Economics and Mathematics

As I argue in Don't shoot me, I'm only the piano, there's nothing intrinsically wrong about using mathematics in economics. The error lies, not in mathematics, but bad mathematics, or not recognising the limits to mathematical reasoning.

There are numerous propositions in economics which, though they seem scientific, are based upon mathematical errors. Many have been known for decades--such as Sraffa's critique of the marginal productivity theory of income distribution, outlined in The holy war over capital. Several new ones were discovered during the process of writing Debunking Economics. This web site provides the mathematical argument for these new critiques, and it may in the future be expanded to explain the old critiques.

At present, the page links to four resources covering three issues:

• A draft paper and accompanying presentation on the invalidity of the model of perfect competition
• The neoclassical comparison of perfect competition to monopoly is invalid. One pre-requisite for the comparison--which concludes that a perfectly competitive industry will produce a higher output at a lower price than the monopoly--is that the supply curves of the two industry types are identical. Some simple calculus shows that this is only possible if marginal cost is constant. But with constant marginal cost, the model of perfect competition falls apart;
• The neoclassical theory of the firm argues that, regardless of industry structure, firms maximise profits by setting marginal cost equal to marginal revenue. There are three critiques of this proposition here: the first a fairly innocuous one, the second and third, I would argue, are devastating:
  • The graphical representation of a firm shows a "U-shaped" average cost curve, and a rising marginal cost curve. Past a certain point (where diminishing marginal productivity sets in), these are normally drawn with fairly similar slopes: the marginal  cost curve is steeper, but not all that much steeper than the average cost curve. However, there is a mathematical relationship between the slopes of these two curves, and the way they're drawn in most microeconomic textbooks is only possible for trivially small levels of output;
  • The theory of perfect competition is mathematically unsound on several levels
  • Setting marginal cost equal to marginal revenue does not maximise profits in a dynamic economy.