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that it is open to any worker to transform himself into an entrepreneur, the difference of remuneration compensating for the efforts and sacrifice attending the transformation.) Professor Chapman rightly states that the answer to the question put is affirmative or negative according as Increasing or Diminishing Return acts. But the sense in which these terms are to be taken is not, I think, stated with sufficient precision. In my view the only appropriate sense is a certain one of the subordinate varieties which the secondary definition may present, as above shown in the case of plural factors.1 Professor Chapman's theorem holds good if by Increasing Return 2 it is meant that (az with x) produces more than a times the product of (z with x). But the theorem does not hold good if by Increasing Return 3 it is meant that (az with ax) produces more than a times (z with x).*

The primary definition is not germane to the question above stated. It will be required if the question is: What is the value of z for which the total product is a maximum? But we may go some way towards answering that question without being able to ascertain the character of the Return in the primary sense; if we make the probable assumption that the product of a firm always increases (in virtue of intensified organisation) with the increase of the number of firms ceteris paribus. For then, as z is increased (from the value determined by competition), the product of the community would continually increase, as far at least as the point at which the entrepreneur's remuneration dwindles to zero.

1 Loc. cit., p. 76.

2 As p. 524, par. 1 (op. cit.) must, I think, be interpreted.

3 As p. 526 note, last par., may, I think, be interpreted.

* The proof of these statements will be found in the original.

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(D)

USE OF DIFFERENTIAL PRICES IN A REGIME OF COMPETITION

[JUSTIFICATION of this Paper, which appeared in the ECONOMIC JOURNAL for 1911, is to be sought in an earlier contribution to the Journal, now reprinted in the Mathematical Section (5). In that article it was argued that differentiation of prices, discriminating between classes of customers whose demands were different, is generally advantageous to both parties in a regime of monopoly; and may well prove so even in a regime of competition. Mr. Bickerdike, with his usual acumen, disputed the latter clause (in the ECONOMIC JOURNAL for 1911); questioning whether in cases where there is "uniformity of charge based on cost of production," under free competition, any system of discriminating prices could be "better all round," more advantageous to both producers and consumers. And his contention is virtually admitted here, upon a certain definition of "cost of production" and a congruent limitation of the methods by which discrimination may be introduced. Consider, for instance, the case put below of two species of seaweed for which the demand is markedly different (one perhaps required as manure, the other for its medicinal qualities). Yet if the capital, manual labour and so forth-all the cost-of-production abstracting the profits of the entrepreneur-are the same per ton for each species, it is good Ricardian economics to argue that in a regime of competition the price of both articles will be the same, the profits of the "capitalists" will be equal. It is the orthodox doctrine and practical truth that the regime of competition is better all round than any mixture of monopoly. A firm consisting of an employer gaining normal profits, employees earning normal wages and so forth, could not with advantage to all parties either raise or lower the price of either article. But it is not necessary so to lump the remuneration of the employer into the cost of production. It is possible—and usual throughout this Collection (see Index, "Entrepreneur ")-to fix attention separately on the motives and action of the entrepreneur (cp.

below, p. 104). In the case before us suppose that the entrepreneurs form a combination for the regulation of buying prices, not affecting the cost of labour and of other factors. It will certainly be to their advantage to raise the price; but not necessarily both prices. Likewise it is probable that the customers may gain in globo by a departure from the old pair of prices. The "demand-schedule" for the respective articles being so different, it is highly probable that the moneymeasure of the total "consumers' surplus" will be increased by raising one price and lowering the other to a certain extent. Thus it is in the interest both of the producers and the consumers to move away from the original position. To be sure, the directions in which they respectively want to move are not the same. But they are most probably not diametrically opposite. Whence it follows that certain changes of price, some degree of discrimination, will in general be advantageous to both parties. The reasoning will be better understood after a study of the second part of , II. p. 407 et seq.

