Mathematical Optimization and Economic Theory provides a self-contained introduction to and survey of mathematical programming and control techniques and their applications to static and dynamic problems in economics, respectively. It is distinctive in showing the unity of the various approaches to solving problems of constrained optimization that all stem back directly or indirectly to the method of Lagrange multipliers. In the 30 years since its initial publication, there have been many more applications of these mathematical techniques in economics, as well as some advances in the mathematics of programming and control. Nevertheless, the basic techniques remain the same today as when the book was originally published. Thus, it continues to be useful not only to its original audience of advanced undergraduate and graduate students in economics, but also to mathematicians and other researchers who are interested in learning about the applications of the mathematics of optimization to economics.
The book is distinctive in that it covers in some depth both static programming problems and dynamic control problems of optimization and the techniques of their solution. It also clearly presents many applications of these techniques to economics, and it shows why optimization is important for economics. Many cchallenging problems for both students and researchers are included.
Problems of optimization are pervasive in the modern world, appearing in science, social science, engineering, and business. Recent developments in optimization theory, especially those in mathematical programming and control theory, have therefore had many important areas of application and promise to have even wider usage in the future.
This book is intended as a self-contained introduction to and survey of static and dynamic optimization techniques and their application to economic theory. It is distinctive in covering both programming and control theory. While book-length studies exist for each topic covered here, it was felt that a book covering all these topics would be useful in showing their important interrelationships and the logic of their development. Because each chapter could have been a book in its own right, it was necessary to be selective. The emphasis is on presenting as clearly as possible the problem to be treated, and the best method of attack to enable the reader to use the techniques in solving problems. Space considerations precluded inclusion of some rigorous proofs, detailed refinements and extensions, and special cases; however, they are indirectly covered in the footnotes, problems, appendices, and bibliographies. While some problems are exercises in manipulating techniques, most are teaching or research problems, suggesting new ideas and offering a challenge to the reader. Most chapters contain a bibliography, and the most important references are indicated in the first footnote of each chapter. The most important equations are numbered in bold face type.