My major point in this post is to draw attention to the existence of Kapeller and Pühringer (2010).

Steve Keen's book, *Debunking Economics*, is mainly a compilation of well-established criticisms of textbook economics. He attempts as popular a presentation as the material will permit. These criticisms, in my opinion, leave textbook economics, both microeconomics and macroeconomics, in tatters^{1}.

Keen, in the first edition, also offered his own original criticism of the textbook theory of the firm under perfect competition. You can find various brouhahas on the internet over Keen's remarks. Between editions of his book, Keen has published, with others, a series of papers developing his criticism^{2}.

Some have asserted theories of perfect competition in models with a continuum of agents provide a defense of the textbook theory. As Kapeller and Pühringer point out, this is a change of subject. A non sequitur should not be a considered an adequate defense of the textbook model. Furthermore, the primary developer of models with a continuum of agents presents his approach as inconsistent with the textbook theory:

"Though writers on economic equilibrium have traditionally assumed perfect competition, they have, paradoxically, adopted a mathematical model that does not fit this assumption. Indeed, the influence of an individual participant on the economy cannot be mathematically negligible, as long as there are only finitely many participants. Thus,a mathematically model appropriate to the intuitive notion of perfect competition must contain infinitely many participants.We submit that the most natural model for this purpose contains acontinuumof participants." -- Robert Aumann (1964).

It seems to me only four possibilities are open here:

- Aumann is not talking, in his critical remarks, about the model of perfect competition taught in almost any intermediate microeconomics textbook.
- Aumann is mistaken.
- The economists who write and teach the self-contradictory textbook model are deliberately teaching self-contradictory models to their students.
- The economists who write and teach the self-contradictory textbook model are ignorant.

I think only the third and fourth options are credible^{3}. I can understand the difficulty of writing and teaching in an intellectually bankrupt discipline.

**Update:** Nick Rowe illustrates the willingness of some economists to teach nonsense to students: "To the individual farmer, who sees only a tiny slice of the whole demand curve, because even a 100% change in his output will cause only a tiny percentage change in total output, it will look perfectly flat." Note that in his post, even when considering the limiting case, he never considers the existence of a continuum of producers.

**Update 2:** Steve Keen, in the *Business Spectator*, re-iterates his critique of the incorrect neoclassical textbook theory of perfect competition. Tim Worstall lies to readers of *Forbes*. It is not true that "everyone subscribes" to the "usual basics of economics" that Keen debunks. It is not true that the bulk of Keen's book is about his "breakthroughs in showing us all the errors of our ways." One can accept almost all of Keen's demonstration of the mendacity of neoclassical textbooks without accepting any claim that Keen says is original with him. In fact, Keen notes that Stigler showed that perfectly competitive firms that are not systematically mistaken, if they produce a positive, non-infinitesimal quantity in equilibrium, will not produce at a level of output where the market price, Marginal Revenue, and Marginal Cost are all equated.

**Footnotes**

- Some areas of economics, such as game theory or the recent popularity of instrumental variables and experiments (natural and otherwise), remain unaddressed by Keen.
- Kapeller and Pühringer point to a 2008 paper published by Anglin in
*Physica A*as a peer-reviewed response. - The existence of the downward-sloping part of the U-shaped average cost curve for the textbook firm hardly seems compatible with the existence of an infinite number of firms, each producing a quantity of zero units of an homogeneous good.

**References**

- Aumann, Robert J. (1964). Markets with a Continuum of Traders,
*Econometrica*, V. 32, No. 1-2. - Kapeller, Jacob and Stephan Pühringer (2010). The Internal Consistency of Perfect Competition,
*The Journal of Philosophical Economics*, V. III, No. 2: pp. 134-152.

## 16 comments:

Keen's book is full of straw-men and factual errors. Of these, his attack on perfect competition is most prominent. The paper you refer to adds nothing new, just repeats Keen's arguments without challenge.

