Price Dispersion and Functional Price Indices

Let S denote a set of consumers who have identical, nondecreasing, ordinal, quasiconcave utility functions u: XS(t) -* uX (t), where XX(t) is the vector of n goods consumed by individual s at time t. Consumers shop at different stores and hence may pay different prices for commodities.4 Let PS(t) and yS(t) denote exogenous vectors of commodity prices and income, respectively, faced by individual s at time t. This does not preclude the existence of a subset, 5, of consumers who all face the same prices, i.e., P5(t) = pS (t) for all s, s'c S. At each instant in time consumers attempt to