for the express purpose of combating Socialist propaganda; the Socialist societies, on the other hand, have adopted Gambetta's view that "Le cléricalisme, voilà l'ennemi." The "Catholics," be it said, are not by any means as intolerant or as priestridden as their name and organisation appear to imply. Thus far, at any rate, they have rendered good service.

The authors read our British distributive co-operators a very useful lesson in pointing out that, in spite of much high falutin language currently in use, their co-operation is one of business. However, they a little underrate the power of the Wholesale Society to influence the business of the retail societies. The "Outline of the History of Co-operation" given will be welcome to not a few readers. And the chapter on "Co-operative Finance" discusses thoughtfully problems of present urgency. Altogether the book is decidedly a valuable addition to co-operative literature. HENRY W. WOLFF

No. 117.--VOL. XXX.

I

NOTES AND MEMORANDA

COST OF LIVING AND WAGE DETERMINATION

THE general increase in prices throughout the world has resulted in computations of index-numbers by the official statisticians of most countries, and has raised in an acute form all the practical and logical difficulties that underlie the problem of making a single measurement of the change in the purchasing power of money. Since in Australia the legal fixation of the minimum wage depends on the level of prices, it is natural that there considerable attention has been given to the subject, and we should expect that Mr. Knibbs, with his usual energy, would have considered the subject in its practical and theoretical bearings. In fact, in Report No. 9 of the Labour and Industrial Branch of the Commonwealth Bureau of Census and Statistics (July, 1919), we find not only detailed statements of the changes in prices, wages, employment, etc., but also an appendix of fifty-five closely-printed pages in which the theory of price-indexes is discussed minutely. It is to this report that the references in the following paragraphs refer.

A convenient notation for the discussion is as follows1: At date A let P1, P2... be the prices of units of commodities, Q1, Q2... the quantities assumed to be purchased; at a later date B, let P1, P2..., 91, 92... stand for prices and quantities. Write r1=p1÷P1, etc., for the ratio changes of prices.

1,

The expenditure in year A is then Q1P1+Q2P2+ . . .= E1 + E2 +...=SE, and in year B 91P1 + q2P2+...=e1 + e2+...= Se.

Since the ratios, r, are more exactly determinable than the quantities, Q, especially in wholesale prices, most of the work on the theory and practice of index-numbers has been directed to choosing commodities, ascertaining their price changes, and then considering how the ratios should be combined. It is well known that, for wholesale prices in times when change has not been rapid and special commodities have not shown abnormal move1 See Statistical Journal, 1919, p. 343, where some aspects of the problem are discussed.

ments in price, very little depends on the choice of weights, or on the choice of the base year in which for computation prices are equated to 100. American statisticians and Mr. Knibbs (pp. 185, 207, etc.), apparently disliking the abstractness of this method and believing that the problem of measurement is capable of exact solution, are inclined to discard the use of ratios, and use the following direct method: The quantities, Q, are ascertained at a standard date either by estimates of the mass of commodities used in the case of wholesale prices, or by working-class budgets in the case of retail, and SE is computed at this date. At a subsequent date the quantities are valued at the new prices, and Q1P1+Q2P2+ =SQp is computed; prices are then said to have changed in the ratio SE: SQp. The resulting index is, of course, 100SEr÷SE, and the method is simply equivalent to weighting the price ratios by the estimated expenditure in the standard year. Writers who use this method have not, however, escaped the difficulties of weighting, for if a different base year had been selected, where the quantities were Q'1, Q'2, etc., the index would have become 100SQ'p÷SQ'P (where, in fact, the price ratios are weighted by Q'P1, etc.), and the choice of a particular year has always been accidental (e.g., a year in which budgets were collected). Mr. Knibbs says (p. 208): "With price-ratio methods we are working in the dark, and it can only be because of this that some economists have ventured the opinion that one may neglect weights altogether. This proposition arises from a wrong apprehension of the essence of the problem." This statement follows paragraphs in which the difference between various methods is shown by illustrations involving only two or three quantities whose price changes are very diverse. Later (p. 225) we read that "the aggregate-expenditure or aggregate-cost method is alone valid." Such a dogmatic statement is by no means justified by the algebraic analysis or arithmetical illustrations given, and it suggests that the writer has not appreciated the reasons which have led to other methods. The controversy is an old one, and it might have been hoped that the principles of measuring price changes in normal times were settled, and that it was understood that in the end the measurement must be approximate and that no definite number could be given as absolutely correct.