The conclusion might be worded more strongly than now at the end of this paper, if there were no danger of its being taken as other than a curiosum. (Cp. below as to the bearing of the argument on Socialism.) At the bar of pure theory my defence might be summed up as follows: Whereas it is alleged that outside Monopoly discrimination can be practised with advantage all round only in some peculiar cases, I reply: firstly, the cases in which discrimination advantageous to both producers and consumers can (theoretically) be practised without any change of the existing regime are very common; and secondly, in cases of pure Competition the advantages of discrimination may (theoretically) be secured by a change of the existing system, substituting Combination for Competition.]

Mr. Bickerdike's criticism is forcible and fairly aimed; yet I hope to show that it is not very damaging. His main contention is thus stated :

"My argument is that increasing returns, or joint costs, must come in in some way or other if discrimination is more advantageous than uniformity of charge based upon cost of production.”

"I question whether any system of discrimination can be better all round than the prices which would be attained under free competition in the absence of any tendency to increasing returns or of joint costs."

VIMU

"It is difficult to see how any discriminating system would be better for the public."

1

"It [such a system] could not be socially economical." In considering the truth and relevancy of this statement, it will be convenient to have before us one of the diagrams 1 em ployed in the article against a part of which the statement is directed. Let the axis of x in this diagram represent (quantities of) a commodity for which the law of production is not that of increasing returns. The axis of y representing price, let the "demand-curve," for the sake of simplicity, be a straight line. This line is not drawn in the figure, but it may easily be constructed from the line BA, which represents half the amount of

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commodity demanded at any price. Thus there would be demanded at the price OR, twice the amount RP, and at the price Ow, twice the amount wa. To consider discrimination of prices, let us suppose that the class of commodity breaks up into species which differ in respect to the demand of the customers, but not in respect of cost to the producers; for instance, equal hauls of goods, equal in weight, bulk, and facility of handling, and all other circumstances affecting cost, but differing in the value which they acquire by transportation. Let the dotted lines form each the demand-curve for one of the differentiated species. Then the average of the amounts of the two species demanded at any oneand-the-same price (e. g., Ow) is represented by the corresponding point on the line BPA (e. g., the point a, since (Oa1 + Oα2)

1 Fig. 2, ECONOMIC JOURNAL, Vol. XX. p. 447.

=

Oa). Beginning with the case in which the cost is constant, let us suppose the constant cost to be Ow. If then the uniform charge based on cost of production is Ow, Mr. Bickerdike's statement, as I understand, imports that this unitary price cannot be replaced by a system of different prices for the different species; with advantage to all concerned, both producers and consumers.

The truth of this statement may be shown by observing that if the customers are to benefit by discrimination, one at least of the prices must be lowered below Ow. Suppose, then, that the price of one of them, e. g., that for which the demand-curve is BPA1, is lowered from Ow to Ow', w' being a point on the axis below w, not shown in the figure. And let the intersection of a horizontal drawn through o' with the demand-curve B1 PA1 be a'a point on that line below a1, the point a1' as well as o' being left to the imagination of the reader. The gain in Consumers' Surplus is then measured by the area of the quadrilateral wa1a1'w'. But the loss of Producers' Surplus is measured by the larger area of a rectangle which includes that quadrilateral, namely, the rectangle (not completed in the diagram) of which one side is ww' and another side w'a'. Likewise if the price is raised above Ow the consumers lose more than the producers gain. Therefore, the public as a whole, producers plus consumers, are losers. A fortiori, if the cost is not constant, but increasing (in accordance with the law of decreasing returns).

Mr. Bickerdike's proposition is true, and it may be added, with reference to State regulation of what M. Colson calls " public works," important. But is it contradicted by the proposition which Mr. Bickerdike impugns? The answer is prima facie affirmative. Mr. Bickerdike has accurately quoted the passage in which it is enunciated that "the gain to consumers [through monopolistic discrimination] may well be so great that they are better off than they would have been, other things being equal, under a regime of competition." He has rightly understood that the proof primarily applied to the case in which there is no cost of production is meant to be extended to the general case of substantial cost. He is right, too, in conceiving my thesis.to imply that in the case supposed the producers as well as the consumers would be better off than under the regime of competition. He has placed a very natural interpretation upon the passages which he criticises. It would have required a degree of intellectual sympathy beyond what can be fairly expected in a critic to have thought of the explanation which I proceed to offer.

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