Jerison, Michael: Nonrepresentative Representative Consumers
World Conference Econometric Society, 2000, Seattle

Michael Jerison, SUNY Albany
Nonrepresentative Representative Consumers
Session: C-9-5  Monday 14 August 2000  by Jerison, Michael
Aggregate demand is often treated as if it were the demand of a single competitive consumer. Such a ``representative" consumer might represent aggregate consumer behavior perfectly in the positive sense (demanding the economy's aggregate demand vector in every possible aggregate budget situation) and still misrepresent the economy normatively. In particular, the representative consumer can be Pareto inconsistent, preferring a situation A to B even though all the consumers in the economy prefer B to A (Jerison (1984) and Dow and Werlang (1987)). (An example by Kirman (1992) does not show this since his ``representative individual" only demands the aggregate demand vector in two budget situations, but no others.) How serious are the possible differences between the representative and the actual consumers' preferences? The answer is not clear because the examples in the literature are not robust with respect to small changes in the preferences of the actual consumers. In this paper I show how to construct examples of large robust Pareto inconsistencies. In one example, the actual consumers require 56\% more wealth than the representative consumer requires in order to be compensated for the doubling of a price. But I show that in order for the representative consumer to differ so much from the actual consumers there must be a Giffen good. If all goods are normal then any Pareto inconsistencies must be small (the compensation required by the representative and actual consumers differ by less than 2\% when a price doubles). A Pareto consistent representative consumer exists if the wealth distribution maximizes a single social welfare function no matter which prices prevail. I show that this sufficient condition for Pareto consistency is not necessary. A weaker sufficient condition for existence of a Pareto consisent representative consumer for economies with two goods and two consumers is that the consumers' demand vectors move apart when their wealth increases.

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