Weber-Fechner's Law and Demand Function

Abstract

We apply the Weber-Fechner's law, which represents the relation between the magnitude of physical stimulus and the magnitude of psychological sense in human being, to the utility function. We conclude that the utility function of n-types of goods is of separable type u(x_1,x_2,..., x_n)=u_1(x_1)+u_2(x_2)+... +u_n(x_n), which give the relation of the demand function in the form p_i=d u_i/d x_i. The explicit quantitative form of each utility function, which is suggested by the Weber-Fechner's law, becomes u_i(x_i)=A_i \log (x_i/x^{(0)}_i). Then we obtain each demand function in the familiar form p_i=A_i/x_i.