The Theory of the Cost-of-Living Index

Summary In this paper I summarize the theory of the “cost-of-living index” and the closely related theory of the “preference field quality index”. The first section is devoted to notation and preliminary background, and the second summarizes the theory of the cost-of-living index. The next two sections discuss upper and lower bounds for the index, and the preference orderings for which these bounds are attained. In Section 5 I examine the effect on the index of the choice of a base indifference curve. Section 6 examines the form of the cost-of-living index corresponding to various specific preference orderings. In Sections 7 and 8 I examine the preference field quantity index, a quantity index which is conceptually similar to the cost-of-living index. I show that it is equal to the expenditure index deflated by the cost-of-living index if and only if the preference ordering is homothetic to the origin. In Section 9 I discuss the use of price indexes in empirical demand analysis and argue that the cost-of-living index is inappropriate for this purpose.

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