Notes on matematical economics

These notes are based on individual lectures of a course on mathematical economics given by the author in the autumn of 1971 in the Faculty of Mathematics and Mechanics of Moscow State University. § 1 describes the properties of neoclassical production functions and types of technological progress, Ramsey's model (distribution of income between consumption and accumulation), and on the basis of a simple example it is shown how Pontryagin's maximum principle is used to find an optimum plan. The exposition is based essentially on the material of [40]. In § 2, following Debreu, the author considers models of pure exchange (without production) and explains the structure of sets of equilibrium states in them; in this analysis, considerable use is made of Sard's lemma on regular values of smooth mappings, and simple considerations on the indices of vector fields.
These notes pursue limited methodical aims; they are intended for mathematicians and economists who show a reserved optimism about the use of mathematical methods in economics.