Mathematical Proof of the Ordinal Marginal Preference Theory Under the Fixed Exchange Conditions.

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. Lin and Peng [A rehabilitation of the law of diminishing marginal utility: An ordinal marginal utility approach, The B.E Journal of Theoretical Economics 22(2) (2022) 453–481] developed the ordinal marginal utility (OMU) theory aiming to solve the above dilemma between the two theories. This paper provides a complete formal axiomatic proof for this new theory by offering the related mathematical definitions, axioms, and their derived properties. We prove that the marginal utility function of a bundle of objects can be derived from the ordinal marginal preference between two bundles of objects, and that this function exists, is continuous, and can keep the property of diminishing marginal utility. [ABSTRACT FROM AUTHOR]