Cycles (Rediscovered Books). Edward R. Dewey
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experienced by our own generation are the foreshadows, as it were, of revolutionary changes that ultimately will give us an entirely new curve in our population growth — to mention just one graph. Simultaneously, many new industries would be born; some older industries would take on a new lease of life; some would doubtless die.
For the present, we shall avoid speculation on matters of this kind, which are still far beyond the realm of statistical projection. Our concern here is not with guesses concerning possible new trends in our economy as they might appear in the future, but with study of the established trends as they can be statistically traced right now.
III
The Growth Trend in Our Basic Industries
To draw the trend lines that Pearl uses in such population charts as were reproduced in the foregoing pages, we need to deal with equations, of which the smooth curve is the graph.* Such a method is too complicated for the average businessman who wants to explore trends. It is not only that he may lack the training in mathematics. Even more important, he will probably not recognize the fact that he is dealing with a logistic curve when he puts figures down on a chart.
[*Thus the equation of the logistic curve for France which Pearl employed was: Y = 6.604 + 35.975 / (1 + 0.808 e-0.0197 X )]
A man who charted the growth of his infant son in pounds, every week from the day the boy was born, would ordinarily know that the rapidly rising line would eventually level out. (He can get weight charts that will tell him just when the “bend-over” in the line is due.) But when he charts his corporate sales he seldom realizes — as he sees the line go steeply up — that something like a logistic curve is being worked out here, too, and that the line will eventually bend over suddenly. Further, when it does eventually bend, he will usually regard this as a temporary slump that will be remedied by a resumption of progress in due course.
It is possible to avoid the dangers leading from such fallacious judgments by charting figures on semilogarithmic, or ratio, scale. That is, instead of using the Pearl type of graph, we can use a ratio scale, then get a curve which, by its changing shape, automatically reveals the falling off in the rate of growth. With such a scale the elongated italic S of Pearl usually becomes a smooth elongated italic parenthesis (.
Let us turn back for a moment to the Pearl chart showing the population growth of the United States, on page 15. Now if we stood at 1920 on this chart, and no dotted line indicating the future were there to warn us, we might well assume that the upward sweep of the line would continue indefinitely. We might assume this, at least, if our knowledge were limited to that of the average American, and if our emotions were geared to the prevailing American sentiment that progress has always existed in this nation and therefore always must — if not at the same rate as in the past, then at a still better one. Only specialized knowledge and training could warn us that this chart (as of 1920) could not justify such expectation.
Fig. 1 on the next page is a chart of our population’s growth on ratio, not arithmetic, scale. Standing at 1920 on this chart, we could have looked back and have been readily aware that we were almost at the top of a long slope that was already slowly leveling out. The steady decline in the rate of growth at this point is clearly evident, and the approximate point at which growth will peter out entirely is clearly indicated by the nature of this simple curve itself. Taking our place on this curve at 1920, we could have projected it into today without vast margin of error, even if we had merely worked freehand with a pencil. This kind of chart, which shows us the rate of growth at a quick glance, is preferable for our purposes on many grounds.
Pearl has taught us something very valuable — that a law of growth exists, and that it operates consistently. In using hereafter a form of chart somewhat different from Pearl’s, the authors are merely charting the operation of that law in a manner they believe the average reader will find more readily useful and applicable to his immediate problems.
It is in this form that the growth of America’s basic industries will be graphed. The reader who then wishes to apply the method to his own business may easily come up with a comparable chart. All he need do is to chart his own figures on a similar grid. He can then know immediately where his business stands, in comparison with other broader national developments, without having recourse to any special mathematical knowledge.
Fig. 1. Population of Continental U. S., 1830-1940
Decennial data. A trend is shown, projected tentatively to 1960. Ratio scale. (For a full explanation of ratio scale, see Appendix I.)
The charts shown in connection with this chapter are rather striking in the uniformity of the story they tell. Consider first our total manufactures, which are shown in Fig. 2 in terms of their growth since 1830, in dollars compensated for changing purchasing power.* The rate of growth of our manufactures has been steadily declining since around 1900. By 1920, as can be seen from the chart, it had become a fraction of the rate prevailing in the late 1800's. In at least one sense we may completely ignore the peak established during World War II. Notice that it reaches far above the trend line, and surpasses all other peaks attained previously.
[*All dollar charts in this chapter and the one next following are so compensated. That is, the values for each year have been divided by the index o£ the average wholesale prices for that year, 1926 being considered as unity.]
Fig. 2. U. S. Manufactures, 1830-1945
Data decennial 1830-1899; quinquennial 1899-1919 with estimates for war years; biennial 1919-1939; annual estimates thereafter. The data have been adjusted for the purchasing power of the dollar, 1926 = 100.
A trend is shown projected tentatively to 1960. The war years, as the text explains, have been ignored in determining trend in this and in all other charts portraying growth. Ratio scale.
Unfortunately — for the purposes of our society — it represents production for purposes of destruction. Being a wartime phenomenon, it tells us nothing beyond the fact that under the centralized compulsion of a war economy we had an enormous capacity to produce.
The underlying trend line tells us much more. What that line says is this: Under the economic system prevailing before the war — to which we are presumably returning — we were closely approaching the upper limit of our ability toproduce and distribute within the frame of that system. Following its wartime peak, our volume of manufactures is bound to fall back toward the trend line, and perhaps well below it, before again stabilizing itself around the trend. Rather than a matter for philosophical argument, this assumption seems supported by the evidence of the pattern that has been established in our economy since the very beginnings of our nation — a pattern that can be approximately determined and, consequently, approximately projected.
Fig. 3. U. S. Merchandise Exports 1830-1945
Data decennial 1830-1910; annual 1910-1945. Data are adjusted for the purchasing power of the dollar, 1926 = 100. A trend is shown projected tentatively to 1960. Ratio scale.
When we compare the chart for manufactures with the charts that show rate of growth in our exports and imports (see Figs. 3 and 4), we meet a consistency that we should now be prepared to expect. Both exports and imports are measured here in dollars that are compensated for varying purchasing power, like the value of manufactured goods charted previously. Let us look first at Fig. 3 showing exports. The basic pattern established by the trend is undeniable, and it tells us something for the future. The export levels we established during World War II, by giving away almost unlimited volumes of goods via lend-lease, mean nothing — except