# Weber-Fechner's Law and Demand Function

Source: [Weber-Fechner's Law and Demand Function](<https://www.sota2.com/research/paper/68fa1fc67a2b558e2932c257>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T19:39:46.431Z

Authors: K. Shigemoto

Published: 2003-03-28T06:12:51.000Z

## 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/physics/0303118>)

[PDF](<https://arxiv.org/pdf/physics/0303118.pdf>)