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History of Political Economy 33.1 (2001) 167-174
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Magnan de Bornier on Cournot-Bertrand:
A Rejoinder to Clarence Morrison
Jean Magnan de Bornier
In his essay in this issue as well as in a 1999 article, Professor Clarence Morrison strongly criticizes some recent literature concerning Augustin Cournot, Joseph Bertrand, and their influence on modern economic theory. One article in that literature is an essay I published in HOPE in 1992.1 Concerning that article, Professor Morrison intends to show that my “thesis will not survive working through [Cournot’s] Recherches, as opposed to merely reading it” (this issue, 161) and that “all of the arguments that Magnan de Bornier gives to support his novel thesis are bogus” (Morrison 1999, 337).
I will try to clarify some of the points in my 1992 article that, in my opinion, seem to have been misunderstood as a result of my failure to state them effectively.
My “New and Novel Interpretation” of Cournot
According to Morrison, I argued in my 1992 essay that “Cournot considered only price rivalry” (this issue, 161). In that article I did not write that Cournot considered price rivalry to the exclusion of quantity rivalry; rather, I intended to demonstrate that any distinction between the two has no meaning in Cournot’s world. [End Page 167]
It hardly seems justified to contend, as most modern literature does, that (produced) quantities, as opposed to price, are the strategic variable in Cournot’s model of oligopoly. Moreover, in this framework, the opposition between price and quantity is meaningless. If the quantity of one of the duopolists is fixed (or considered as such), the other owner will behave like a monopolist with residual demand as regards his output and decide on the market-clearing price by considering the whole supply that will result; he can, as we have seen, maximize profit either with regard to price or with regard to quantity. The notion of a strategic variable is empty in Cournot’s market, where sellers are supposed to have the power to modify the price easily. (628)2
Professor Morrison only adds confusion to this empty opposition between price and quantity strategies when he writes that price is “a tactical variable rather than a strategic variable” (this issue, 162).
The Unimportance of the Optimization Variable
Professor Morrison then criticizes my statement that “only one section out of forty … that deal with price theory … is written with quantity as the apparently strategic variable” (630). I would indeed be naive to offer this kind of statement as self-sufficient evidence; I only consider the statement as one element of a demonstration, and this should be obvious to anyone who reads my article.
Professor Morrison does not only think that this method of counting sections is inappropriate; he also writes it is false: “The systems of equations (5) in section 46 and (6) in section 47 (as well as equations (1) and (2)) could only have been obtained by differentiating with respect to quantities” (this issue, 162).
First note that systems (5) and (6) are no more than reformulations of (1) and (2) when additional assumptions are made (a “limitation of [the] productive powers” of the producers in (5), and the introduction of production costs in (6)). But more important, the statement that these systems could only be obtained differentiating with respect to quantities is simply false. It has to be remembered that, for Cournot, each proprietor behaves as if he were a monopolist with residual demand, and that monopoly behavior can be written indifferently with price or quantity as [End Page 168] the optimization variable. (Professor Morrison shows in his article in this issue his knowledge of this elementary property.)
Let us show that equations (1) and (2) can be obtained without differentiating with respect to quantities. Making use of the standard demand function D = F( p), the profits that the proprietors endeavor to maximize are as follows:
p1(p) = p[F(p) - D2], and
p2(p) = p[F(p) - D1]
where the expressions [F...