Extension of domain of utility function with two reference points and confirmation of its prospect-theoretical properties.

Abstract

Conventional consumption functions are obtained by solving the condition that the Cobb-Douglas utility function is maximized under the budget constraint equation. Nakazawa (2014) constructed a model in which the consumption in the utility function is replaced by its ratio or difference to the reference point. This paper draws, using numerical calculation software, the surface of the utility function with two reference points, which were constructed in Kazama and Kitamura (2018) and cannot be algebraically solved, and confirms its prospect-theoretical properties. Also, for cases with one and two reference points, time variations of optimum consumption in two persons and two goods are numerically calculated. By comparing the two cases, we clarify the features of the utility function with two reference points.