200 goods), the approximation is good enough. However, the equal spending condition has (at least) one unpalatable consequence. It can only be satisfied if everyone buys every good. If A does not smoke, and B does and would smoke more if he had more money, then redistributing money from A to B will change the demand for tobacco, and such behavior cannot be accommodated with only a representative consumer. It does not require any sort of econometric analysis, or appeal to the data in the CEX, to know that people consume different subsets of goods (even at the 200-plus commodity level), so that aggregate demand must depend on the distribution of income. If one insists on the fiction of the representative agent, one will be blind to changes in the social cost of living that are brought about by changes in the distribution of income. Conversely, one will also be blind to changes in the distribution of income that are brought about by changes in relative prices. An increases in the price of tobacco redistributes real income from (relatively poor) smokers to (relatively rich) nonsmokers. The representative consumer approach does not recognize such a possibility.
Suppose, contrary to the argument above, that the conditions hold that allow one to construct the analytic fiction of a representative consumer. One then constructs a COLI for this fictitious person to compare prices in period 1 with prices in period 0. Because the representative consumer’s behavior is the average of the behavior of each consumer in the economy, one might hope that the representative agent’s COLI is the average of the COLIs for the individual consumers. Note that nothing in the construction guarantees this. The representative consumer was constructed to represent average behavior, not the average cost-of-living index. And, in fact, the result is not true. The COLI for the representative agent is the plutocratic COLI obtained by averaging the individual COLIs with weights proportional to individual incomes. That this should be the case is intuitively clear from the fact that the representative consumer is constructed to represent average demand and that the rich contribute more to the average than do the poor, simply because they are richer and so spend more. Even though the representative consumer’s purchases of each good is a simple average of individual purchases, the representative agent’s COLI is not the simple average of the individual COLIs. Consequently, the use of a representative consumer framework in the context of plutocratic weights assigns more importance in the overall index to changes in the cost of living facing the rich than to those facing the poor.
There are alternative definitions of the representative consumer that get around the plutocratic bias. For example, one could average, not the quantities purchased by each consumer, but their budget shares, defined as the fraction of their budget allocated to each good. One could then ask whether it is possible to construct a representative agent with a representative level of income whose budget shares are always equal to the average of the budget shares for each