Knowledge that Transforms

1. Deference to the reader calls for a blueprint of the article's contents. Its contributions are of two distinct varieties. The first and prime contribution consists in the extension of existing analyses for finite numbers of commodities to the case of infinitely many. Hotelling and others have emphasized the desirability of stating the results of entrepreneurial and consumer demand theories for infinite numbers of goods. Apart from its utility in treating commodity groups embracing large, though not necessarily infinite, numbers of items, the economic properties of which shade from one member to the next, the extension is stamped with true intellectual concinnity. The finite theories are contained, as very special cases, in the infinite analyses. A more distinctly economic flavor breathes from the second species of offering. It includes propositions and economic tools novel even to the finite analyses. The theorem that an entrepreneur's derived demand functions for factors of production are stable in the sense of Hicks' extension of the classical definition is an example.' Evolution of the inverse utility function (more properly functional), described in ?2, is another. Unlike its counterpart, the inverse utility function is a function of prices. Economically, it is the negative of the maximum utility attainable by the consumer, income specified, when a stated price regime prevails in the competitive market. Noteworthy operational properties characterize the inverse utility function. Designate the consumer's budgetary limitation, prices constant and quantities varying, direct. Term it inverse when quantities remain constant and prices vary. Maximization of the utility function subject to the direct budgetary limitation results in individual consumer demand functions. Maxi-

I APPRECIATE the opportunity of replying to Professor Guthmann's gracious note. In the hope that some sources of confusion in my paper may thus be eliminated, I shall consider what I believe to be his principal contentions: (1) That my chart' shows the dividend-earnings ratios for 1936 and 1937 significantly below normal; that this implies the undistributed profits tax had the effect of causing retention of earnings; and that this extraordinary result casts doubt on the validity of the analysis. (2) That a better understanding of the effects of the tax is to be obtained from his time series chart of the Cowles Commission indexes of dividends and earnings; and that this chart shows the proportion of earnings distributed in 1936 and 1937 to have been exceptionally high. (3) That from the point of view of individual business men the effect of the tax upon aggregate earnings distribution isimmaterial; and that the law as drafted was inequitable, in that it placed the greatest burdens on small corporations without access to the capital market, and on corporations with large debts or deficits. First, the chart referred to (p. 344) was presented as a simple scatter diagram and not as a regression analysis precisely because I was unwilling to assign a normal percentage of earnings to be distributed at each level of business activity. While a general negative relationship between the dividend-earnings ratio and activity is familiar to all students of this problem, and is borne out by the scatter diagram, the myriad factors other than business activity which must influence corporate distribution decisions would make dependence on a mathematical equation relating these two factors alone foolhardy in the extreme. While I believe industrial activity to be the most important single variable influencing the dividend-earnings ratio, I recognize that only a third (31 per cent actually) of the variability in the latter may be accounted for by the former. If the years in which dividends exceeded earnings be omitted (a procedure Professor Guthmann advocates elsewhere in his note, but with which I cannot agree-cf. pp. 343, 345), the points for 1936 and 1937 lie even closer to the regression line; they are certainly neither significantly above nor below it.