Equivalence scales for continuous distributions of expenditure

Research background: In the actual sizable populations of households, the standard microeconomic concept of equivalence scales is intractable since its necessary condition of equality of household welfare levels is unlikely to be fulfilled. Purpose of the article: This paper aims to develop a concept of an equivalence scale, which can be suitable for continuous distributions of expenditures in the population. Methods: Using household welfare intervals, we get the random equivalence scale (RES) as the ratio of expenditure distributions of the compared populations of households. Findings & value added: We derive the parametric distribution of RES for the lognormal distributions of expenditures. The truncated distribution of RES is applied to account for possible economies of scale in the household size. A society's inequality aversion can be helpful when selecting a single equivalence scale. We estimate RES for Poland using microdata on expenditures and subjective assessments of household welfare intervals. The estimated equivalence scales turned out to be very flat and dependent on welfare.