Inequality Aversion and the Measurement of Real Income

Even under identical preferences, non-homotheticity makes the measurement of real income ethically consequential. Money-metric utility and related welfare indices require a choice of reference prices, and different admissible choices can change conclusions about growth comparisons, inflation inequality, and aggregate welfare. This paper derives welfare cardinalization from society's attitude towards inequality. Building on Okun's leaky-bucket thought experiment, an increasing, concave function ϕ specifies the leaky equalizing income transfers that society must accept at every common price vector. The proposed principle of ϕ-prioritarianism selects the least inequality-averse social ranking satisfying this requirement. Together with standard axioms and regularity conditions, it characterizes a unique social ranking and the class of real-income representations that implement it. Under additional conditions, the ranking can be written as a prioritarian sum of money-metric utilities with an endogenously selected reference price system. The paper then derives explicit formulas for standard non-homothetic demand systems, including Gorman polar form, PIGL, and non-homothetic CES, and expresses selected real-income normalizations as corrections to Divisia-style growth indices. Finally, the extension to heterogeneous preferences highlights the logical distinction between interpersonal comparability and welfare cardinalization. Conditional on an independently specified interpersonal ordering, ϕ-prioritarianism disciplines the common transformation through which comparable welfare levels enter social aggregation.