A much more important question is the measurement of the change in the cost of living when the standard budget, established at one date, is no longer applicable owing to changed conditions of supply or of habits. So long as no radical change has taken

place, the method formerly used of calculating the movement, first by the quantities at date A (SQp÷SQP), and then by the quantities at date B (Sqp÷SqP), and then averaging the results, is likely to give a reasonable measure; Mr. Knibbs suggests taking the average of the quantities for each commodity separately (}S(Q+q)p : }S(Q+q)P), which is no doubt a good plan, but hardly, as he says (p. 219), “the only valid basis of comparison between two years in which the usage is different." This is surely another case, in which there is no unique theoretically true method, and the test of validity is that different plausible methods give approximately the same results. The practical difficulty in application is the determination of a second standard to give q, unless we can depend on estimates of changes of consumption of wheat, meat, etc., for the nation as a whole; for it is always a very troublesome business to obtain an adequate collection of budgets, and till equilibrium is attained the collection ought to be annual.

When, as at present in the United Kingdom, the regimen has been substantially changed, by the alteration in the proportion of home and foreign meat, the shortage of sugar and eggs, and the substitution of butter and margarine, the method of averaging becomes unreal and may lead to absurd results. Mr. Knibbs apparently despairs of making any measurement in such cases (p. 229, xxvii., xxxiii.); yet some solution must be found, not only in Australia where wage determinations depend legally on the cost of living, but here also, where arbitrations and wage arrangements take it definitely into account. The existing method of computing the cost of a pre-war standard, based on a period in which sugar, eggs and butter were freely obtainable, is certainly not valid at the present date. The problem is to determine the present cost of a standard modified in detail, but giving the same nourishment and the same pleasure or satisfaction, as the pre-war standard. A method was suggested last May (Statistical Journal, May, 1919, p. 351) in which the change of standard was measured by the ratio of the present budget to the pre-war budget both at pre-war prices (SqP÷SQP); this ratio is a tentative measurement of the ratio of the satisfactions or pleasures obtained at the two dates, and is perhaps more in accordance with reality than a measurement based on calories; and on a further assumption (loc. cit.) it is suggested that a prewar wage multiplied by Sqp÷SqP would afford the same purchasing power as before. In this there is evidently something too rigid; to take two commodities, suppose 2 lb. of butter at 1s. 6d.

and 1 lb. of margarine at 6d. (in all 3s. 6d.) have been replaced by 3 lb. of margarine at 1s. 4d. (in all 4s.); the latter costs 4s. now (qp) and would have cost 1s. 6d. (qP) before, and the ratio of satisfaction is 1s. 6d. to 3s. 6d., or 3/7ths. To replace the satisfaction derived from the former 3s. 6d., we should then have to multiply the 4s. by 7/3rds, obtaining 9s. 4d., which, of course, need not be spent on 7 lb. of margarine, but on milk to supply vitamines or jam or other comestible. This is an extreme instance, but it shows that the validity of the method depends on the averaging away of errors, and in analysing the process we come across many difficulties in the measurement of satisfaction which have no numerical solution. It may, however, be affirmed that when prices of commodities increase at unequal ratios, a purchaser can in general evade part of the injury by buying more of that whose price increases less than the average and less of the more appreciated; if plum jam doubled in price and strawberry jam increased only 50 per cent., a housekeeper who had been buying them in equal quantities would now buy more strawberry and less plum.

It is doubtful whether any algebraic process will give reliable results, and in fact the only practicable method at present appears to be to frame a new budget of goods obtainable, and in fact purchased, by housekeepers with the same skill of adjusting purchases to desires as in the case of the earlier budgets. Instead of measuring the satisfaction by formula, we may recognise that it is subjective and a matter of opinion, and obtain from representative working-class women a budget which in their opinion. would now give the same variety and pleasure as a selected budget of 1914, care being taken that the energy value is the same. The result would give a new conventional budget, the ratio of whose cost to the pre-war budget would give a rough measure, perhaps as accurate as any possible more refined measure, of the change of that vague entity "the cost of living." Where economic theory yields insufficient equations and the refinements of mathematical statistics fail, we may still fall back on common sense to obtain an opportunist solution.

A. L. BoWLEY