Nonrepresentative representative consumers

Representative consumers can be very Pareto inconsistent. We describe a cornmunity, with equal income distribution, where all consumers require 56 % higher aggregate income than the representative consumer requires in order to be compensated for the doubling of a price. Such large inconsistencies are ruled out if the representative consumer is homothetic, or if the consumers' income shares are fixed and all goods are normal. We show that optimality of the income distribution rule is not necessary for Pareto consistency of the representative consumer, and we give a weaker sufficient condition for Pareto consistency in cornmunities with two goods and two consumers