A proof of the existence of diminishing marginal benefit under ordinal inter-domain marginal preferences

Ordinal utility theory cannot meaningfully accommodate the concept of diminishing marginal utility (DMU) due to the sign indeterminacy of second derivatives under monotonic transformations. While cardinal utility theory could restore DMU, it relies on measurability assumptions that are generally regarded as unacceptable in modern microeconomics. This paper proposes an alternative framework based on ordinal interdomain marginal preference (OIMP) theory, in which preferences are defined through marginal exchange relations rather than total utility over bundles. Within this framework, we establish a rigorous connection between the geometry of iso-marginal preference curves (IMPC) and the behavior of marginal benefit. We prove that diminishing marginal benefit arises under simple conditions characterized by the slope of the IMPC and the configuration of exchange preference regions. The results show that most standard goods—including normal, inferior, and Giffen goods—exhibit diminishing marginal behavior in a purely ordinal setting, while deviations arise only for specific cases such as addiction-like and Veblen-like goods. The OIMP framework thus provides a complete foundation for economic analysis, preserving diminishing marginal utility while revealing its structural origin.