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difficulty about the function of Margins in Economics which is felt by some who have not specially attended to maximum problems. No one has expressed these difficulties more strikingly than Mr. J. A. Hobson. The following extract is typical of his objections to Dr. Marshall’s doctrine of the «Marginal Shepherd».
«In order to measure the productivity of the last dose of labour let us remove it. The diminution of the total product may be 8%. This 8% 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 product might be 10%. This 10% 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%. What would be the effect of a simultaneous withdrawal of the last dose of each factor? According to Marshall’s method clearly 28%. But is this correct»1
Quite correct, I have elsewhere replied2, adding, with reference to objections continued in the same vein as the passage above quoted: «Imagine an analogous application of the differential calculus in physics.... An objector substituting x wherever a mathematician had used dx or Δx».
To which Mr. Hobson retorts: «Professor Edgeworth appears to think that the Differential Calculus will assist him to find the productivity of the Marginal Shepherd by starting from the productivity of an infinitesimal margin of him»3.
To which I rejoin that the introduction of Δx in conjunction with dx in the passage above quoted was not without significance. There was understood the presumption which must be borne in mind wherever, as in the present papers, we deal with application of the Differential Calculus to Economics — that propositions true of differentials may often be extended to small finite differences4 with sufficient
- Hobson, The Economics of Distribution, page 146.
- «Quarterly Journal of Economics». Feb., 1904, p. 167.
- «Journal of Political Economy». 1904. Vol. XII, p. 460.
- In virtue of that continuity of functions which is commonly experienced. Compare «Economic Journal», vol. XVIII, 1908, p. 399; and below page 100.