It seems to me that this echoes part of Steve Keen's point in *Debunking Economics* and, further, Keen's *Physica A* paper with Russell Standish:

"...the analysis has rested on one or another of several finite general-equilibrium models which share assumptions that together imply market power on the part of all households and firms and which also share the assumption of price taking by all households and firms.

The possible inconsistency of these assumptions has long been overlooked - since the pioneering work of Walras (1874) and continuing through to the modern period dominated by Arrow and Debreu (1954) and McKenzie (1954). Only very recently has it attracted attention; see Kemp (2005) and Kemp and Shimomura (2005). here I note only that the internal consistency in the models relied on can be maintained by adding the additional assumption that each household is incompletely informed (about the economy of which it is a member) or incompletely rational (unable to appreciate the implications of membership for its market power) or both." -- Murray C. Kemp (2010).

I learned from Keen that the textbook presentation of perfect competition assumes a curious mixture of omniscience on the part of firm managers and an inability to learn from systematic errors^{1}. As far as I know, no introductory or intermediate microeconomics textbook clearly states these assumptions.

Kemp is concerned with perfect competition in the theory of international trade, for example, in the theory of the small open economy. Is there literature assuming that each country produces infinitesimal quantities of whatever commodities they produce, analogous to the literature on the assumption that each firm in a market for a specific commodity produces an infinitesimal quantity? I do not see how such an assumption^{2} can be consistent with the use of U-shaped cost curves in the textbook treatment of perfect competition. In the long-run, we are taught, the firm produces at the minimum point of the U-shape average cost curve. The existence of the downward-sloping portion of these U-shaped curves implies that the level of production in the long-run must be a strictly positive, non-infinitesimal quantity^{3}.

**Footnotes**

- I have recently learned that the literature on limiting behavior in models of mechanism design may be of relevance here. (Al Roth's whining and boundary patrolling is not encouraging.)
- It would be some combination of mistaken to intellectually dishonest to cite Aumann (1964) in defense of an argument in which perfect competition is supposedly found as the limit in a model with a finite number of firms, as the number of firms increases without bound. Aumann explicitly argues that perfect competition cannot be derived as such a limit, and the cardinality of a continuum is bigger than the cardinality of the set of natural numbers.
- It would be intellectually dishonest to "address" the logical inconsistencies of the theory of perfect competition described in this post by insulting Keen, based on his further arguments about monopoly. Those further arguments in Keen and Standish, for example, seem to assume firms treat variables over which they do not have control as decision variables. I do not find the logical aspects of those further arguments compelling, although I do find of interest their simulations, in which they do not make this error. But this footnote deals with a change of subject from this post.

**References**

- Steve Keen, Russell Standish (2006). Profit Maximization, Industry Structure, and Competition: A Critique of Neoclassical Theory,
*Physica A*: pp. 81-85 - Murray C. Kemp (2005). Trade Gains" The End of the Road?,
*Singapore Economic Review*, V. 50: pp. 361-368 [To read]. - Murray C. Kemp (2010). Normative Trade Theory under Gossenian Assumptions, in
*Economic Theory and Economic Thought: Essays in Honour of Ian Steedman*(ed. by J. Vint et al.), Routledge. - Murray C. Kemp and K. Shimomura (2005). Price Taking in General Equilibrium,
*American Journal of Applied Sciences*, V. 6: pp. 95-97. [To read]

## 4 comments:

If I'm interpreting you correctly, this is exactly in line with my thoughts. Keen's argument has two main points:

1. The 'price taker' assumption is untenable if you assume firms are perfectly rational profit maximisers.

2. The result is that they will produce at the same price and quantity as a monopoly.

(2) is wrong. 1 is, however, right, and shows that the existence of the supply curve as taught is not logically justified. Furthermore, an analogous argument can be made for demand curves.

It would be a sign of non-negligible ignorance to claim that "The possible inconsistency of these assumptions has long been overlooked", as Kemp does. The idea that perfect competition could (and perhaps should only) be properly justified in situation with a large/infinite number of participants goes back to 19. century, when it was postulated by Edgeworth. And far from ignoring the problem, Edgeworth's conjecture was subject of much interest from leading GE theorists (Debreu, Scarf, Aumann, Hildenbrand,...). I can only assume that those guys wouldn't have spent their time on the subject if they thought that the tension between price-taking behavior and finite number of participants could be just ignored. For further references, see the New Palgrave entry on "Large Economies" by John Roberts [1].

I agree that it would be mistaken to cite Aumann's paper, not because of using a continuum of agents, but simply because it deals with exchange economies without production. The question about whether one could construct a consistent model with infinity of firms, each of which has nonconvex technology (the U curve of average costs), could be an interesting one. My guess is that the answer is no.

In such a case, we would predict that there would be a finite number of firms in the market, and their behavior could be "realistically" modeled through some kind of oligopoly structure. If the number of firms was large, the resulting allocation would be typically close to the competitive one, so that perfect competition could be used as a convenient approximation. If their number was low, then perfect competition would not be appropriate - which is why we have developed models of monopoly, oligopoly and strategic interaction in general. Last time I checked, those are covered in undergraduate textbooks too.

[1] https://gsbapps.stanford.edu/researchpapers/library/RP892.pdf

"I do not see how such an assumption can be consistent with the use of U-shaped cost curves in the textbook treatment of perfect competition."

I think every microeconomist will agree that perfect competition does not work if average cost is larger than marginal cost or, which is the same, if average cost is decreasing. Therefore, fixed costs in general are not compatible with perfect competition. That is why today's mainstream modelling often uses the Dixit-Stiglitz model of monopolistic competition (not of perfect competition).

Thanks for the comments.

I do not think intro teaching on perfect competition can be defended by pointing out that undergraduate teaching often describes market forms other than perfect competition. I think one also needs, at least, an assertion that perfect competition is a limiting case of some other model. Better would be an argument. I have not read it, but, ivansml, do you think Kreps book should have had a bigger impact on undergraduate teaching?

I found the suggested Roberts'

New Palgravearticle useful. I still do not see how a limit asnincreases without bound can justify a model with a continuum of firms. I know I do not understand non-standard analysis, but, as I understand it, that is a different issue. Admittedly, I could try to read more about the core.Post a Comment