On Plutocratic and Democratic CPIs

Prais (1958) showed that the standard CPI computed by most statistical agencies can be interpreted as a plutocratic weighted average of household price indexes because the weight of each household in the official CPI is determined by its total expenditures. In this paper, we decompose the difference between the standard CPI and a democratically weighted index as the product of a measure of income inequality and the sample covariance between the elementary individual price indexes and a parameter which is a function of the income elasticity of each good.