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Lerner index

Collapse a firm's market power into one dimensionless number, the markup of price over marginal cost as a fraction of price, L = (P − MC) / P, which under profit maximization also equals the reciprocal of the demand elasticity the firm faces.

Core Idea

The Lerner index is a scalar measure of a firm's market power, L = (P − MC) / P — the markup of price over marginal cost as a fraction of price. It ranges from zero (perfect competition, price equals marginal cost) toward one (pure monopoly facing inelastic demand). For a profit-maximizer it equals the reciprocal of the absolute demand elasticity the firm faces, L = 1/|ε|, so an observed margin reveals the elasticity, and elasticity predicts the markup. It measures power as exercised, not structural concentration.

Scope of Application

Computable, and meaningful, wherever a profit-maximising firm prices against downward-sloping residual demand with price and marginal cost measurable in money.

  • Industrial organization and antitrust — the home: price-cost margins flag imperfect competition (~0.3–0.4).
  • Regulated-industry rate-setting — gauging how far a regulated firm prices above its floor.
  • Banking-competition literature — industry-aggregated indices from financial statements.
  • Health-care pricing studies — regional inpatient indices, often correlated with market HHI.
  • New Empirical Industrial Organization — backing out conduct from prices and quantities.

Clarity

The index makes legible the difference between power as exercised (the actual price-cost deviation) and structure as concentrated (share, HHI), naming cases the proxies misread — a dominant-share firm priced near cost, or a small differentiated firm pricing high. Being dimensionless, it makes power comparable where dollar prices do not. And the identity L = 1/|ε| turns an observable margin into a window on the unobservable demand elasticity.

Manages Complexity

A thick competitive dossier — share, rivals, substitutes, differentiation, entry barriers, price scale — compresses into one scale-free scalar anchored at two reference points, read directly off cost data for first-cut screening. Two features sharpen it: the index isolates power as exercised rather than concentration, and the identity L = 1/|ε| collapses two quantities into one, so computing the markup and inferring competitive conduct become a single act.

Abstract Reasoning

The index licenses measuring power as exercised rather than inferring it from structure, bidirectional inference through L = 1/|ε| (a markup reads as inelastic demand; an elasticity predicts a markup), scale-free cross-industry comparison, boundary-drawing against structural measures with a known complementarity, and a first-cut screening move that lets one number stand in for the market-structure file at the triage stage.

Knowledge Transfer

The index is a constructed measure, so a precondition governs travel: it transfers literally wherever a profit-maximising firm faces residual demand with measurable price and marginal cost — across antitrust, rate-setting, banking, and health-care studies, all co-instances. Beyond that setup a look-alike normalized-slack ratio (a CPU's thermal headroom) is a formal coincidence, not the Lerner mechanism. What genuinely generalizes is the parent move — measure deviation from a benchmark as a normalized scale-free ratio — carried by efficiency_frontier-style gap-to-benchmark normalization, not by the Lerner index.

Relationships to Other Abstractions

Local relationship map for Lerner indexParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Lerner indexDOMAINPrime abstraction: Elasticity — is part of, conditionalElasticityPRIMEDomain-specific abstraction: Market power — presupposesMarket powerDOMAINPrime abstraction: Measurement — is a decomposition ofMeasurementPRIME

Current abstraction Lerner index Domain-specific

Parents (3) — more general patterns this builds on

  • Lerner index presupposes Market power Domain-specific

    The Lerner Index presupposes market power as the target attribute whose exercised price-cost wedge it maps onto a scale.

  • Lerner index is part of, conditional Elasticity Prime

    Under interior profit maximization, the index contains the reciprocal residual-demand elasticity identity that makes markup and responsiveness two readings of one parameter.

  • Lerner index is a decomposition of Measurement Prime

    Removing firm and price vocabulary leaves an attribute mapped by a stated procedure onto a dimensionless scale with fixed anchors and interpretation conditions.

Hierarchy paths (4) — routes to 3 parentless roots

Neighborhood in Abstraction Space

Lerner index sits in a crowded region of the domain-specific corpus (5th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Market Structure & Price Equilibrium (25 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-07-12