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 errors1. 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 assumption2 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 quantity3.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.
- 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]