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Still other papers have indicated plus and minus deviations which do not reveal definite characteristic phases and do not recur.3 In spite of these researches, no successful attempt to relate the theory of business cycles with economic theory has been made. It is this problem which I attack here. 2. Methods of procedure.—I make use of the theoretical results which I have obtained in developing a dynamical theory of economics to show that there actually seems to be a general mathe 2 'For example, H. L. Moore, Economic Cycles: Their Law and Cause (1914). W. C. Mitchell, Business Cycles, National Bureau of Economic Research (1927). 3 Irving Fisher, "The Business Cycle Largely a Dance of the Dollar," Jour. Amer. Stat. Assoc., Vol. XXVIII (1923). C. F. Roos, "A Mathematical Theory of Depreciation and Replacement," Amer. Jour. Math., L (1928), 147-57, hereafter designated "I." On pages 153-54 this paper contains several algebraical and clerical errors which are corrected here. See also, Roos, “A Dynamical Theory of Economics," this Journal, XXXV these equations we single out X1 (the percentage change in the quantity of sugar demanded) as the important variable in relation to Xo (the percentage change in price) by putting the other variables X2, X3, Xn equal to zero, we have examples of the static law of demand. "These variables X2, X3,....,. Xn must be equal to zero since they severally represent percentage changes, and the general hypothesis in mind when the static law of demand is formulated is that there shall be no changes in other economic factors."27 Though the method of multiple correlation is, as we have just seen, the best method for dealing with the problem of the disturbing factors, it will not be employed in this study. In the case of sugar, we have excellent reasons for believing that the really important disturbing factors which obscure the relation between the prices and the amount of the commodity are not the changes in the prices of glucose, corn sugar, and honey, but the growing popularity of sugar as an article of consumption, the increasing population, and the changes in the general price level. And the effects of these long-time changes may be eliminated by one of two simple statistical devices quite as well as by the method of multiple correlation. These statistical devices, first applied to such problems by Professor Moore, are: (1) the method of relative changes, and (2) the method of trend ratios. The method of relative changes consists of finding the functional relationship, not between the absolute prices and absolute quantities, but between the relative change in the price of the commodity and the relative change in the quantity demanded. By taking the relative change in the amount of the commodity that is demanded, instead of the absolute quantities, the effects of increasing population are approximately eliminated; and by taking the relative change in the corresponding prices instead of the corresponding absolute prices, the errors due to a fluctuating general price level are partially removed. If the observations should cover the period of a major cycle of prices, and the commodity under investigation should be a staple commodity, . the above method of deriving the demand curve will give an extremely accurate formula summarizing the relation between variations in price and variations in the amount of the commodity that is demanded.28 "H. L. Moore, op. cit., p. 152. 28 H. L. Moore, Economic Cycles, pp. 69-70. |