The structure of representative preference

Abstract

In an environment of Samuelsonian aggregation, we characterize those social welfare functions which (i) map concave utility profiles to concave representative utility functions and (ii) map quasiconcave utility profiles to quasiconcave representative utility functions. Case (i) holds for any concave social welfare function, while case (ii) holds only for generalized maxmin social welfare functions. Lastly, we establish a simple duality result for computing the representative utility under a maxmin social welfare function: the representative expenditure function is the sum of the individual expenditure functions, which we use to study the aggregation of generalized Leontief utilities.