Knowledge that Transforms

The note by Professor Duncan is chiefly an elaboration of the qualification presented without ambiguity in the concluding section of my study of corporate cash balances.' However, one point that has been made by Professor Duncan requires clarification. If correlation coefficients and trend lines are laid aside Professor Duncan recognized that from 1935 to 1937 the data verify the liquiditypreference theory. It is evident, however, from the analysis of the series involved that the accumulation of which began in 1929 reached its peak in 1932 and decreased to its lowest point in 1937; but at that low point it still formed 20 per cent of cash balances. During this period (1929-37) the falling volume of marketable securities held by large manufacturing corporations was negatively correlated with rising prices of U. S. Government bonds without exception for each year. The liquidation of marketable securities during the thirties, at a time when there was free money, undoubtedly reflects the liquidity preference of the corporations which joined in the thirties the bear brigade, to use Keynes's expression. Therefore, the singling out of data for 1935-37 is arbitrary. In addition, Professor Duncan's calculations for this period are incomplete inasmuch as they do not take into account the rate of profit which reflects the business expectations of the corporations. Indeed, the actual volume of idle money is the combined result of the sales of marketable securities and the amount of money released or absorbed by the transaction sphere of large manufacturing corporations. The accumulation of idle money in the thirties should, therefore, be explained by the rate of profit and the rate of interest simultaneously, and that explanation can be achieved only by the use of the multiple-correlation technique.

IF the variable X represents the price of an active stock, it is well known that the tendency of X to change is an increasing function of price itself, say f(X). If the tendency to relative change with respect to price were constant, graphs whose amplitude of fluctuation is uncorrelated with price could be constructed by (1) plotting log X on ordinary arithmetic scale or (2) plotting X on semilogarithmic scale. However, the tendency to relative change f(X)/X has been found to be a decreasing function of X and hence any constant-amplitude scale for plotting stock prices must be based on some function other than log X, say F(X), whose derivative is inversely proportional to the tendency to change with respect to price. In other words, the desired function is any solution of the differential equation

F. R. MACAULAY' and other writers2 have noted a tendency for changes in the square roots of common-stock prices to be constant regardless of price level. This phenomenon has naturally suggested that when such prices are represented graphically the charts be designed so that vertical distances from the origin are proportional to the square roots of the prices indicated in the margins. There is some reason to believe that charts of this kind might also be useful in plotting other kinds of data. Assume that n sales are distributed at random over 1/p firms during some interval of time, and that u1, u2, *, u1/, are the actual numbers of sales made by the different firms F1, F2, , Fil, Then, a priori, the probability that a particular firm will make one of these sales is p, and the mean and variance of the u's will tend to be

If divisible commodities in a barter market are cleared by higgling until no further exchange takes place, prices may be shown to be a simple function of the quantities traded. Assume that A, B ***, N units (pounds, bushels, yards, etc.) of various commodities are sold in portions Ai+A2+ +An =A) Bi+B2+ * +Bn=B, C1+C2+.. +Cn=C, etc., at theoretical prices, respectively, a, b, ***, n to be deduced, then barter in terms of commodities, irrespective of persons, may be expressed by the equations appearing in Table 1, in which each column as well as each row totals zero. If, therefore, the quantities AI+A2+ * * * +An=A, etc., are given, the ratios a:b:c: ... :n are determined. And if a price standard is assumed-e.g., the value of a pound of A =$1.0-then all prices may be computed.' The same market may be pictured as a money economy by assuming that each trader correctly estimates the value of the commodity he brings to market and obtains bank credit in this amount. This credit finances all the purchases, and at the end of the market day each trader is able to pay back the borrowed credit. If the services of the banker are included as one of the commodities exchanged, the market balances as before.