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A TREATISE ON MONEY

BK. II

the two positions and have found (in the notationof p. 110 above) that p = q approximately. In thethird place we assume that the successive small errorsof approximation—and this is the most serious assump-tion—are not cumulative so as to add up to a sub-stantial error, when the procedure is repeated a numberof times over a succession of positions.

If each pair of successive positions are closelysimilar to one another, the second of these assump-tions may be justified. But the third one is moredangerous, especially in the type of case for whichthe Chain Method is commonly recommended, namely,for the comparison of a chronological series. Forexample, the Chain Method will show a cumula-tive error if each substitution which we assume asapproximately equivalent is progressively a slightimprovement, i.e. if each new composite is slightlybetter for the purpose in view than its predecessor,and is not just as likely to be slightly worse. Forthis reason it will mislead us when it is employedover a period of time during which habits are gradu-ally changing as a result of progressively improvingopportunities ; that is to say, it will in such con-ditions underestimate the purchasing power of moneyat the later dates as compared with the former.The Chain Method assumes in effect that, whenmargarine first comes in, the advantage is tri fl i n g,and that the margarine consumed is practically theequivalent in advantage of the butter (or other con-sumable goods) displaced by it, and so on with eachgradual transference of consumption to the new orimproved or relatively cheaper product.

It is a further serious objection to the Chain Methodthat the comparison between two positions is depend-ent on the path which prices and the character of con-sumption have pursued over the intervening positions.For example, it might be that prices and consumptionare such and such, that a serious disturbance—such as