On application of Newton’s Method to solve optimization problems in the consumer theory. Expansion’s Paths and Engel Curves

The paper continues investigations concerned with numerical modeling of the neoclassical theory of consumption begun in our previous paper [Strasburger et al. (2009)] This time we are interested in expansion’s paths and Engel curves for separable utility functions.. The used numerical procedure is based on Newton’s approximation method, implemented in the MATLAB environment. Based on the prior determination of the approximate solutions of the optimum problem we determine in this paper the expansion paths and Engel curves and compare them with their standard form studied in econometrics