The Economic Approach to Index Number Theory: the Many-household Case

18.1 In the previous chapter on the economic approach to index numbers, it was implicitly assumed that the economy behaved as if there were a single representative consumer. In the present chapter, the economic approach is extended to an economy with many household groups or many regions. In the algebra below, an arbitrary number of households,H say, is considered. In principle, each household in the economy under consideration could have its own consumer price index. In practice, however, it will be necessary to group households into various classes. Within each class, it will be necessary to assume that the group of households in the class behaves as if it were a single household in order to apply the economic approach to index number theory. The partition of the economy into H household classes can also be given a regional interpretation: each household class could be interpreted as a group of households within a region of the country under consideration. 18.2 The concepts of a plutocratic index and a conditional index are introduced in paragraphs 18.3 to 18.13. Using the plutocratic concept, each household in the economy is given a weight in the national index that is proportional to the household’s expenditures on commodities for the two periods under consideration. A conditional index is an index that depends on environmental variables that might affect household expenditures on commodities. One example of an environmental variable is the weather: if the weather is cold, then households will spend more on heating fuel. In paragraphs 18.14 to 18.22 it is shown how a national Fisher price index can approximate a plutocratic cost of living index. Finally, paragraphs 18.23 to 18.35 consider an alternative conceptual framework for a national index, the democratic index. Using this index concept, each household in the economy is given an equal weight in the national index (as opposed to the plutocratic concept where households that spend more get a higher weight in the national index).