him to a monopolist who does not control the prices of the factors of production, nor yet the price of the product, the latter being fixed by a maximum law, or, rather, the case being that in which the monopoly is just becoming extinct, as Cournot would say, by the introduction of competitors, so that this entrepreneur can no longer sensibly alter at will the price of the product. Under such circumstances each entrepreneur will vary all the variables under his control up to the margin at which his own advantage becomes greatest. If he or we be content with a rough estimate of this advantage, it may be measured by the 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.1 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.2 It follows 3

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1 Some function of the amounts.

2 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.

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 8 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

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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.'

So far supposing the entrepreneur's work to be a constant quantity. In a more exact estimate the quantity which the entrepreneur seeks to maximise is the utility to be derived from his net income minus the disutility incident to its production. From this consideration it follows that the increment of utility due to the increment of product which is produced by the last increment of entrepreneur's work is just balanced by the increment of disutility due to that work.

To this condition is superadded the tendency towards equal net advantages in different occupations, resulting, as Professor Marshall has shown, not so much in the equal advantageousness as in the equal attractiveness of different occupations. The remuneration of the entrepreneur thus corresponding to his services may be classed along with the remuneration of the workman as " earnings," from a certain point of view, which is doubtless proper to the publicist and philosopher. As Mangoldt points out," the circumstance that certain services do or do not attain a market price" does not "essentially alter the measure of their compensation." But there is another point of view which is proper to those who study the mechanism of distribution. As Professor Taussig well observes, "The cobbler who works alone in his petty shop gets in the main a return for labour as much as the workman in the shoe factory"; but " with regard

broadest footing," an objector substituting x wherever a mathematician had used dx or Ax !

=

1 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, π its 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 entrepreneur may then be written (abstraction being made of the entrepreneur's own effort) P f (a, b, c) — р1а — P2b — Pc. In order that this expression may be a maximum, the law of decreasing returns must hold in the first of the two senses elsewhere distinguished (below, p. 67 and p. 152). The condition must still be postulated when account is taken of the entrepreneur's subjective feelings,-effort and sacrifice in the way of production balanced by satisfaction immediate or prospective in the way of consumption. Nor is the case essentially altered when account is taken of the possibility (noticed by Professor Pareto, Cours, Art. 718) that the factors are not independent. Suppose that the amount of labour must always be in proportion to, or on any definite function of, the amount of land. Then, eliminating one of these quantities, we may treat the other as independent.

to the machinery by which distribution is accomplished he [the cobbler] belongs in a different class from the hired labourer." 1

The tendency to equality of net advantages of course only exists with respect to positions between which there is industrial competition. Accordingly, if the union in one person of natural abilities and money constitutes him a member of a noncompeting group," there is no presumption that the remuneration of such an entrepreneur will be exactly equal to the interest which he might have obtained by lending his money plus the salary which a person of his ability could command as a hired manager. There exists an excess above that sum, corresponding to what Mangoldt calls Unternehmergewinn. There may be excesses somewhat similarly caused by different degrees of ability and resources; the various "rents" enumerated by Mangoldt, which, as he observes, tend to diminish with the progress of society, so far as education becomes more diffused and it becomes. easier for persons properly qualified to obtain the use of capital.

Some additional light on the functions of the entrepreneur may be obtained by comparing the profits in businesses of a different size. Suppose (for the sake of the argument) that the work and worry of the "boss" do not increase 2 with the scale of operations, how is the equality of net advantages which theory leads us to expect brought about? Ceteris paribus, might we not expect the entrepreneur's residue to be larger in the large industries? 3 The answer seems to be that, as equilibrium is approached under the joint influence of Commercial and Industrial Competition, the amounts of the factors are so varied as to fulfil the condition that equal efforts and sacrifices on the part of the entrepreneur are attended with equal remuneration.5 This equality is irrespective of identity in the relation between factors and product. It may exist whether that identity is supposed to

1 Quarterly Journal of Economics, Vol. X. (1895) p. 88. Professor Taussig goes on, For an understanding of the machinery by which distribution is accomplished in modern times, the classification of sources of income should thus be different from that to be adopted for an explanation of the fundamental

causes.

2 That the trouble does not increase proportionately would be a more concrete supposition. As Sidgwick says, Though it is more troublesome to manage a large factory than one half the size, it can hardly be twice as troublesome." Political Economy, Book II. chap. ix. § 3.

