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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes
be necessary to offset the effects of inflation on “consumer living standards.” Similar phrases are often used to describe substitution effects in response to price changes. Sometimes the language refers explicitly to the representative consumer, sometimes to a “typical” or “average” consumer.
Pollak (1981), in a paper on social cost-of-living index numbers, showed how to define an aggregate or average COLI without any appeal to the existence of a representative agent. For example, there is a well-defined COLI for each person or family, and one can average them. This would be a democratic COLI and could be approximated by a democratic Laspeyres index (for example). Or one could work with a plutocratic COLI in which the amounts of money needed to hold living standards constant are added up over all consumers and compared with the sum of actual expenditures for all consumers. Neither of these constructions involves representative consumers of any sort, and neither is very difficult to understand, certainly not the former.
Nevertheless, the idea of a representative agent is often appealed to, though we have tried hard to avoid it in this report. One danger of the usage is that it is easy to fall into the trap of thinking of the welfare of the representative agent as representing the welfare of everyone. For example, when one talks about the COLI as being calculated (and perhaps paid, as in social security) so as to keep “consumer living standards” constant, it might be taken to mean that everyone’s living standards are being held constant. Instead, the best one can hope for is that some average of living standards is being held constant, with some people gaining and some losing. These distribution effects of price changes can sometimes be important.
Another danger of the idea of a representative consumer is that it distracts attention from the need to think explicitly about how to aggregate over different people and families. The economic theory of consumer behavior is a theory of individuals, not of groups, and the analytical results that come with it are results about individual behavior. The theory provides many insights about such topics as substitution effects, the cost of living, and welfare. It provides an apparatus to think about substitution effects and why, when price goes up, demand goes down, as well as some less obvious results, such as the equality between good i’s substitution response to the price of good j and good j’s substitution response to the price of good i. But these results are for individual consumers, not for the aggregate or average of consumers. As we discuss in Chapter 2, the theory can be used to think about cost-of-living index numbers for groups or nations, but the transition from the individual to the group is not straightforward, and it requires a good deal of explanation. So it is sometimes tempting to avoid the complications, and to apply the theory to average or aggregate behavior, thinking about the country as a whole as a “representative consumer.”
In this technical note we discuss two issues. First, what has to be true for the representative consumer to exist, in the sense that the analytic fiction will give the same answers as working with the underlying individuals and thinking about the