The Positive Theory of Capital

Eugen v. Böhm-Bawerk, from the Warren J. Samuels Portrait Collection
Böhm-Bawerk, Eugen v.
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William A. Smart, trans.
First Pub. Date
London: Macmillan and Co.
Pub. Date
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Book IV, Chapter III

One-Sided Competition


First: of one-sided competition of Buyers. Accommodating the conditions of our illustration to the requirements of the new typical case, let us assume that A1 finds a competitor, whom we shall call A2, already in the field, and that he also has the intention of purchasing the horse. The circumstances of this competitor are such that he counts the possession of the horse worth as much as £20. What will happen now? Each of the competitors wishes to buy the horse, but only one, of course, can buy him. Each of them wishes to be that one. Each, therefore, will try to persuade B to sell the horse to him, and the means of persuasion will be to bid a higher price. Thus ensues the familiar phenomenon of mutual overbidding. How long will this last? It will last till the rising bids have reached the valuation of the least capable competitor, who, in this case, is A2. So long as the bids are under £20, A2, acting on the motto "rather a small gain than no exchange," will try to secure the purchase by raising his offer, which attempt, naturally, A1 acting on the same principle, will counteract by raising his offer. But A2 cannot go beyond the limit of £20 without losing by the exchange. At this point his advantage dictates "better no exchange than a loss," and he leaves the field to his competitor.


This is not to say that the price A1 pays must be just £20. It is possible that B, knowing A1 to be in urgent want of a horse, will not be content with £20, and will try, by holding back and by skilful bargaining, to extort a price of £25, £28, or even £29:19s. The one thing certain is that the price cannot exceed £30 (the valuation of A1 who concludes the purchase) and cannot be under £20 (the valuation of A2, the excluded competitor).


Assume now that, in addition to A1 and A2, three other buyers, A3, A4, A5, compete for the horse, and that their circumstances are such that they count the possession of the horse equivalent to £22, £25, and £28 respectively. It is easy to show, in the same way, that, in the ensuing competition, A3 will bid to the limit of £22, A4 to £25, and A5 to £28; that the most capable competitor, A1, will always be the successful one; and that the price will be fixed between £30 as higher limit, and £28—the valuation of the most capable of the excluded competitors—as lower limit.


The results of this investigation may therefore be expressed in the following general proposition:—


In one-sided competition of buyers—where there is one seller and more than one buyer—the most capable competitor will be the purchaser; that is, the one who puts the highest value on the commodity he wishes to buy in comparison with the good he wishes to sell; and the price will lie somewhere between the valuation of the purchaser as higher limit, and the valuation of the most capable among the unsuccessful competitors as lower limit—always understood that the price can in no case be lower than the subsidiary lower limit of the seller's own valuation. Comparing this proposition with the result arrived at under the former typical case, we see that competition of buyers has the effect of narrowing the sphere within which price is determined, and narrowing it in the upward direction. Between A and B the limits within which price was determined were £10 and £30; by the added competition the lower limit was moved up to £28.


Second: of one-sided competition of Sellers. This forms the exact converse of the foregoing. Entirely analogous tendencies lead to entirely analogous results—only in an opposite direction. The statement of this need not detain us long.


Suppose that our friend A is the only buyer, and that five dealers, whom we shall call B1, B2, B3, B4, and B5, are competing to sell him a horse. We assume that all the horses are equally good, but B1 values his horse at £10, B2 values his at £12, B3 at £15, B4 at £20, and B5 at £25. Each of the five rivals tries to utilise the present as the sole opportunity of sale, and endeavours to secure a preference over his competitors by underselling, as in the former case by overbidding. But as no one will care to offer his commodity for less than what it is worth to himself, B5 will cease offering at £25, B4 at £20, B3 at £15; then B1 and B2 will compete for a while till, finally, at £12 B2 finds himself "economically excluded,"*6 and B1 alone keeps the field. The price at which he remains a seller must necessarily be higher than £10—otherwise there would be no use in the exchange, and therefore no motive for it—but neither must it be higher than £12, otherwise B2 will continue his competition.


In general terms, then, we have the following proposition. In one-sided competition of sellers—where there is one buyer and more than one seller—the most capable competitor will be the actual seller; that is, the one who puts the lowest value on the good he wishes to sell in comparison with the commodity he wishes to buy; and the price will lie somewhere between the valuation of the seller as lower limit, and the valuation of the most capable among the unsuccessful competitors as higher limit.*7 Compared, therefore, with the case of isolated exchange, where, according to the first formula, the price had to lie between £10 and £30, the sphere within which price is determined will be narrowed by the competitions of sellers, and narrowed in the downward direction.

Notes for this chapter

Menger, p. 183.
Always without prejudice to the second or subsidiary upper limit formed by the valuation of the buyer, which the price can in no case go beyond. Where there is anything like full competition of sellers, however, this is seldom of practical importance.

End of Notes

30 of 55

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