II.—The Diagrammatical Representation Get access A. P. Lerner A. P. Lerner London School of Economics Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 1, Issue 1, October 1933, Pages 68–71, https://doi.org/10.2307/2967440 Published: 01 October 1933

Journal Article The Diagrammatical Representation of Elasticity of Demand Get access A. P. Lerner A. P. Lerner London School of Economics Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 1, Issue 1, October 1933, Pages 39–44, https://doi.org/10.2307/2967436 Published: 01 October 1933

Journal Article The Elasticity of Demand from Family Budgets Get access A. C. Pigou A. C. Pigou King's College, Cambridge, England Search for other works by this author on: Oxford Academic Google Scholar The Quarterly Journal of Economics, Volume 47, Issue 2, February 1933, Page 342, https://doi.org/10.2307/1883692 Published: 01 February 1933

Sources and nature of the data used. The extent of the ground covered, 3.— Numerical comparisons for U. S. (1925) and U. K. (1924), 6. — Arrangement of data for comparison, 7. — Relative importance of chief industrial groups in the two countries, 10.— Variations in net outputs (and in aggregate wages) in relation to numbers occupied, 14.— Some explanations suggested, 15.— Contrast between the U. S. averages and the U. K. 16.—Question whether the larger U. S. figures should be interpreted in terms of higher prices or of greater volume of output, illustrated from various trades, 17.—Differences appear to reflect mainly volume of output, 25.— Movements between the years 1907 and 1924 of the British inquiries considered in relation to U. S. data for 1909 and 1925, 26.— Extension of this comparison to 1930 (U. K.) and 1929 (U. S.), 33.— Differences in time of the inquiries sufficient to account for the major part of the changes in the measure of relative magnitude of output per head, 34.— Some concluding reflections, 37.

I. Marginal productivity ignores important forms of investment, 627; and is inaccurate even for "productive" investment, 628.— The "law" of diminishing productivity vague and subject to serious exceptions, 630.— Marshall's doctrine of marginal net product does not explain general wages, 631; but throws light on the process of equilibrium-seeking, 632.— The application of labor to land, 633.— II. "Demand for labor" a misleading expression, 634.— Factors which determine it, 635.— The "method of increments" not involved, 638.— In what sense wages are residual, 639.— III. Practical implications: for changes in working hours, 640; consumer borrowing, 641; raising of wages above equilibrium rate, 642; elasticity of demand for labor, 643.

THERE has been, to some extent, a divergence of purpose between the work of mathematical statisticians and mathematical economists. The former have studied variation, such as the form and measurement of frequency groups, and the correlation between two or more variables; the latter have studied equations of equilibrium, in which the data represent totals, margins, the representative, the average-single quantities in general-where heterogeneity does not enter into the argument. Econometricians have, indeed, worked on variation and covariation, but most attention has been given to examples where time is one of the variables, that is to time series; and the relationships obtained have been in the form of a demand curve in one group of studies, to periodic curves in time in another, and to correlation between quantities which are paired in time, but not variable at a given instant of time. I wish to direct attention to a field which has not been thoroughly explored, and in which, so far as I know, little work is being done. What are the forces which produce the variation found in common phenomena, how far are they economic, what changes in frequency distributions are produced by economic forces, how can they best be described or measured? To name one example, which has already been studied: Incomes in certain circumstances are distributed in accordance with Pareto's equation. What has produced this particular form; is the form modified by economic change, or rather by changes in the sociological or legal spheres; how can the effects of these best be measured? Variation has been studied in many fields and it may be well to mark off those which are not primarily economic from those which are. We will exclude anthropometry and biometry, and statistics of mortality and morbidity. Demographic statistics generally would enter only in their economic aspects, such as age distribution in occupations, and concentration of population. Within the economic sphere proper, there are many distributions which have been the subject of careful work: price changes in time, local variations in price, prices of securities, size of industrial firms, rates of profit and dividends, ratio of

T HE various trade and production indexes which have been compiled during recent years are valuable in furnishing students of economic history with a continuous record of the fluctuations of general business. To mention a few such indexes, Colonel Leonard Ayres has compiled an index of general business extending backto I790; the Index of Industrial Production and Trade prepared by Dr. Warren Persons covers the years since I875; and the American Telephone and Telegraph Company has a compositeindex of business activity from I877 to date. In the case of these averages, as well as of some others that might equally well have been mentioned, the purpose has been to secure a continuous record of the general economic situation in the United States. By the use of one or more of these compilations the relative magnitudes of cyclical movements may be compared. It is to be assumed that the element of long-time growth has been carefully measured 'and eliminated, and therefore, in order to measure the relative severities of depressions, or the relative intensities of booms, it should theoretically be necessary only to compare (in some manner or other) the displacements from the normal line. Such an approach, however, lacks objectivity, for the choice of a line of trend may be based in part upon the reasonableness of the degree of 'prosperity and depression that it indicates. The determination of the secular trend of an economic series is never wholly a precise mathematical operation; moreover, the fixing of the normal level for a given year is probably somewhat more dependent upon personal judgment than is the determination of the normal rate of increase. It seems desirable, accordingly, to utilize a more direct approach to the problem of measuring the amplitude of cyclical movements in this country. An examination of the size of the fluctuations occurring in the most important series of business data should throw some light upon the character of cyclical down-turns, and should prove useful in supplementing the story presented by the several composite indexes. Such an examination, if based upon monthly items, would be greatly handicapped by the scarcity of series extendingback more than fifty years. For annual series, on the other hand, the amount of available material is large. It is not necessary here to recount the advantages and disadvantages involved in the use of annual data. It is perfectly clear that for certain kinds of analysis yearly figures are far inferior to monthly. In particular, they are not satisfactory for the determination of time relationships among series in cases when the lags are in terms of months rather than of years. The conclusion, however, that annual data cannot serve a useful purpose in recording the magnitudes of cyclical movements does not seem warranted. On the contrary, it appears likely that any business decline important enough to be recognized by economic historians would be definitely noticeable in the annual record of almost every series relating to important business activities. This should be equally true whether the valley of the depression was shallow and wide, or deep and narrow. During periods of rapid growth, of course, it might happen that a mild down-turn would be reflected merely in the failure of the series to achieve more than a part of 'its full normal year-to-year increase. For the' measurement of such minor declines, annual data may often prove less dependable than monthly items. On the other hand, the use of yearly figures brings certain definite advantages in the measurement of cydes over a-long period of years. It makes available a much larger number of series upon which the investigator may base compan'sons. ' In addition, it automatically eliminates the problem of determining seasonal movements, and thus increases the objectivity of the results. Our choice of the period to be examined was based in large part upon economic considerations. From the point of view of American economic history, the years since I870 possess a sufficient amount of economic homogeneity to render appropriate the comparison of business conditions and tendencies. Numerous comparisons of the present situation with that in the seventies and in the nineties, revealing considerable similarities, have been made. Comparisons with the panics of I837 and of I857 are much less frequent, and are made with the realization that the United