I've discussed this in more detail elsewhere, so just briefly: in a model of perfect competition, firms are price takers by assumption (you can imagine that there is a centralized market with auctioneer who doesn't allow trade outside posted prices, if you want). Therefore, equations such as (5) in Kapeller and Puhringer make no sense given assumptions of the model and thus prove nothing (if one firm produced more, price would stay the same and there would be excess supply instead). And Keen's rejection of Cournot solution because firms could obtain more profits if they acted as joint monopolist only demonstrates that he simply doesn't understand elementary concepts of best response and Nash equilibrium.

Keen doesn't know what he's talking about (and that's putting it politely), and you and other heterodox economists taking him seriously just diminishes your own credibility. But confirmation bias is hard to beat, I guess.

Mm-hmm. Please tell me more about how mainstream economics generally, and yourself in particular, predicted the global financial crisis.

In as far as there is any point of substance in ivansml's comment, I guess, he is saying Aumann is mistaken in the quote in my post.

I suppose I better admit it: there is a Hyde dwelling inside this Jekyll.

I truly enjoy when the arrogant, incompetent and dimwitted rush head first against a wall. There's a kind of perversely sadistic satisfaction in that.

And what better than to claim "confirmation bias" after a selective reading. Delightful irony!

Aumann is not mistaken, but your interpretation of his paper is. He writes:

"Thus, a mathematically model appropriate to the intuitive notion of perfect competition must contain infinitely many participants."So what Aumann is saying is not that models of perfect competition with finite number of participants contain mathematical errors, but that their assumptions are not realistic according to our intuition about perfect competition. This may seem as "sophistry", but since Keen claims to have discovered literally a mathematical error, the difference between error and unrealistic assumption matters a lot.BTW, I'd be more interested about what you or other commenters think about my second point (about claim that individually "optimal" action of firms will lead to joint monopoly solution), which I consider more important. But judging by comments so far, I'll better revise my expectation for replies with actual and relevant arguments downwards.

Blissex writes:

Oh there. Previous posts in this blog have been numerous on topics related to the Cambridge capital controversy.

So "intellectually bankrupt" is too kind an assessment for a theory of Economics that does not have a working (or any at all beyond mere wishful thinking) theory of capital, and yet its practitioners talk about equilibrium, markets, and even functions of production.

In addition to what you say, nearly all the crass inconsistencies and mathematical mistakes in the mainstream theory of Economics are designed to uphold its central verity: that the optimal distribution of income is unique and a mathematical property of competitive markets, and therefore Economics is not political, just as the distribution of income is a fact, not a decision.

Which is just propaganda, but in our time Economics is meant to be a vehicle for propaganda just like Theology was in the middle ages, and when an Economist talks is like a preacher in the middle ages telling the serfs that God has ordered men in priest, warrior, merchant and serf castes and they should accept that ordering because it is God's will.

Blissex writes:

«have traditionally assumed perfect competition, [ ... ] the influence of an individual participant on the economy cannot be mathematically negligible, as long as there are only finitely many participants. Thus, a mathematically model appropriate to the intuitive notion of perfect competition must contain infinitely many participants.»

«I've discussed this in more detail elsewhere, so just briefly: in a model of perfect competition, firms are price takers by assumption»

So yes it seems that a previous commenter assumes that Aumann is wrong, and that what Aumann thinks is the «intuitive notion of perfect competition» can be simply ignored by wishfully assuming into existence that «firms are price takers».

A trivial technique of sophistry ("petitio principii"): it is not that firms are price takers because markets are perfectly competitive, but firms, no matter their number or size, are «by assumption» price takers, therefore markets are perfectly competitive.

That is not intellectually bankrupt in the sense that it can lead far away from bankruptcy to a rewarding career, up to becoming chairman of the CEA, generously sponsored by those in whose interest the sophistry has been designed.

That sophistry reminds me of the ontological proof of the existence of God, that since God is the most perfect entity, and existence is an aspect of perfection, he must exist.

In this case the model more modestly assumes that God is an infinitely powerful and all knowing auctioneer as in «you can imagine that there is a centralized market with auctioneer who doesn't allow trade outside posted prices».

And the words used are just too revealing: «by assumption» and «imagine», never mind the entirely arbitrary words «does not allow trade», which make a mockery of the very notion of free markets.

Wishful thinking? As long as it upholds the politically useful verities, it works well.

