State Constraints.
Report
"will be useful for graduate students and researchers wanting a thorough guide to solving a few dimensional optimal control problems in economic theory." --Economic Journal
"...can be recommended to any advanced economist. It will be valuable for everyone who is concerned with dynamical systems in economic theory. Moreover for a textbook it makes an essential contribution to the theory of optimal controls." --Journal of Economics, 1989
St. Jørgensen
"a valuable addition to the literature on optimal control of economic processes." --Zentralblatt für Mathematik
"I highly recommend the book which is in my opinion the best text on economic applications of optimal control theory being on market. Moreover, there is no doubt that it is also of interest to non-economists." --Zeitschrift für Operations Research - Series A: Theory
