Front Page Titles (by Subject) APPENDIX II THE MEASUREMENT OF ELASTICITIES OF DEMAND - The Economics of Welfare
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APPENDIX II THE MEASUREMENT OF ELASTICITIES OF DEMAND - Arthur Cecil Pigou, The Economics of Welfare 
The Economics of Welfare (4th ed.) (London: Macmillan, 1932).
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|Workmen under 20s....||1.16|
|From 20s. to 25s....||1.31|
|From 25s. to 30s....||1.62|
|From 30s. to 35s....||1.25|
|From 35s. to 40s....||2.46|
Apart from the drop in the ratio for workpeople earning from 30s. to 35s.—and it may be remarked in passing that the instances from which the average in this group is made up are only half as numerous as those in the two adjacent groups—these figures are continuous and in no wise incompatible with what we should expect from general observation. It is natural that among the very poor the demand for clothes should be nearly as inelastic as the demand for food, and that, as we proceed to groups of greater wealth, its relative elasticity should grow. This small experiment, therefore, is not discouraging, and it is much to be desired that some economist should undertake a more extended study along similar lines.52
[46.] Principles of Economics, pp. 109 et seq.
[47.] Professor Moore, in his Economic Cycles (chapters iv. and v.), makes calculations of the "elasticity" of demand for certain commodities without resort to the allowances stipulated for in the text. But, as he himself fully recognises, the elasticity, which his method enables him to measure, is not the same thing as, and is not, in general, equal to, the elasticity of demand as defined by Marshall and employed here. Marshall's elasticity, if known, would make it possible to predict how far the introduction of a new cause modifying supply in a given manner would affect prices; Professor Moore's to predict with what price-changes changes in supply coming about naturally, in company with such various other changes as have hitherto been found to accompany them, are likely to be associated. That this distinction is of great practical importance is shown by the fact that, whereas the elasticity of the demand for pig-iron, in Marshall's sense, is, of course, negative—that is to say, an increase in supply involves a fall in price—the elasticity in Professor Moore's sense, as calculated from his statistics, is positive. The reason for this is that the principal changes in the price of pig-iron that have in fact occurred are mainly caused by expansions of demand (general uplifts in the demand schedule), and not by changes in supply taking place while the demand schedule is unaltered. In certain conditions it might be possible to derive Marshall's elasticity from Professor Moore's elasticity, provided that the reactions exercised by supply changes upon prices could be presumed to take place very rapidly. Apart from this presumption derivation would be impossible, however ample the statistical material.
[48.] Economic Journal, 1914, pp. 212 et seq.
[49.] The direct method and any possible indirect method are seriously hampered by the fact that the elasticity of demand for a thing may be different in respect of different amounts. Thus suppose we start with a consumption A at a price P: that the price rises by p per cent, and that this rise is the direct and sole cause of a fall in consumption of a per cent. We cannot infer that the elasticity of demand either for consumption A or for consumption is equal to unless p is small—strictly unless it is infinitesimal. If p is not small, some assumption as to the relation of neighbouring elasticities must be made before any inference can be drawn. One possible assumption is that the demand curve is a straight line. On this assumption the elasticity of demand in respect of consumption A will be : and in respect of consumption it will be . Another possible assumption is that the elasticity of demand is constant for all amounts of consumption from A to . On this assumption it can be proved, as Dr. H. Dalton has pointed out to me, that the said elasticity is not but This must lie between and : and is probably not far from
[50.] Strictly, of course, such a change must involve some alteration in the marginal desiredness of money, unless the demand for the commodity in question has an elasticity equal to unity. If the elasticity is anything other than this, a change in the consumption of the commodity will be accompanied by a transference of money from expenditure upon it to expenditure upon other things, or vice versa. This must affect the marginal desiredness of money spent on these things, and its marginal desiredness, if affected in one field, is, since it must be the same in all, affected in all.
[51.] Professor Vinci, in his very interesting monograph L' elasticità dei consumi, suggests that the method described above can be extended to yield an absolute measure of elasticity by reference to the distinction between nominal and real prices. The money price paid by the higher income group is the same as that paid by the lower income group. But the real price is, he holds, less than this, in the proportion in which the income of the higher income group exceeds that of the lower. Thus, if the higher income group has 10 per cent more income, an equal money price paid by it implies a real price 10/11ths as great; and the elasticity of demand is obtained by dividing a virtual price difference of 1/11th into whatever fraction represents the associated consumption difference (loc. cit. p. 22). This procedure is, however, illegitimate, because, on the assumptions taken, the virtual price of all commodities to the higher income group is 10/11ths of what it is to the lower income group. Consequently, the difference in the consumption of any particular commodity is not due solely to the difference in price of that commodity, and cannot, therefore, in general, be inserted in the formula for elasticity of demand. Professor Vinci has, in fact, tacitly assumed that the marginal desiredness of money is equal for the two groups—an assumption which would only be warranted if the demand of both for the sum of commodities other than the particular one under investigation had an elasticity equal to unity.
[52.] Cf. my article "A Method of Determining the Numerical Value of Elasticities of Demand," Economic Journal of December 1910.