## Sunday, July 12, 2015

### “Rationality” in the Theory of the Firm... Part 3

Previously: Introduction; Part 1; Part 2

Keen and Standish continue their response, writing
The theory we’re critiquing is the Marshall theory of the firm, which like the Cournot oligopolists, consists of price-taking agents operating in a clearing market with the market prices determined by a given function of total production $Q$. There is [sic] no separate supply and demand $Q$s, or if there are, they are identical, always. The Marshall model also supposes perfect competition, namely that the individual firms have no influence on market price, or ${\partial P}/{\partial q_i}=0$, which as Rosnick agrees with us, is simply incompatible– a logical fallacy.
Putting aside for a moment the complete theory salad that they offer here, the last statement is completely and utterly false. I never agreed that ${\partial P}/{\partial q_i}=0$ is incompatible with theory. Rather, I argue that it follows directly from Keen and Standish’s definition of $P$. It is true even in their own theory. As I began Section 4.2,
[N]ote that $P$ is defined as inverse demand– a function of quantity demanded and not of any firm’s quantity supplied. By definition, then, ${\partial P}/{\partial q_i}=0$.
I have absolutely no idea where they got the idea that I agreed with their alleged finding of a logical fallacy. I do agree that price-taking is incompatible with Cournot oligopoly. I do agree that– unlike perfect competitors– Cournot firms must have market power. But the fact that ${\partial P}/{\partial q_i}=0$ does not enter into it, and Keen and Standish have nowhere supported their claim to the contrary with a mathematically sound argument based on the assumptions of perfect competition.

With that out of the way, let me explain why I call their quote above a theory salad. Start with the idea that Cournot oligopolists are price-taking agents. This is like saying that hydrogen is oxygen, or zero is one. Cournot oligopolists are not price-takers. As I explained in Section 2 of my Comment, Keen and Standish can only say this because they redefine price-taking to mean something other than the commonly-understood definition.

Now, when I set out about reviewing their work, the very first thing I tried to understand is what, precisely, was the model they were critiquing. As I saw it, there were two possible models which might be called “Marshall theory of the firm.” The more obvious choice was textbook firm behavior under perfect competition, because they hang much on price-taking. The other choice I considered was “Marshall equilibrium,” which is Cournot oligopoly with endogenous entry and exit of firms. However, Keen and Standish always consider a fixed number of firms in their analyses, so this made no sense even though their firms seemed to operate as a Cournot oligopoly.

Uncertain, I pressed the authors for clarification. Permit me to repeat my as-of-yet uncontested description of our exchange (specifically, footnote 1 of my Comment)
In private correspondence, Keen confirmed that “modern textbook model of perfect competition” was a safe interpretation on the part of any reader when reading “the theory of atomistic competition” or “Marshall’s pure case” or “the standard Marshallian theory of the firm” or “standard Marshallian analysis.”
So long as the model under discussion is perfect competition, no analysis of firms with market power can serve to prove perfect competition internally inconsistent. One cannot logically argue that a theory of firms assumed to have no market power is internally inconsistent by changing the definition of price-taking so that the firms do have market power. It matters not whether their error is intentional or deliberate. In substituting their own assumption in lieu of one employed in the textbook model, the first thread of their critique goes straight to the grave.

The remainder of my Comment regarding the first thread is less aimed at picking apart their argument as it is explaining their confused discussion. As with the quoted passage above, Keen and Standish persist in arguing that there is a theory of perfect competition in which quantities supplied and demanded are indistinguishable– where the market is assumed a priori to clear. This is fundamental to Cournot oligopoly, but utterly backwards for perfect competition.

In Cournot oligopoly, firms all produce what they will, and then the price adjusts to clear the market. Under perfect competition, the market delivers a price to firms, and then the firms produce. Under perfect competition, only if firms happen to produce the quantity that consumers demand at that price does the market clear. Under perfect competition, market clearance is conditional on delivering to firms one particular price. Now, one may also extend the theory so that in a perfectly competitive market the correct price happens always to be delivered. But that is very, very different from assuming that the market clears ex post no matter what choices perfectly competitive firms make after the price is delivered. It is not the assumptions underlying the model, but Keen and Standish’s understanding of perfect competition which which leads to the supposed fallacy. Their response simply does not address this fatal error; they merely restate their flawed description of perfect competition.

To be continued in Part 4.

Read my original Comment (including Technical Appendix) at World Economic Review.