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Distribution of Labour. - William Stanley Jevons, The Theory of Political Economy 
The Theory of Political Economy (London: Macmillan, 1888) 3rd ed.
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Distribution of Labour.
We now come to consider the conditions which regulate the comparative amounts of different commodities produced in a country. Theoretically speaking, we might regard each person as capable of producing various commodities, and dividing his labour according to certain rules between the different employments; it would not be impossible, too, to mention cases where such division does take place. But the result of commerce and the division of labour is usually to make a man find his advantage in performing one trade only; and I give the formulæ as they would apply to an individual, only because they are identical in general character with those which apply to a whole nation.
Suppose that an individual is capeble of producing two kinds of commodity. His sole object, of course, is to produce the greatest amount of utility; but this will depend partly upon the comparative degrees of utility of the commodities, and partly on his comparative facilities for producing them. Let x and y be the respective quantities of the commodities already produced, and suppose that he is about to apply more labour; on which commodity shall he spend the next increment of labour?—Plainly, on that which will yield most utility. Now, if an increment of labour, Dl, will yield either of the increments of commodity Dx and Dy, the ratios of produce to labour, namely,
will form one element in the problem. But to obtain the comparative utilities of these commodities, we must multiply respectively by
expresses the amount of utility which can be obtained by producing a little more of the first commodity; if this be greater than the same expression for the other commodity, it would evidently be best to make more of the first commodity until it ceased to yield any excess of utility. When the labour is finally distributed, we must have the increments of utility from the several employments equal, and at the limit we have the equation—
When this equation holds, there can be no motive for altering or regretting the distribution of labour, and the utility produced is at its maximum.
There are in this problem two unknown quantities, namely, the two portions of labour appropriated to the two commodities. To determine them, we require one other equation in addition to the above. If we put
l = l1 + l2,
we have still an unknown quantity to determine, namely, l; but the principles of labour (pp. 172-177) now give us an equation. Labour will be carried on until the increment of utility from any of the employments just balances the increment of pain. This amounts to saying that du, the increment of utility derived from the first employment of labour, is equal in amount of feeling to dl1, the increment of labour by which it is obtained. This gives us then the further equation—
If we pay regard to sign, indeed, we must remember that dl is, when measured in the same scale as du, intrinsically negative, but inasmuch as it is given in exchange for du, which is received, it will in this respect be taken negatively, and thus the above equation holds true.1
[]While revising this edition it seems to me probable that this, as well as some other parts of the theory, might be more simply and generally stated, but what is given is substantially true and correct, and it must stand for the present. [See also the Errata for this page, which reads "for 'in this respect be taken negatively,' read 'in this respect be taken positively.' ".—Econlib Editor.]