Pagina:Scientia - Vol. VII.djvu/105

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on the use of the differential calculus etc. 97


accuracy for practical purposes. Such is the proposition now in question that the effect of taking (or rejecting) in succession two or more small «doses» of different factors of production is sensibly the same as taking (or rejecting) both the doses together. Mr. Hobson has presented a contrary result by selecting for his illustration too large doses, not typical of the fine adjustments practised by the organisers of modern industry. A similar objection may be taken to an illustration which he has given in his latest treatment of the subject1 where the tenth dose, the difference between a a «tengroup» and a «nine group» of shepherds adds 20 sheep, while the eleventh dose adds only 5 sheep. There is a discontinuity between the returns to successive doses which is hardly typical of an establishment in which many operatives are employed.

Let me take my own illustration. Let there be two factors of production x and y (e. g. common labour and a certain kind of machinery); and let the Fig. 2amounts of each factor which a certain entrepreneur employs be respectively x and y. Let these amounts be measured from the point O along the abscissa and the ordinate respectively of Figure 2. Let the net return — the difference between the gross receipts and the total outlay2 — be represented by z the perpendicular distance measured downwards from any point (x, y) in the plane of the paper to the corresponding point on the

  1. The Industrial System, p. 110.
  2. We might represent the gross receipts by adding to z as above defined kx + ky, the perpendicular distance from the point (y, x) to the corresponding point in a plane above the paper, whose section with the plane of the paper is the tangent to the circle at O, its equation being z = kx + ky. Of course in general the coefficients of x and y would not be equal, the line in which the plane thus designated cuts the plane of the paper, would not make a half right angle with each of the axes. The coefficient k may be interpreted as the price of the corresponding factor, «accumulated», as explained by Dr Marshall, so as to be comparable with prospective receipts.
Vol. VII 7*