Deadweight losses 3 (updatred)

Over at The Standard Steve Keen responses to Matt Nolan's comment. In part Keen writes,

My critique of neoclassical pricing theory has been published in Physica A, long after that exchange with Auld. The maths passed the scrutiny of physicists, who leave economists in the dust when it comes to mathematical reasoning.

An appeal to authority argument. Most people will know what to do with this. But I'm not sure its even true given the number of economists who have graduate and PhD training in mathematics. Keen goes on,

Furthermore, though the Cournot-Nash is mathematically correct, the Nash equilibrium is meta-unstable: independent competitive behaviour will lead instrumental profit maximisers to diverge from it without collusion. The only way to maintain the equilibrium is to presume competitive firms have “perfect knowledge” of each other’s strategies, which makes a nonsense of the concept of competition to agree with.

Now I'm not sure what Keen means by "meta-unstable" but note that by definition a Cournot-Nash equilibrium is where the best response functions of the firms intersect, and thus no one has any incentive to change their behaviour given their (correct) beliefs about the other players behaviour. The collusive equilibrium, on the other hand, is off the best response functions of all players and thus all players have an incentive to change their behaviour.

As to the information requirement, players need to be able to form (correct in equilibrium) beliefs about the other players possible actions, that is, they know the other players best response functions. They do not need or have perfect knowledge about the actual strategy being played by the other players. Martin Osborne explains the belief formation:

On what basis can such a belief be formed? The assumption underlying the analysis in this chapter and the next two chapters is that each player's belief is derived from her past experience playing the game, and that this experience is sufficiently extensive that she knows how her opponents will behave. No one tells her the actions her opponents will choose, but her previous involvement in the game leads her to be sure of these actions.

(More details are provide in a later section of his book on the question of how a player's experience can lead them to the correct beliefs about the other players' actions.)

Note however that the information requirements are really no stronger than those needed for the perfect competition model or the monopoly model.

Keen continues in response to part of Matt Nolan's comment on my posting,

For those on this blog, what Matt wrote was:

“MR-MC = (n-1)/n * (P – MC)”

As perfect competition assumes “many firms” (read infinite) n-1 converges to n, implying that P=MR.”

This is the formula for an individual firm, not the economy as a whole. The convergence Matt notes applies because the firm output “q” in the MR formula for the single firm (MR(q)=P+q*dP/dQ) must go to zero if the number of firms in an industry goes to infinity.

But we are looking for the equilibrium output for a single firms thus q makes sense. The condition MR=MC is for a single firm, and industry output will be n times the individual firm output given that each firm is the same under perfect competition. Under a Cournot oligopoly the total equilibrium out will be Q^N= n/(n+1)(a-c/b). This goes to the competitive equilibrium as n gets large and if n=1 it equals the monopoly output. Inverse demand is P=a-bQ. If we think of the residual demand curve that a given firm faces after all other firms have produced their output, and let the firm act as a monopolist within this residual market, as in the Cournot model, the quantity they produce will decrease as more firms enter the market as the residual market will get smaller. But the firm will still be setting MR=MC no matter how small the residual market is and MR will not be zero. All seems to be working as it should.

Keen also says,

Perfect competition is and always has been a crock that has stopped economists from actually confronting the real world. Though I despair of ever getting neoclassical economists to realise this, I hope that non-believers can appreciate this and start to ignore the irrelevant theories of neoclassical economists.

Another possible approach to rigorously deriving perfect competition is to assume there exists a continuum of firms. In such a situation , it is literally true that any firm can change its output without changing price, even when the market demand is smooth and downward-sloping. Aumann, R. (1964) ("Markets with a continuum of traders," Econornetrica 32:39-50) is a standard reference.

Update: Matt Nolan discusses The basic frame of a firm: Cournot.