‘Debunking Economics’, Part II: Perfect Competition, Profit Maximisation and Non-Existent Supply Curves

The second chapter of Steve Keen’s Debunking Economics explores a number of arguments: the incoherence of perfect competition; that idea that equating Marginal Cost (MC) to Marginal Revenue (MR) does not maximise profit; and, eventually, that a supply curve cannot be derived. I will offer a brief summary of each of these arguments, but I encourage further reading (Keen’s book being the obvious candidate), as this is complicated stuff and a blog post can only serve as an introduction and overview.

Perfect Competition

Keen’s first point is that, under perfect competition, the demand curve for an individual firm is not horizontal, as taught in economics textbooks, but the same as the market demand curve. Analysis of perfect competition makes the basic mistake of confusing infinitesimally small firms with firms whose size is 0 – in other words, it says that a market demand curve can be split into an infinitely small amount of flat demand curves. However, if you add up any number of flat demand curves, the result will be a flat demand curve, not a sloped one. Therefore the demand curve for any individual firm must be sloped, however shallow the slope is.

Again, it was a neoclassical economist, George Stigler, who discovered this flaw in perfect competition. Stigler’s argument is that since, by assumption, firms do not react to each other’s strategies, any change in output by a firm will change market output by the same amount, and hence affect price. This means the demand curve for an individual firm cannot be horizontal (a change in output does not affect price), but must be the same as the market demand curve (a change in output changes industry output by the same amount).

Keen’s discussion of perfect competition also notes something obvious – the use of the word ‘perfect’ is obviously value laden, despite economist’s claims that their science is value free. I’d add that whilst ‘perfect’ may have a specific definition, the broader value judgement of ‘competition is good’ is undeniably present in economics.

Marginal Cost =/= Marginal Revenue

Keen goes on to argue that the basic neoclassical theory of the firm, that firms maximise profit where Marginal Cost (the cost of producing one extra unit) equals Marginal Revenue (the revenue received from selling one extra unit) is incorrect. This is because it is vulnerable to a fallacy of composition – whilst it is rational for individual firms (at least according to neoclassical principles), it is collectively irrational for an industry, and will result in firms losing money if they all pursue it as a strategy.

The neoclassical profit maximising formula only focuses on the effect of changes in a firm’s own output on revenue, ignoring the impact of changes in industry. Whilst perfect competition assumes firms do not change their output in response to one another, the above result shows that industry output will change by the same amount as a firm’s output. If I’ve interpreted Keen correctly, the reduction in price resulting from this industry change (assumed away by neoclassical theory) is missing from neoclassical formula, so revenue will be lower than predicted, and equating MC and MR will yield a loss.

Is there a supply curve?

It is well known that a supply curve can only be derived for a perfectly competitive market – if firms are price takers. However, once firms have some market power, price cannot be taken as a given, because if they produce more (less), the price will fall (rise), meaning MR and demand diverge. Once this happens, MC will equal MR and not price; a change in price will not cause a firm to move smoothly along its MC curve (which is the supply curve), but instead will depend on MC, MR and demand.

As Keen notes, this explains why economists have been so keen to cling to perfect competition, with its blatant lack of real world corroboration and its seeming incoherence. However, Keen’s own arguments suggest that even under perfect competition, firms have some impact on industry output, and MC cannot be equated to price without making a loss on some sales. Therefore, unless individual firms behave irrationally – something that is obviously contrary to core tenets of economic theory – a supply curve cannot be derived as taught in economics textbooks.

I had a hard time getting my head around this but eventually became convinced of Keen’s arguments. Once you take into account a perfectly competitive firm’s own impact on industry output, the standard analysis of MC = MR breaks down and all the problems with deriving a supply curve, previously assumed away by economic theory via perfect competition, return. This bears something of a resemblance to the problems with demand curves, which were well-known but assumed away by Hicksian demand functions, only to return once you introduced more than one consumer.

The general impression Keen has given me so far is that economic theory is disturbingly aware of its own flaws.

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  1. #1 by Isaac Izzy Marmolejo on July 3, 2012 - 4:02 pm

    “…economic theory is disturbingly aware of its own flaws”

    Keen is pretty fond of saying that neoclassicals do not understand neoclassical economics.

    • #2 by Unlearningecon on July 3, 2012 - 9:20 pm

      Yes – as I mentioned in my opening post to this series, they are less likely to root through its foundations if they accept it.

  2. #3 by Roger Chittum on July 3, 2012 - 10:17 pm

    I’m just writing to let you know I’ve been following your blog for several months and derive a lot of value from it–easier to read your stuff than write my own. :-)

  3. #5 by Blue Aurora on July 5, 2012 - 3:37 pm

    Sorry to go off-topic Unlearningecon, but did you get my e-mail? If so, could you please respond to it?

  4. #7 by ivansml on July 7, 2012 - 10:50 pm

    Late to comments, but anyway: I’m a graduate student of what you might call neoclassical/mainstream economics. Some time ago, I actually tried to understand this particular criticism of Keen in more detail (by reading his Physica A paper on this topic), and I feel confident to say that it’s simply wrong.

