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An Axiomatic Derivation of the Logarithmic Function as a Cardinal Utility Function on Money Income Levels
Graduate School of Economics and Management, Tohoku University, Sendai, Japan
- 1 Graduate School of Economics and Management, Tohoku University, Sendai, Japan
Theoretical Economics Letters·Volume 04 (2014)·Pages 7–11·Published 12 February 2014·DOI10.4236/tel.2014.41002
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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.
KeywordsLogarithmic Utility FunctionSuppes’ HypothesisBernoulli’s HypothesisWeber-Fechner LawLevel ComparisonDifference ComparisonMonotonicity AxiomConsistency AxiomHomogeneity Axiom
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