Mathematical Proof of the Ordinal Marginal Preference Theory

Abstract

The model in which an individual maximizes the ordinal or cardinal total utility subject to her budget constraint has long been the paradigm of individual choice theory in economics. The ordinal total utility theory has the advantage of utility immeasurability, but the disadvantage of being inconsistent with common sense such as the principle of diminishing marginal utility. The cardinal total utility theory is consistent with the aforementioned common sense, but suffers from the problem of utility measurability. This leads to a dilemma when one develops a utility-maximization model: she either needs to abandon common sense, or needs to postulate measurability for utility. This puzzling riddle, as of today, is still unsolved. The purpose of this paper is to present a new theory — the ordinal marginal utility theory — to solve this puzzle, and offers a complete formal axiomatic proof.