Samuelson's Foundations: Its Mathematics

Abstract

AS ONE interested in applications of mathematics though not conversant with economic theory, I have been asked to comment on the mathematical aspects of Paul A. Samuelson's Foundations of Economic Analysis.' The announced aim of this book (p. 3) is to demonstrate that a comparatively small number of mathematical propositions contain the formal (or logical) basis of much of economic theory. If the economic analyses contained in this book are a representative sample of economic analysis in general, the demonstration is successful, for these do indeed show great mathematical unity. Thanks to this unity, few mathematical topics are drawn upon, almost all being among those which find everyday application in such diverse fields as physics and statistics. The principal topics, in addition to those ordinarily taught in elementary calculus, are the implicit function theorem, Lagrange multipliers, systems of linear differential equations (and the like), and matrix algebra. The book is reasonably comprehensible to anyone somewhat familiar with most of these topics, especially since it contains (in special appendixes and elsewhere) a considerable amount of mathematical exposition well suited for review and supplementary study. With the exception of matrix algebra, the foregoing topics are likely to have been encountered by any student who has pursued mathematics for a year beyond the first year of calculus. Matrix algebra is recognized by mathematicians to be of immense value in almost every