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¶
Current abstraction Lerner index Domain-specific
Parents (3) — more general patterns this builds on
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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.
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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.
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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
- Lerner index → Market power → Bargaining Power → Asymmetry
- Lerner index → Elasticity
- Lerner index → Measurement
- Lerner index → Market power → Positional Advantage → Asymmetry
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
- Market power — 0.89
- Monopsony power — 0.88
- Edgeworth Paradox — 0.88
- Bertrand Paradox (Economics) — 0.88
- Modigliani–Miller theorem — 0.87
Computed from structural-signature embeddings · 2026-07-12