Economists' Mathematical Manual

The practice of economics requires a wide-ranging knowledge of formulas from math- ematics and mathematical economics. The selection of results from mathematics included in handbooks for chemistry and physics ill suits economists. There is no concise reporting of results in economics. With this volume, we hope to present a formulary, targeted to the needs of students as well as the working economist. It grew out of a collection of mathematical formulas for economists originally made by Professor B. Thalberg and used for many years by Scandinavian students and economists. The formulary has 32 chapters, covering calculus and other often used mathemat- ics; programming and optimization theory; economic theory of the consumer and the firm; risk, finance, and growth theory; non-cooperative game theory; and elementary statistical theory. The book contains just the formulas and the minimum commentary needed to re-learn the mathematics involved. We have endeavored to state theorems at the level of generality economists might find useful. By and large, we state results for n-dimensional Euclidean space, even when the results are more generally true. In contrast to the economic maxim, 'everything is twice more continuously differentiable than it needs to be', we have listed the regularity conditions for theorems to be true. We hope that we have achieved a level of explication that is accurate and useful without being pedantic.