Front Page Titles (by Subject) Quantitative Notions concerning Capital. - The Theory of Political Economy
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Quantitative Notions concerning Capital. - William Stanley Jevons, The Theory of Political Economy 
The Theory of Political Economy (London: Macmillan, 1888) 3rd ed.
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Quantitative Notions concerning Capital.
One main point which has to be clearly brought before the mind in this subject is the difference between the amount of capital invested and the amount of investment of capital. The first is a quantity of one dimension only—the quantity of capital; the second is a quantity of two dimensions, namely, the quantity of capital, and the length of time during which it remains invested. If one day's labour remains invested for two years, the capital is only that equivalent to one day; but it is locked up twice as long as if it were invested for only one year. Now all questions in which we consider the most advantageous employment of capital turn upon the length of investment quite as much as upon the amount. The same capital will serve for twice as much industry if it be absorbed or invested for only half the time.
The amount of investment of capital will evidently be determined by multiplying each portion of capital invested at any moment by the length of time for which it remains invested. One pound invested for five years gives the same result as five pounds invested for one year, the product being five pound-years. Most commonly, however, investment proceeds continuously or at intervals, and we must form clear notions on the subject. Thus, if a workman be employed during one year on any work, the result of which is complete, and enjoyed at the end of that time, the absorption of capital will be found by multiplying each day's wages by the days remaining till the end of the year, and adding all the results together. If the daily wages be four shillings, then we have
We may also represent the investment by a diagram such as Fig. X. The length along the line ox indicates the duration of investment, and the height
attained at any point, a, is the amount of capital invested. But it is the whole area of the rectangles up to any point, a, which measures the amount of investment during the time oa.
The whole result of continued labour is not often consumed and enjoyed in a moment; the result generally lasts for a certain length of time. We must then conceive the capital as being progressively uninvested. Let us, for sake of simple illustration, imagine the labour of producing the harvest to be continuously and equally expended between the first of September in one year and the same day in the next. Let the harvest be then completely gathered, and its consumption begin immediately and continue equally during the succeeding twelve months. Then the amount of investment of capital will be represented by the area of an isosceles triangle, as in Fig. XI., the base of which corresponds to two years
of duration. Now the area of a triangle is equal to the height multiplied by half the base; and as the height represents the greatest amount invested, that upon the first of September, when the harvest is gathered; half the base, or one year, is the average time of investment of the whole amount.
In the 37th proposition of the first book of Euclid it is proved that all triangles upon the same base and between the same parallels are equal in area. Hence we may draw the conclusion that, provided capital be invested and uninvested continuously and in simple proportion to the time, we need only regard the greatest amount invested and the greatest time of investment. Whether it be all invested suddenly, and then gradually withdrawn; or gradually invested and suddenly withdrawn; or gradually invested and gradually withdrawn; the amount of investment will be in every case the greatest amount of capital multiplied by half the time elapsing from the beginning to the end of the investment.