difference between his incomings and outgoings. His incomings may be regarded as the product
multiplied by the price thereof, the amount of the product depending in some definite manner on the
amounts of the factors of production which are employed.14 The outgoings may be regarded as a sum
of terms, each of which is the amount of a factor of production multiplied by its price.15It follows16
that in a state of equilibrium the increment of value produced by the last increment of a factor is just
equal to its price. “The marginal shepherd... adds to the total produce a net value just equal to his
own wages.”17
14. Some function of the amounts.
15. Or, rather, the accumulated price, in the sense explained by Professor Marshall (Principles of
Economics Book V. chap. iv, §2, p. 432, 4th edition): “Looking backwards, we should sum up the
net outlays, and add in accumulated compound interest on each element of outlay.” Compare note
xiv. of his mathematical Appendix Abstraction was made of this sort of correction in the British
Association Address to which reference has been made. For instance, it Was tacitly assumed that the
entrepreneur might have as much labour as he could pay for (at a prevailing rate of wages) at the
time when the value of the finished product was realised. Professor Barone has pointed out the need
of greater accuracy and a means of obtaining it by employing his remarkable conception of “capital
of anticipation.” Giornale degli Economisti, February, 1896.
16. Marshall, Principles of Economics, Book VI. chap. i, §8, 4th edition. Mr. J. A. Hobson's criticism
of this doctrine exemplifies the difficulty of treating the more abstract parts of Political Economy
without the appropriate mathematical conceptions An elementary discipline in the differential
calculus would have corrected the following passage and its context: “In order to measure the
productivity of the last dose of labour, let us remove it. The diminution of the total product may be
5 per cent. This 8 per cent, according to Marshall’s method, we ascribe to the last dose of labour. If
now, restoring this dose of labour, we withdrew the last dose of capital, the reduction of the product
might be 10 per cent. This 10 per cent, is regarded as the product of the last dose of capital.
Similarly, the withdrawal of the last dose of land might seem to reduce the product by 10 per cent.
What would be the effect of a simultaneous withdrawal of the last dose of each factor? According
to Marshall’s method, clearly 28 per cent. But is this correct?” The Economics of Distribution, p.
146. Quite correct, if in the spirit of the differential calculus we understand by dose an increment as
small as possible, not as large as the objector pleases. He goes on: “Put the same experiment upon
its broadest footing, and the overlapping fallacy becomes obvious. Take the labour, capital, and land
as consisting of a single dose each; now withdraw the dose of labour, and the whole service of
capital and land disappears. Is the destruction of the whole product a right measure of the
productivity of the labour dose alone? “(loc. cit., p. 147). Imagine an analogous application of the
differential calculus in physics, “put upon its broadest footing,” an objector substituting x wherever
a mathematician had used dx or Ax !
17. It being assumed that the function expressing the product in terms of the factors of production
is such that for the values of the variables with which we are concerned the net income of the
entrepreneur may be a maximum, let P be the amount of the product, πits price, a, b, c, amounts of
factors of production, p1, p2, p3, etc., their respective prices—their actual prices—for a first
approximation, their accumulated prices for a more accurate statement. The net income of the