    Price taking is not an implication of perfect competition, it is an ASSUMPTION. Given this assumption, the theory is logically consistent. Of course if you relax this assumption and let firms simultaneously choose both quantity and price subject to aggregate demand curve, you get different result, more specifically that of Cournot oligopoly (which however converges to perfect competition as number of firms increases). If you go even further and allow firms to maximize their joint profits, you get again a different result (which, BTW, would be unstable, as it doesn’t constitute Nash equilibrium, at least in a static setting). But now you are speaking about completely different situation. To sum up, this doesn’t, in any way, refute the original theory.

    The confusion about demand curves comes from the fact that under perfect competition, the word “price” has two distinct meanings. With perfect competition, market price is set exogenously from firms point of view. True, in textbooks we might draw flat demand curve to illustrate this fact, but in that case the market price and variable on Y-axis are two different things – market price is a parameter that shifts the curve up and down, the Y-axis variable is a hypothetical price set by the individual firm. So it’s not correct to say that the firm faces a flat demand curve – it faces a whole family of flat demand curves, indexed by exogenous market price, and therefore this whole nonsense about “summing up flat demand curves” is meaningless.

    For more, see discussion by younotsneaky under this post: http://robertvienneau.blogspot.cz/2008/01/is-there-anything-worth-keeping-in.html , and also response to Keen’s paper at http://www.sciencedirect.com/science/article/pii/S0378437107008874

    • #8 by Unlearningecon on July 8, 2012 - 1:26 pm

      Thank you for a constructive comment.

      It’s funny that YouNotSneaky’s & your comments centre around the fact that perfect competition doesn’t require a flat demand curve for an individual firm, because actually I don’t think Keen’s critique needs it, either.

      The point is that, by assumption, firms do not alter their production in response to other firms (do you agree with this point?) Furthermore, by assumption, the market demand curve is downward sloping. This means a change in output must have an impact on price. I don’t think collusion necessarily comes into it.

      • #9 by ivansml on July 8, 2012 - 3:24 pm

        Yes, under perfect competition firm responds only to the market price, not to decisions of other firms. And yes, change in output will eventually have impact on prices, but that impact is not internalized by the firm. If the firm produces more, there will be an excess supply of its good at old prices. When that happens, presumably, prices would somehow adjust to clear markets, while still taken as given by everyone.

        If you want, imagine a centralized market with Walrasian auctioneer, who adjusts prices by tatonnement until excess demand is zero, and then trade can take place at only those prices.

        This, of course, sound silly when interpreted literally, but it can be sometimes justified by large number of agents – e.g. price in Cournot oligopoly converges to competitive price if there are many firms, or the core of an exchange economy converges to competitive allocation when number of agents goes to infinity.

        Collusion is part of Keen’s argument, since he’s the one making big fuss about competitive price not maximizing joint profits, yet maximizing joint profits is a definition of collusion.

      • #10 by Unlearningecon on July 8, 2012 - 8:54 pm

        If firms ignore that their output change will have an impact on price, this is surely irrational behaviour?

        I think this is the part that Keen changed in response to criticisms. His conclusion is that MC=MR doesn’t maximise profit, because it fails to take into account the effect of output changes on price. It’s not about maximising joint profits but the profits of that firm only.

      • #11 by ivansml on July 9, 2012 - 12:16 am

        It is not irrational if it is ruled out by assumption. You may not like the assumption, but that’s totally different from claiming to have found a mathematical mistake, as Keen does.

        When you drop the assumption, you get a model of oligopoly, which is not only routinely taught to undergraduates, it also converges to competitive allocation for large number of firms, so in that case MC=MR holds approximately. If Keen abandons his silly collusion argument, I don’t really see what’s left of his claims.

      • #12 by Unlearningecon on July 9, 2012 - 5:20 pm

        OK we risk going round in circles here, but surely that amounts to an assumption that firms are irrational?

        Keen thinks there is a mathematical mistake in equating profit maximisation with MC=MR. So far you haven’t really disagreed with that, but keep mentioning collusion. I honestly don’t see how Keen’s model requires collusion, though I’m perfectly willing to entertain the possibility that it does.

        MC might approximately equal MR (questions of whether this analysis is valid at all aside) but Keen’s equation simply adds one more variable to make it that bit more accurate. This seems like a scientific approach to me.

      • #13 by ivansml on July 9, 2012 - 8:13 pm

        OK, I’ll try to summarize my thoughts once more. So what really is Keen’s model? As far I as I understand, he makes two points:

        1) perfect competition and price-taking is inconsistent, because firms should consider impact of their choices on price. This is to some extent true, but as I tried to argue, it’s about assumptions and economic interpretation, not about mathematical correctness. The argument about flaw in summing horizontal demand curves if confused. And if you simply assume price-taking, MR=MC is correct formula. The difference between unrealistic assumption and mathematical error may seem subtle, but since Keen frames his critique as discovering mathematical mistake made by generations of economists, it is highly relevant.

