Forward-looking individuals recognize that decisions made today affect those to be made in the future, at least in part, by expanding or contracting the set of admissible choices, that is, by lowering or raising the cost of a future choice. Such intertemporal linkages reside at the core of all dynamic processes in economics. Consequently, mathematical methods that account for such intertemporal linkages are fundamental, in principle, to all economic decisions. This book presents an introductory but thorough exposition of the fundamental mathematical formalism used to study continuous time dynamic economic processes and to interpret dynamic economic behavior, namely, optimal control theory and its ancillary techniques.

The style of presentation distinguishes the book from several other excellent texts on the subject. First of all, there is a continual emphasis on the economic interpretation of the mathematics and the models, aided dramatically by way of the method of comparative dynamics, from both a primal and dual point of view. In my twelve years of teaching the course upon which the book is based, I have found that this approach permits the students to garner a deeper conceptual understanding of intertemporal economic models. One of the keys to a deeper conceptual understanding, I believe, is the introduction of the dynamic envelope theorem relatively early in the presentation of optimal control theory. This strategy paves the way for many of the succeeding chapters of the book to be built around this vital theorem, and not only complements the aforementioned emphasis on economic interpretation and conceptualization, but also leads to motivated proofs of the transversality conditions, an area long on technicalities and short on intuition.