Journal Article Rationing and Index Numbers Get access J. L. Nicholson J. L. Nicholson Oxford Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 10, Issue 1, Winter 1942, Pages 68–72, https://doi.org/10.2307/2967497 Published: 01 December 1942

Also published in: A.H. Hansen and R.V. Clemence (Eds), Readings in Business Cycles and National Income, Allen & Unwin, London, 1953, pp. 357-375

CONSURlPTIONT H E fact that consumption outlay of indi- viduals as well as of groups of individuals depends on their income is well known.Although this statement will hardly be doubted, it may be tested statistically from family budget statistics, as has been done by various investigators.These statistics can show only that consumption outlay by different people, having different incomes a t the same moment, depends on income.Consumption outlay by the same family in different years, showing varying income, will not necessarily depend on income in the same way that is shown-by family budget statistics.This latter relation plays a highly important r61e in the causation of business cycles, a fact perhaps most stressed by Rlr.Keynes, who created the term "propensity to consume" and who used this notion in various deductions.The importance of the propensity to consume for the quantitative approximation of some business-cycle problems has led a number of authors to measurements of that coefficient.How large the propensity to consume may be is not the only important question.Another question is "What lag exists between income changes and changes in consumption outlay?"Tke longer this lag, the more slowly will the economic system react to changes in income and the longer, other things being equal, will be the process of adjustment (e.g., a business cycle).The answer to this question -put by Mrs. Gilboy in this REVIEW -cannot be given by family budyet data, as already stated.The only pos~ible method of securing an answer is by use of t i ~n e series.The use of time series, however, a1wzj.simplies the difficulty that a number of cctcris pasibus clauses are no longer fulfilled.S o t only changes in income are the causes of any given changes in consumption outlay; other

Costs calculated in terms of probability, 69. — Deriving particular specifications of supply from given probabilities of cost: initial conclusions, 71. — More complex conditions: dispersion and skewness of cost expectations, 74; variations in dispersion, 78; in skewness, 85; in both, 86. — Influence of dispersion and skewness on monopoly, 86. — "Marginal probability of net revenue, " and "marginal production risk, " 87. — Conclusions, 88.

Introduction: the problem studied, 385. — The cycle in yields of certain crops, 388. — Sunspots and the solar constant and the cycle in yield of cotton, 392. — Solar and sky radiation and the cycle in yields of cotton and apples, 396. — Reasons for the correlation observed, 398. — Misconceptions in earlier investigations, 403. — Summary and conclusions, 403.

The evolution of machinery, 256. — Commodity prices and money wages, 257. — Real wages, 260. — Profit inflation, 262. — The utilization of mechanical inventions, 263. — Capital formation and the factory system, 264. — Real wages and the market, 267. — Comparisons with other countries and periods: Spain, 267. — France, 270. — The Price Revolution, 270. — Conclusions, 272.

A PROBLEM COMMONLY TREATED in monopoly theory is the effect of a shift in demand on monopoly price and output. In most instances attention centers upon the positive or negative character of the shift, and on occasion the accompanying change in elasticity is considered. The direction of shift in demand is usually ignored, however. This would appear to be a serious omission. The following analysis indicates that the direction of shift in demand may have significant bearing on the results and that it is advisable in all cases to give it explicit consideration. 1 That the addition of a constant increment to the quantities that will be taken at various prices (a horizontal shift in demand) is not in general the mathematical equivalent of the addition of a constant increment to the prices that will be paid for various quantities (a vertical shift in demand) is readily demonstrated. Geometrically one need only shift a demand curve to the right by a constant amount at all levels and then shift the same curve upward by a constant amount for all abscissa points to note that the two new demand curves are not the same. Algebraically it may be shown as follows: Let x = F(p) be the equation of the demand curve in which the quantity is expressed as a function of the price and let p =f(x) be the inverse relationship. Then if a small constant amount is added to the quantity that will be taken at any price, the first equation becomes x' = F(p) +Ax and if Ax is small, the inverse becomes approximately p'=f(x) -f'(x)Ax. Hence the amount that would have to be added to the price at each quantity level to yield the practical equivalent of adding a constant amount to the quantity that will be taken at each price depends upon the slope of the demand curve f'(x) at each point. A linear (constant slope) demand curve is thus the only instance in which the addition of a constant amount horizontally is the equivalent of adding a constant amount vertically. The frequent use of linear demand curves in graphic analysis is possibly one reason why the direction of shift in demand has not been given more consideration.