        2) once we drop price-taking assumption, what happens next? Standard answer is the Cournot oligopoly, where market power of firms decreases with their number. Keen argues against this, and claims that the correct outcome of optimizing firms will be the one that maximizes joint profits. This is wrong.

        Why? I haven’t read Keen’s book so I don’t know what he writes there, but looking at http://www.paecon.net/PAEReview/issue53/KeenStandish53.pdf (his latest paper on the topic), I see him arguing for collusion right at page 7 (of pdf), where he argues that “objective” profit maximum is obtained by setting price equal to industry-wide marginal revenue. Well, I’m not sure what is meant by “objective”, but OK, the equation is correct by itself. Then he claims that:

        “With this error corrected, the correct profit-maximizing rule for a competitive firm is very similar to that for a monopoly” (p. 8)

        What? First of all, it is not clear why this equation is relevant at all. Individual firm chooses its own quantity, not aggregate quantity. Second, there is confusion about objectives of individual firm and of industry as a whole. Even if the firm believed that all other firms choose collusive quantities, its optimal choice is to produce more than that (this will decrease price and hurt profits of all other companies, but competitive firm does not care about that). Maximizing joint profits is not a Nash equilibrium!

        Then the paper shows some simulations which are meant to support the claim that it is “optimal” for firms to choose collusion. Since the firms are not optimizing, just adjusting their quantities is some ad-hoc way in response to changes in their profits, it’s hard to tell what is driving the results. Then we see some attempt to refute Cournot result, but instead of going through standard Nash equilibrium computation (which doesn’t contain any mathematical mistakes – I’ve solved enough homeworks to be confident about this), Keen presents some convoluted model where firms respond to other firms choices in fixed proportion, and derives that optimal level of strategic interaction is zero. Only problem is that he again assumes that optimum = maximizing joint profits.

        Finally, Keen adresses the question whether collusion would be stable, and he admits that individual firms would have an incentive to deviate (as argued above). WTF? So how could they be optimizing then? Does that mean that everything he did before is wrong? Keen instead invokes theory of repeated games, where collusion could exist as Nash equilibrium under threat of punishment. But then, static Cournot result would also be an equilibrium of the repeated game, and one would have to argue about equilibrium selection, etc. In any case, we are now so far away from original accusations of calculus mistakes that I can hardly remember what’s the point.

        I should conclude, because, although it was fine procrastination, I’ve spent too much time with this (and sorry for a long post). It seems to me that Keen doesn’t really understand the logic of neoclassical models, and instead he is just pointlessly manipulating equations and derivatives to prove his point, which however does not really follow from his arguments. At the same time however, his criticisms of neoclassical theory are pretty aggressive and arrogant (“It therefore seems extremely important to emphasize and demonstrate again that their microeconomics is irreparably flawed.”, p. 1). That is not how science should be done.

      • #14 by Unlearningecon on July 11, 2012 - 7:42 pm

        Ah, Keen doesn’t explore all of this in his book, though he references that paper in a footnote. I think that explains some of our mutual incomprehension. Thanks for the discussion, I will bear your criticisms in mind when I get round to reading it.

  5. #15 by soup on July 18, 2012 - 4:07 pm

    you should check out the sections on imperfect competition in an intermediate micro book like nicholson and snyder “microeconomic theory: basic principles and extensions”

    • #16 by Unlearningecon on July 18, 2012 - 4:33 pm

      I have textbooks, though not that one – what was the specific point to which you were referring?

  6. #17 by soup on July 18, 2012 - 6:56 pm

    sorry, i meant for that comment to follow the discussion between you and ivansml. from the assumptions used in the partial equilibrium competitive model mc=mr. this is mathematically correct and any attempts to argue that mc does not equal mr are mathematically wrong in this framework as ivansml outlines.

    of course the partial equilibrium competitive model is not necessarily what we want to use when thinking about firms as the assumptions as you point out are not necessarily applicable. However, it gives us a way of thinking of how a perfectly competitive market might behave and some economists are more attracted to this model as a theoretical tool than others. if we relax some of these assumptions we have imperfect competition which is presented at an intemediate undergraduate level in the form of cournot with a small number of firms, bertrand with capacity constraints, and stackelberg models. in all three of these models mr does not equal mc. these models are presented in many (well i’m not sure exactly how many but certainty all of the modern advanced ones) textbooks and the many approaches outlined have advantages and disadvantages responsible economists should highlight.

    • #18 by Unlearningecon on July 18, 2012 - 7:26 pm

      I think you are correct to say that it is mathematically correct within the assumptions outlined, and Keen is wrong to say there is a mathematical error.

      You are also correct to say that few people leave an economics course thinking markets are anywhere close to perfect competition. However, the problem arises because these models also imply there is no supply curve, yet people generally use it in day to day analysis. I think this is Keen’s main point.

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