Front Page Titles (by Subject) Effect of the Duration of Work. - The Theory of Political Economy
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Effect of the Duration of Work. - William Stanley Jevons, The Theory of Political Economy 
The Theory of Political Economy (London: Macmillan, 1888) 3rd ed.
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Effect of the Duration of Work.
Perhaps the most interesting point in the Theory of Capital is the advantage arising from the rapid performance of work, if it is capable of being done with convenience and with the same ultimate result. To investigate this point, suppose that = the whole amount of wages which it is requisite to pay in building a house, and that this does not alter when we vary, within certain limits, the time employed in the work, denoted by t. If the work goes on continuously, we shall, during each unit of time, have an amount invested equal to the tth part of ****w. The whole amount of investment of capital will therefore be represented by the area of a triangle whose base is t and height w; that is, the investment is ½ tw. Thus when the whole expenditure is ultimately the same, the amount of investment is simply proportional to the time. The result would be more serious if the accumulation of compound interest during the time were taken into account; but the consideration of compound interest would render the formulæ very complex, and is not requisite for the purpose in view.
We must clearly distinguish the case treated above, in which the amount of labour is the same, but spread over a longer time, from other cases where the labour increases in proportion to the time. The investment of capital, then, grows in an exceedingly rapid manner. Neglecting the first cost of tools, materials, and other preparations, let the first day's labour cost a; during the second day this remains invested, and the amount of capital a is added; on each following day a like addition is made. The amount of capital invested is evidently
and so on. If the work lasts during n + 1 days, the total amount of investment of capital will be
a + 2 a + 3 a + 4 a +... n a.
The sum of the series is
which increases by a term involving the square of the time. The employment of capital thus grows in proportion to the triangular numbers
1, 3, 6, 10, 15, 21, etc.
If we regard the investment as taking place continuously, the whole absorption of capital is represented
by the area of a right-angled triangle (Fig. XII.), in which ob1, b1, b2, b2b3, etc., are the successive units of time. The heights of the lines a1b1, a2b2 represent the amounts invested at the ends of the times. The daily investment being a, the total amount of investment will be
, increasing as the square of the time.
Cases of this kind continually occur, as in sinking a deep mine, of which the requisite depth cannot be previously known with accuracy. Any large work, such as a breakwater, an embankment, the foundations of a great bridge, a dock, a long tunnel, the dredging of a channel, involves a problem of a similar nature; for it is seldom known what amount of labour and capital will be required; and if the work lasts much longer than was expected, the result is usually a financial disaster.