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These notes are the result of an interrupted sequence of seminars on optimiza tion theory with economic applications starting in 1964-1965. This is mentioned by way of explaining the uneven style that pervades them. Lately I have been using the notes for a two semester course on the subject for graduate students in economics. Except for the introductory survey, the notes are intended to provide an appetizer to more sophisticated aspects of optimization theory and economic theory. The notes are divided into three parts. Part I collects most of the results on constrained extremf of...

It is not an exaggeration to state that most problems dealt with in economic theory can be formulated as problems in optimization theory. This holds true for the paradigm of "behavioral" optimization in the pursuit of individual self interests and societally efficient resource allocation, as well as for equilibrium paradigms where existence and stability problems in dynamics can often be stated as "potential" problems in optimization. For this reason, books in mathematical economics and in mathematics for economists devote considerable attention to optimization theory. However, with very few...

Contrary to widely held beliefs, microeconomic theory bears no rela tion to the size of the product under consideration; indeed a micro theorist can just as easily discuss the sale of a whale as he would discuss a whale of a sale in amoebae. In fact, it possibly is true that a theorist, and a microeconomic theorist in particular, does not have any specific products in mind when he bandies his propositions about. Nor does he have to. For these in the final analysis are just that; propositions. They are propositions that are motivated by economic reality as observable, not to mention...

This book is devoted to the mathematical analysis of models of economic dynamics and equilibria. These models form an important part of mathemati cal economics. Models of economic dynamics describe the motion of an economy through time. The basic concept in the study of these models is that of a trajectory, i.e., a sequence of elements of the phase space that describe admissible (possible) development of the economy. From all trajectories, we select those that are" desirable," i.e., optimal in terms of a certain criterion. The apparatus of point-set maps is the appropriate tool for the...