The entry below was written shortly after the book was published. I have since dramatically expanded the critique: as time went on, I found more and more ways in which the theory was at fault, and what began as a critique of the mathematical realism of perfect competition finally resulted in a disproof of the neoclassical "rule" for profit-maximization. Two papers on this (the most recent published in Physica A) are available here; I have yet to write a "words only" exposition on this, so to follow the critique properly you'll need some mathematical fluency. This Powerpoint Presentation provides a gradual treatment of the topic, from the most basic level to a quite complex combined critique of both Marshallian and Cournot-Nash theories of competition.
The proof below, which relies on a Taylor series expansion of the terms in the profit statement for a single firm, is still correct, so I'll leave it here. But those who want to assess my argument fully--mainly economists of course--should consult the presentation and Physica A paper.
Two damning but rather technical arguments against the neoclassical theory of the firm were left out of the book because the technicalities could confuse a first-time reader. These are (1) that the conditions required for economists to be able to reach their definitive conclusion that monopolies are worse for welfare than perfectly competitive industries are contradictory; (2) that setting price equal to marginal cost does not maximise profits for the supposedly profit-maximising perfectly competitive firm.
The key logical flaw in the theory of
perfect competition can be seen more clearly if we first assume that the theory
is correct—that the intersection of supply and demand does set market price,
and that each firm produces where this price equals its marginal costs—and then
seeing what happens if a single firm reduces its output. If economic theory is
correct, this exercise should show that this firm reduces its profit, since the
theory asserts that it is already producing at a point which maximises its
profit.[1]
If, for whatever reason, a single firm
reduces its output, then the market supply curve must move to the left—supply
falls, however slightly. Since the market demand curve is assumed to be
downward sloping, this causes a slight rise in the market price.
Because it has reduced its output slightly,
it and all other firms in the industry benefit from an increased price. But
there are three other forces acting in opposite directions on the individual
firm's bottom line. Firstly, though its sale price has risen, its quantity sold
has fallen—so its total revenue has probably fallen.[2] But since marginal cost is assumed to rise, it also means that the
firm's costs have fallen.
This bit is somewhat tricky to understand
without maths, but since the firm was originally producing where the sale price
equalled its marginal cost, these two forces cancel each other out. Revenue has
fallen by the change in quantity times the original price, and costs fall by
the change in quantity times the marginal cost. Since marginal cost and price
were assumed to be equal, the net effect is zero.
This leaves the third force, which is the
product of the interaction of the two forces. This interaction term is
positive: the firm's profits will increase.[3]
This contradicts the initial assumption
that the firm was already producing at a profit-maximising level. So one of our
initial assumptions cannot be correct—and the obvious candidate is the
assumption that the market price is that set by the intersection of supply and
demand. This is a 'proof by contradiction' that the equilibrium of a perfectly
competitive market cannot possibly be where price equals marginal cost.
The contradiction is amplified when we
consider the behaviour of other firms in the industry, and the behaviour of
firms outside the industry which might be considering entry.
All the other firms in the industry—the
ones that held their outputs constant—unambiguously gain from the reduction in
output by the single firm, since they benefit from the increase in price
without sacrificing any sales. Since this increase in their profit is caused by
a rise in price, and a rise in price implies a reduction in supply, they are
likely to 'take the lead' from the single firm that reducing output is a good
idea. So the tendency to reduce output will propagate through the industry.
Firms outside the industry that are genuine
profit-maximisers are unlikely to enter an industry in which marginal cost
greatly exceeds marginal revenue. The absence of entry from outside the
industry, coupled with a tendency for all firms to reduce output, means that
the price set by equating price to marginal cost cannot possibly be an
equilibrium. Instead, the only possible equilibrium is where price is set by
equating marginal revenue to marginal cost.
Therefore, the equilibrium price for a competitive industry will be the same as for a monopoly—the price set by the intersection of industry marginal revenue and marginal cost.
[1]I thank John Legge for putting this
critique into mathematical form. The maths of this argument is available on
this Web at Maths/Size.
[2]Whether or not it actually does fall
depends upon elasticities of demand. Mathematical analysis implies that revenue
will almost certainly fall.
[3]This is one of the few times where I’ve
decided that a verbal explanation of the maths would just be too hard to
make–though the maths itself is fairly simple. The change in profits boils down
to two of the three components of the change in revenue, since the most direct
term–the fall in revenue caused by the fall in quantity–is cancelled out by the
fall in costs. The second term is positive, and equal to the product of the
change in output, the slope of the market demand curve, and the quantity the
firm was originally producing. The third term is negative, and equal to the
change in quantity squared times the slope of the demand curve. For small
changes in output (compared to the actual level of output), the second term
outweighs the third and the firm’s profit rises.