Keen's argument seems to be to be incredibly simple and replies such as ivansml's tend to muddy the water rather than dealing with it directly.

The argument is that there is no way an individual firm can have absolutely zero effect on price, so MC=MR will not quite maximise profits.

Now, you can assume, as ivansml does, that they are price takers by assumption so they act 'as if' their output change will not have an effect (apparently a theory of perfect competition is really a theory of central planning, but I digress). The problem is that equating MC and MR will still not quite maximise profits. In fact, if every firm does it the MR and demand curves will diverge as they did under monopoly and so there will be no supply curve.

There is no need to invoke Cournot or game theory. Can somebody please to respond to this basic argument without muddying the waters?

"The problem is that equating MC and MR will still not quite maximise profits. In fact, if every firm does it the MR and demand curves will diverge as they did under monopoly and so there will be no supply curve."You may consider this to be incredibly simple, but I don't follow. What does "not quite maximize" mean? First of all, MR=MC will always maximize profit (if revenue and cost functions are differentiable, maximum exists, etc.). The question is of course what is MR - for price taking firm (from its point of view), MR is constant and equal to price, by assumption. If the firm internalizes effect of its decision on price, then MR will depend on its quantity, but surely also on choices of other firms, and you need to make some assumptions about outcome of their strategic interactions.

"but surely also on choices of other firms, and you need to make some assumptions about outcome of their strategic interactions."

Right but the standard model of perfect competition already assumes that they don't strategically interact, so one firm's change in output will change the entire industry's output by the same amount, and because the industry demand curve is downward sloping, this will have an effect on price, however small.

"MR is constant and equal to price, by assumption."

Surely this contradicts the downward sloping demand curve at the industry level? I guess if there is a central authority setting price you might get around it. But this sort of contradicts the notion we are studying perfect competition.

Don't get me wrong, but the question of continuity or not seems to me to be of secondary importance. As Sraffa has shown in 1926 the problem with perfect competition, in the marginalist sense of an infinite number of infinitesimally small agents, in a partial equilibrium setting, is problematic since there is no reason for diminishing returns (you need external economies to the firm, but not the industry, a rare case indeed). And for the general equilibrium case (with uniform rate of profit) the marginalist case cannot guarantee well behaved demand curves at all.

"MR is constant and equal to price, by assumption"

In which case it is not a theory about the economy, is it? Since if the economy is a real subsystem of a real society, relations between price and marginal returns would be cause and effect relationships, rather than presumptions.

Keen does indeed proceed on the basis that the theories stated as economic theories are theories about economies, and critiques them as such. If one insists that this is arguing from a false premise, then it seems one only carries the point at the cost of conceding the debate.

As far as diminishing returns, diminishing returns may of course exist in the short term, for a given productive set-up, which in the real world must have a given maximum ideal capacity and which, as operations research established, will face increasing delays as the operator attempts to push production toward maximum ideal capacity.

In the long run, as Sraffa argues, there is no reason to suppose they are very common: in the long run, when productive capacity is not a given, diminishing returns in partial equilibrium requires a peculiar combination of in-firm and extra-firm, in-industry scale economies.

However given that the long run is a fiction, empirical testing of returns in the long run requires some fabrication along the way.

For what it is worth, Nick Rowe has put up a sort-of post directly on Keen. We learn Keen's argument fails because he publishes in "non-mainstream journals and books" and because he seems like an "angry guy standing on a soapbox."

On the other hand, "Evan", in the comments, draws our attention to two papers, by Steff en Huck, Hans-Theo Normann, and Jorg Oechssler, that confirm Keen's simulation.

Well, the second half is half right ~ Steve Keen IS standing on a soap box.

But Nick Rowe suggesting that Steve Keen is "an angry guy" suggests that Nick Rowe either likes to say stuff without finding out first whether its right or not, or else is abysmally bad at reading emotion.

I had all but forgotten this discussion.

So, let me see if I understand the state of the discussion:

"The question is of course what is MR - for price taking firm (from its point of view), MR IS CONSTANT AND EQUAL TO PRICE, BY ASSUMPTION."

And here I was, thinking that was a theorem deduced from the assumptions of the profit maximization problem. Silly me. :-)

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