A convergent process of price adjustment and global newton methods

Abstract

Section 1 One goal of this paper is to give a relation between such diverse parts of economic theory as the Arrow-Block-Hurwicz dynamics of price adjustment and Scarf’s algorithm for finding economic equilibria. The underlying concept is an ordinary differential equation, which we call a ‘Global Newton’ one, associated to a system of IZ real functions,f, , . . . ,f,, of n real variables, x1, . . . , x,. The key feature of this differential equation is that, under suitable hypotheses, its solution will tend to a vector (XT, . . . , AT,*) satisfying fi($, . . ., x,*) = 0, . . .,h(xT, . . .) x,*) = 0, (1) or in vector notation, f(x*) = 0. (1’) In fact in this way an algorithm for solving (1) is provided. The differential equation itself has the form