# Optimization in Economic Theory

## Synopsis

Building on a base of simple economic theory and elementary linear algebra and calculus, this broad treatment of static and dynamic optimization methods discusses the importance of shadow prices, and reviews functions defined by solutions of optimization problems. Recently revised and expanded by the author, the second edition of this popular student text will be a valuable resource for upper level undergraduate and graduate students.

## Excerpt

Making optimal use of scarce resources, that is, maximizing subject to constraints, is the central theme of economics. But students of economics are often taught the mathematics of constrained maximization as a branch of mathematics, and its economic applications follow separately. An integrated treatment that relates the mathematics to the economics from the beginning has the potential for providing a quicker and deeper understanding. This book aims to give such an exposition. I emphasize economic intuition rather than mathematical rigor. Proofs of the mathematical theorems are structured to bring out points of economic interest and facilitate economic applications. The illustrative examples and exercises are also chosen for their economic interest and usefulness.

The first edition of this book was published in 1976. The central aim of the book is still valid, but the subject has changed a great deal over the years. Therefore I have revised the text very substantially. A chapter on uncertainty, with some treatment of topics like finance and asymmetric information, is now indispensable. I have added such a chapter, and have also expanded the chapter on dynamic programming to treat uncertainty.

Most chapters have been thoroughly rewritten, and many new examples and exercises added. One innovation deserves special mention. When the first edition was written, the main mode of exposition in elementary and intermediate microeconomics was geometric, based on the tangency between a budget line and an indifference curve, or a cost line and a production isoquant. Nowadays this shibboleth of tangency seems less prevalent. Therefore I have used a starting-point that is simpler and economically more intuitive, namely the search for costless improvements through 'arbitrage' operations. This allows an integrated treatment of tangency and corner optima, and its intuition extends much more readily to situations involving time, uncertainty etc.

In the years since the first edition of this book was published, the mathematical training of economics students has improved substantially. I have taken advantage of this by going a little deeper into some topics, letting the pace pick up in the last three chapters, and sketching the proof of the central result of constrained maximization - the Kuhn - Tucker theorem - in a mathematical appendix. But the book remains aimed at the majority of economics . . .

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