3 Cp. Marshall, Economics of Industry, Book II. chap. xii. § 4, 1st edition. 4 The factors generally, and sometimes also the form of the function expressing the quantity of the product in terms of the quantities of the factors used, the function designated ƒ in note to p. 20.

5 The equality is that of an ordinary equation, not an identity.

The function which expresses the amount of the product in terms of the

factors (including entrepreneur's work).

be present between industries of different sizes or, as in general to be supposed, there is no identity in the relation between factors and product for different individuals and industries.

The sort of adjustment thus postulated may be illustrated by a more familiar kind of surplus, that which accrues to the landlord according to the received theory of rent. Let there be a homogeneous tract of land equally adapted to the cultivation of wheat and barley, owned by a set of competing landlords, who accordingly obtain an equal rent per acre whether wheat or barley is to be grown thereon.1 Now let a tax be imposed on the rent of land used for growing barley. There must result a new equilibrium, in which it remains true that owners of homogeneous land obtain equal rent per acre for whichever purpose used, and that cultivators of wheat and barley obtain, ceteris paribus, equal profits. These conditions can be fulfilled if the extent of the land applied to the cultivation of wheat is increased while the intensity of cultivation is diminished, and contrariwise for barley the extent is diminished and the intensity increased. This proposition holds good whether or not the relation between outlay and product corresponding to the shape of the curve in the illustration which Professor Marshall has made familiar 3-is supposed identical for wheat and barley, and even if the cultivator seeking the greatest possible profits is able to vary that relation in accordance with the "law of substitution." It is here assumed that the case of manufacture is not so different from agriculture, but that an analogous adjustment of "margins " must be considered to take place between large and small businesses under the conditions specified, and generally between different industries where industrial competition acts.

A similar adjustment must be postulated when we entertain the third definition of entrepreneur, and consider competing investors in the stock of companies which may at first be supposed equal in respect of risk, though not in size. The competitors being free to invest units consisting, say of £100 or less in any kind of business (of the given riskiness), large or small, it follows that a return to a dose anywhere invested tends, ceteris paribus, to be the same. This result, which is by no means a deduction 1 Compare II. 78.

2 The function expressing the product in terms of the outlay.

Economics of Industry, 1st edition, p. 83. Principles of Economics, 4th edition, p. 232.

• Accordingly, in order that equilibrium should be stable in this regime, investment in each industry ought to be pushed up to a point at which the law of decreasing returns is fulfilled in its second sense,—that the rate of total cost to total product increases with the increase of product.

from the general formula considered under our second head, may be supposed to be brought about by an adjustment of margins of the sort which has been explained.

Now at length the Ricardian theory of rent as ordinarily stated becomes exact, the payment for land rented by a joint stock company ought to be just the difference between the returns (after capital has been replaced and labour paid) and the amount of capital laid out, multiplied by an average rate of profit.

Though the class of shareholder is the principal, it is not the only species, of the third kind of entrepreneur, if defined so as to include all risk-takers. As Mr. Hawley observes,1 workmen take some risk, entrepreneurs who have no capital of their own run the risk of not being paid for their trouble. Enterprise may be taken as the essential attribute of a wide class entitled to a share in the national dividend along with the purveyors of land, labour, and capital. It does not seem to be a fatal objection that enterprise is hardly to be found in the concrete, separate from other factors of production. As Mr. Hawley replies,2 labour and waiting, the attributes of familiar classes, are not to be found in abstract purity.

To some there may seem a more serious scruple: whether the undertaking of risk does even in thought constitute a fourth factor, whether the distinction between interest and the reward for risk is radical. It is all very well for Jevons to distinguish by different coefficients, p and q, the depreciation of future goods due to uncertainty and to remoteness. But, since the distant pleasure is always uncertain, can we really disentangle the two causes of depreciation ?

Fortunately, these questions of logical definition and psychological analysis do not affect the important lessons respecting the participation of risk which have been taught by Professor J. B. Clark,—“ that a corporation can run risks which the individual could not with prudence," that by forming corporations "we reduce the initial terrors of business enterprises." It is an exemplification of the old maxim not to put all one's eggs in one basket. If a hundred persons are carrying each a hundred eggs, each independently running the risk of tripping and by the loss of all or many of his eggs being exposed to great privation, this great danger will be averted, this chance of great disaster will be commuted for a somewhat higher probability of a much more

1 Quarterly Journal of Economics, Vol. VII. (1893), p. 470.

2 Ibid., Vol. XV. (1900) p. 78.

3 "Insurance and Business Power," Ibid., Vol. VII. (1892) p. 40, et seq.