Lerner Index of Market Power

Abba Lerner published this in the Review of Economic Studies in 1934 as a measure of "the degree of monopoly power", and its virtue is that it is a pure number between 0 and 1 that can in principle be computed for any seller. Zero means price equals marginal cost, the perfectly competitive outcome. Approaching one means price is enormously above the cost of the next unit.

The denominator of the fraction is where most of the misuse happens: it is MARGINAL cost, not average cost. Marginal cost is what the next unit costs to make — materials, the electricity to run the machine, the shipping. It excludes everything already spent: the factory, the research, the software that took four years to write. A pharmaceutical company that spent a billion dollars developing a drug and can press a pill for forty cents has a Lerner index near 1, and this tells you almost nothing about whether the company is profitable. Software, recorded music, textbooks, semiconductors and pharmaceuticals all have high Lerner indices as a structural consequence of having nearly no marginal cost at all.

This is why the index is a poor stand-alone diagnosis. A high Lerner index measures the SHAPE of a cost structure at least as much as it measures conduct. An industry that must recover large fixed costs from a price cannot price at marginal cost and survive, and observing that it does not is not evidence of anything in particular. What the index is genuinely good for is comparison — the same firm over time, or two firms with similar cost structures — and as the theoretical bridge to elasticity.

That bridge is the reason the index appears in every microeconomics course. Setting marginal revenue equal to marginal cost, which is what a profit-maximizing firm does, and substituting the Amoroso–Robinson relation gives $L = (P - \mathit{MC})/P = -1/E_d$, and this is a striking result: at the optimum, the markup is determined entirely by the elasticity of demand and not at all by the cost. Demand elasticity of −5 gives a 20% markup; −2 gives 50%; −1.25 gives 80%. Cost enters only in setting the price level, never the markup fraction. It also explains why the two sides of the equation are two ways of measuring the same thing, and why an estimated elasticity and an observed markup that disagree badly are telling you the firm is not maximizing short-run profit — which is common, and usually deliberate.

Practical difficulty: marginal cost is rarely observable. Accounting systems produce average costs, because that is what allocating overhead produces, and substituting average for marginal understates the index — sometimes enormously, in exactly the fixed-cost-heavy industries where the index is most interesting. Regulators and courts that use markup evidence spend most of their effort on this measurement problem rather than on the arithmetic.

Finally, an index below zero is a real thing and not an error. Loss-leading, penetration pricing, a regulated tariff below cost, a below-cost export price — all give a negative index. It is simply outside what the measure was built to describe.