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 weIl 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 It grew out of a collection of mathematical formulas for economists originally made by Professor B. Thalberg and used for many years by Scandinavian students and economists.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 commcntary 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 thc 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.

1. Functions of one variable. Complex numbers.- 2. Limits. Differentiation (one variable).- 3. Partial derivatives.- 4. Elasticities. Elasticities of substitution.- 5. Systems of equations.- 6. Inequalities.- 7. Series. Taylor formulas.- 8. Integration.- 9. Difference equations. (Recurrence relations.).- 10. Differential equations.- 11. Topological concepts in Euclidean space.- 12. Convexity.- 13. Classical optimization.- 14. Linear and nonlinear programming.- 15. Calculus of variations and optimal control theory.- 16. Discrete dynamic optimization.- 17. Vectors. Linear dependence. Scalar products.- 18. Determinants.- 19. Matrices.- 20. Characteristic roots. Quadratic forms.- 21. Special matrices. Leontief systems.- 22. Kronecker products and the vec operator.- 23. Differentiation of vectors and matrices.- 24. Comparative statics. Value functions.- 25. Properties of cost and profit functions.- 26. Consumer theory.- 27. Topics from finance and growth theory.- 28. Risk and risk aversion theory.- 29. Finance and stochastic calculus.- 30. Non-cooperative game theory.- 31. Statistical concepts.- 32. Statistical distributions. Estimators.