adds up all the required amounts over all families in the economy to get the total amount of money that would be needed to keep them all just as well off as before. The ratio of this total to the total amount of money spent in the base period is the social cost-of-living index.
An alternative to the social cost-of-living index would be to take the cost-of-living index number for each family and average those numbers over all families to get a national cost-of-living index. This democratic COLI is not the same as the social cost of living defined above, which is in fact the plutocratic COLI defined as a total expenditure weighted average of each family’s COLI. Indeed, the plutocratic and democratic COLIs bear exactly the same relationship to one another as do the plutocratic and democratic basket price indexes. The aggregation of index numbers over the population, or over groups, is not an issue that separates cost-of-living and basket price indexes.
Not surprisingly, the over- and underestimation results linking COLIs to the Paasche and Laspeyres indexes carry through to the social (and, indeed, to the democratic) cost-of-living index. If the CPI is computed as a plutocratic Laspeyres index, Pollak (1980) showed that the CPI is at least as large as the social cost-of-living index using each family’s base level of living. Similarly, if the CPI is a plutocratic Paasche, Diewert (1983) showed that the CPI is no larger than the social cost-of-living index using each family’s current cost of living. Once again, the aggregate (plutocratic or democratic) Laspeyres need not be larger than the (plutocratic or democratic) aggregate Paasche. But as Konüs (1924) showed for the individual consumer, there is at least one set of intermediate levels of living for which the (plutocratic or democratic) COLI lies between the (plutocratic or democratic) Paasche and Laspeyres indexes. Also as before, one can calculate aggregate superlative indexes, such as the Fisher ideal index (see Diewert, 2000a, for the precise arguments). These indexes will capture the effects of substitution in the aggregate and will provide closer approximations to one particular social cost-of-living index than either the Paasche or Laspeyres indexes. An aggregate superlative index of this kind is one candidate to supplement the Laspeyres-type CPI in the United States. But a superlative index cannot entirely replace the Laspeyres because it cannot be produced in as timely a manner.
Ultimately, an assessment of the ability of a superlative index to approximate a measure of the ratio of expenditures required to maintain a consumer’s base period standard of living depends on a judgment about the extent to which changes in the pattern of quantities purchased are driven by changes in income and tastes or by substitution responses to changes in relative prices.
One central insight of economics is that people respond to changes in prices by selecting away from relatively expensive goods toward relatively cheaper goods. More simply, demand curves slope down. Cost-of-living theory incorpo-