PRICE INDEX DISTRIBUTION AND UTILITARIANSOCIAL EVALUATION FUNCTIONS

Living standard indicators are complex nonlinear statistics based on fundamen-tal components (income or consumption data, prices, household characteristics andenvironment). The statistical distributions of these components, which are oftenincompletely obseved, are central to study utilitarian social evaluation functions(USEF) and associated inequality measures. One important case on which wefocus is when the living standard indicator can be represented as a ratio of twoweakly statistically associated components. Our typical example is that of theeect of the distribution of price indices on USEFs or on inequality measures.First, we provide theoretical decompositions into the eect of change in priceindex dispersion and the eect of change in aggregate level of prices, with knowndirections of components. Second, new notions describing aversion and sensitivityof USEFs to price dispersion are derived. Third, Atkinson's inequality measuresare shown to belong to an interval whose bounds are inequality measures withoutprice index dispersion...