Hong Life CalculatorsUnderstanding the Lerner index calculator — concept and principle
This calculator measures a firm's market power with the Lerner index, the gap between price and marginal cost as a share of price. It also shows the markup over marginal cost, the demand elasticity implied by the margin and, if you enter the firm's price elasticity of demand, the index and profit-maximizing price that elasticity predicts. Economics students and competition analysts use it.
How it is calculated
- Lerner index L = (P − MC) ÷ P
- Price–cost margin = L × 100
- Markup over marginal cost = (P − MC) ÷ MC × 100
- Elasticity implied by the margin = −1 ÷ L
- Lerner index predicted by elasticity = −1 ÷ Ed (for Ed < −1)
- Profit-maximizing price = MC ÷ (1 + 1 ÷ Ed)
The principle
Under perfect competition a firm cannot raise its price above marginal cost without losing all its customers, so P = MC and L = 0. A firm with market power can set price above marginal cost; the larger the gap, the greater its power. Abba Lerner proposed this index in 1934. A profit-maximizing firm sets marginal revenue equal to marginal cost, which leads to the inverse-elasticity rule (P − MC) ÷ P = −1 ÷ Ed: the less elastic the demand it faces, the higher its margin. The rule only works when demand is elastic (Ed below −1).
Worked example
Defaults: price 400, marginal cost 300, elasticity −4.
- L = (400 − 300) ÷ 400 = 0.25, a price–cost margin of 25%.
- Markup over MC = 100 ÷ 300 × 100 = 33.3%.
- Elasticity implied = −1 ÷ 0.25 = -4.
- Index predicted by elasticity = −1 ÷ (−4) = 0.25.
- Profit-maximizing price = 300 ÷ (1 − 0.25) = $400.00.
The current price is therefore exactly the profit-maximizing price for that elasticity.
| Price per unit | Lerner index |
|---|---|
| 100 | -2 |
| 200 | -0.5 |
| 300 | 0 |
| 400 | 0.25 |
| 500 | 0.4 |
| 600 | 0.5 |
| 800 | 0.625 |
How to read the result
L ranges from 0 (no market power) towards 1. A high value can reflect brand strength, product differentiation or barriers to entry, but also high fixed costs that must be covered from the margin, so a high L does not by itself prove abuse. If the actual price is below the predicted optimum, the firm may be pricing for growth or facing more elastic demand than assumed.
Common mistakes
- Confusing the margin on price (25%) with the markup on cost (33.3%).
- Using average total cost instead of marginal cost without saying so.
- Entering elasticity as a positive number.
- Applying the pricing rule when demand is inelastic.
Frequently asked questions
What does a Lerner index of 0 mean?
Price equals marginal cost, as in perfect competition: the firm has no market power.
Why must elasticity be below −1?
A profit-maximizing firm never prices where demand is inelastic, because raising the price there would increase revenue and lower costs.
What if marginal cost is unknown?
Analysts often use average variable cost as an approximation.
Sources: A. P. Lerner, "The Concept of Monopoly and the Measurement of Monopoly Power", Review of Economic Studies (1934) · A. Barkley, The Economics of Food and Agricultural Markets, section 3.5 "Monopoly Power" (Kansas State University Libraries, 2020)