PROFESSOR THEIL [5] recently gave the derivation of the best linear (B. L.) index number formulae for price and quantity. In an application of the formulae to Dutch import and export data, Kloek and DeWit [3] found that there is some slight, though persistent, bias to the effect that the index vectors yield larger current values than the individual data do. As this feature is related conceptually to the factor reversal test, they considered it desirable to devise a method which would control this bias on the average and worked out what may be called the best linear average unbiased (B. L. A. U.) index number. The aim of the present note is to indicate what relationship the B. L. and the B. L. A. U. indexes bear to the factorial indexes, that is, to those obtained through the factorial approach [1, 2, 4]. We conclude that the factorial indexes2 appear to compare well with the B. L. A. U. indexes. Incidentally, it is also pointed out that it might be possible to obtain a closer algebraic approximation to the B. L. index number formulae.

Percentage changes in marginal utility are found to be invariant to utility transformations. They are quantifiable in the ordinary sense, and price and income elasticities can be expressed in terms of them. Definitions of necessityluxury, independence and complementarity-substitutability in terms of the measurable utility changes lead to insights for empirical studies. A POTENTIALLY rich source of insights about demand behavior is the wantsatiation characteristics of goods, i.e., degree of necessity or luxury of goods and degree of complementarity or substitutability between them. These characteristics have been stubborn against attempts to bring them into demand analysis. Despite decades of interest, the literature does not appear to have produced satisfactory definitions of complements and substitutes. Previous necessity-luxury analyses have rested on assumed differences in algebraic form of demand functions. Necessity-luxury attributes have not been expressed in terms of the usual utility concepts of consumer choice theory. 2 In the present article, measurable want-satiation characteristics of goods are derived by considering changes in marginal utility when expenditures are shifted within the consumer's budget. It is demonstrated that the percentage change in marginal utility of a good is invariant to utility transformations and can be related to price and income elasticities. This result is due to the previously overlooked fact that the percentage change in the marginal utility of a good, when moving along a given indifference curve, is identical to a change in the marginal rate of substitution brought about by moving from one indifference curve to another. The measurability of percentage changes in marginal utility is thus seen to be as reasonable as the measurability of the marginal rate of substitution. Two systems of percentage changes in marginal utility are developed. The ei system is appropriate for considering one good vis-a-vis all other goods. In this system, an increase in expenditure on a particular good is accompanied by an equal reduction in expenditure distributed among all other goods so