Welfare Evaluation in a Heterogeneous Agent Model: How Representative is the CES Representative Consumer?

The present paper investigates the impact of asymmetric price changes on welfare in a model with heterogeneous consumers. I consider consumer heterogeneity a la Anderson et al. (1992). The standard welfare equivalence between the CES representative consumer and the discrete choice model breaks down in presence of asymmetric price changes. In fact, asymmetric variation in prices produce differential gains among heterogeneous consumers. I show that there exists no feasible Kaldor-Hicks income transfer such that the gains are equally redistributed. Intuitively, in presence of decreasing marginal utility, aggregation creates an insurance mechanism: the CES representative consumer softens the impact of price changes reallocating consumption among the available varieties. Individual consumers, instead, purchase a single product and do not internalize the effects of changes in prices of other available varieties. This result suggests that only symmetric policy-induced price changes minimize the utility losses across heterogeneous consumers.