TITLE:
An Axiomatic Derivation of the Logarithmic Function as a Cardinal Utility Function on Money Income Levels
AUTHORS:
Mitsunobu Miyake
KEYWORDS:
Logarithmic Utility Function; Suppes’ Hypothesis; Bernoulli’s Hypothesis; Weber-Fechner Law; Level Comparison; Difference Comparison; Monotonicity Axiom; Consistency Axiom; Homogeneity Axiom
JOURNAL NAME:
Theoretical Economics Letters,
Vol.4 No.1,
February
12,
2014
ABSTRACT: This note elaborates
Suppes’ (1977, Erkenntnis Vol. 11,
No. 1, pp 233-250) derivation of the logarithmic function as a consumer’s
cardinal utility function on money income levels, in which the consumer’s
preferences are specified by a level comparison relation and a difference
comparison relation. Without assuming Suppes’ hypothesis (Bernoulli’s
hypothesis or Weber-Fechner law), which asserts that the utility values are
proportional to the logarithmic values of income levels, it is shown that the
representability of the two relations by logarithmic utility function can be
characterized only by the three (mutually independent) axioms on the relations.