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At What Price?: Conceptualizing and Measuring Cost-of-Living and Price Indexes
a well-integrated, low-transport-cost economy like that of the United States, the assumption works well for many consumer goods, but there are obvious exceptions, of which shelter and medical care are almost certainly the most important. Nevertheless, imagine an economy in which everyone faces the same prices, and differs only in the total amount they spend and in the how they divide it among different goods. In the individual Laspeyres indexes, prices are weighted in proportion to individual expenditures, while in the national Laspeyres index, prices are weighted by aggregate expenditures. It is useful to think of the Laspeyres index as a weighted average of the “price relatives,” which are the ratios of current to reference prices for each good. The Laspeyres weights are the shares of each good in total expenditure, whether for the individual family or the nation (for the equations, see the “Technical Note” at the end of the chapter). The national Laspeyres then differs from the individual Laspeyres only in the weights used: For the national index, the weights are the shares of each good in national total expenditure; for each individual family’s index, the weights are the shares of each good in the family’s total expenditure.
Is the national price index an average of the price indexes for each family? Yes, but it is a weighted average, not a simple average. Because the national index uses national expenditures as weights, and because families who spend more contribute more to the national expenditure than do families who spend less, those who spend more get a higher weight in the national index. Indeed, the national Laspeyres price index is a weighted average of the individual families’ Laspeyres price indexes, with weights equal to the total expenditure on all goods by each family. This weighting was termed plutocratic by Prais (1959); the rich—or at least the rich who consume more—get a higher weight in the price index than do the poor. The obvious alternative, in which each family makes an equal contribution to the index, is called the democratic price index and would be calculated from the individual price indexes by simple averaging. In general, the democratic and plutocratic price indexes differ, and they will move differently whenever the prices of goods consumed by different income groups change at different rates. A recent example is the price of cigarettes, which makes up a larger share of the budgets of people with lower incomes. Increases in cigarette prices increase a democratic price index by more than a plutocratic index.
The Laspeyres price indexes produced by statistical offices around the world are always plutocratic, not democratic, indexes. Elsewhere in the report, we argue that, were it possible to calculate a democratic price index at reasonable cost, it should be preferred to a plutocratic index for many purposes, especially those to do with compensation. But we also argue that there are real practical difficulties in constructing the democratic index. Those difficulties help explain the universal reliance on plutocratic indexes.
The relationship between national and individual price indexes is much murkier if one allows for the fact that different people often pay different prices