One view on the problem of optimization in the theory of consumer choice

Abstract

This article presents a grapho-analytical method of solving the problem of optimization of consumer choice in microeconomics, including the computer code in MATLAB, which could be used advantageously in education or praxis. Motivation comes from the fact that this very important subject is not always treated appropriately in the domestic literature. As a starting point, we have taken one outstanding example of falsely solved problem of consumer optimization, coming from the very eminent new domestic literature. We point to the most common reasons for errors, develop an intuitive, visual grapho-analytical method of solving, which can easily be extended to any similar problems, regardless of the form of the utility function and the budget line in question. Also, we have compared this graphical method with the rigorous analytical method, based on the Karush-Kuhn-Tucker theorem, with the aim to examine, to what extent does the analytical method give any advantage over an intuitive grapho-analytical method. We have also discussed the inherent limitations of the grapho-analytical method, whereupon we have stressed that only the rigorous analytical procedure can render complete certainty and generality.