Knowledge that Transforms

THE FOLLOWING THEORY of business fluctuations is claimed to be simple in the mathematical sense as stated by Jeffreys2 and also to represent the simplest possible dynamic extension of the Walrasian system. It explains the business cycle as a purely speculative short-run equilibrium phenomenon. Assume an economic system consisting of n commodities. The buyers and sellers take into account not the actual but the anticipated price. Assume further with Evans that they form their anticipations upon the prevailing price and the price tendency, i.e., the rate of change of the price in time.' If all relationships are linear (as first approximations), we get, for the demand for the ith commodity,

IN THE JANUARY, 1937, number of ECONOMETRICA I had an article entitled in Theory and Income Taxation in Practice. One of its contentions was that to tax and later to tax income from those savings, involves a subtle form of double taxation. I had made this same contention in 1906 in The Nature of Capital and Income. Long afterward, through Professor E. R. A. Seligman, I learned that John Stuart Mill had also called attention to this double taxation. Apparently he was first to do so. Strange to say, such double taxation, though ably affirmed by many other writers, notably Marshall and Pigou in England and Einaudi in Italy, has not, to this day, been universally accepted. In a forthcoming book on Tax Spendings not Savings, I am including a general review of whole question-if question it be. In course of renewed study involved, I have gradually become conscious of a companion principle. Apparently it has hitherto been overlooked. This principle is that to tax works extensive destruction upon and spendings. Because of this destructiveness, several paradoxes emerge which have both theoretical and practical interest. In an article on this subject published in Taxes, the Tax Magazine, in August, 1941, I have excluded, as unsuitable for such a journal, underlying mathematics, merely asserting that contentions made can be mathematically demonstrated. The present article gives demonstrations referred to. At close of year zero, say 1900, let Co be value of a certain capital-for instance an automobile plant. Let j be rate at which this initial value Co would increase during first year (1901) without taxes; and, for simplicity, let us suppose that said rate continues uniformly for n years, at end of which period-say at end of 1940-the owner of capital dies. Then Coj would be capital-increase in dollars in first year (1901) (called savings in title to this article); and capitalvalue C1 at end of that year would be C1 = Co(l +j). At end of second year, capital value would be C2= Co (1 +j) 2; of rth year (1) C,r = Co(1 + )r,

PROFESSOR HOTELLING'S PAPER, Relations between Two Sets of Variates,'l should be widely known and his method used by practical statisticians. Yet, few practical statisticians seem to know of the paper, and perhaps those few are inclined to regard it as a mathematical curiosity rather than an important and useful method of analyzing concrete problems. This may be due to two reasons: first, that Hotelling's paper makes use of rather complicated mathematics and does not spell out in detail the methods of numerical computation; and, second, that although the paper applied the methods to two sets of statistical data, the major emphasis is on mathematical theory, and only rather incidental consideration is given to the meaning of the results obtained in actual statistical work. This paper will try to do two things: first, and most important, it will apply these methods to two different kinds of problems in the hope that this will suggest other practical applications; second, it will develop the methods of analysis in somewhat simpler terms, and discuss numerical computation in greater detail than Hotelling's paper.

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