# Lerner Index

Lerner Index is a measure of monopoly power which equals the markup over marginal cost as percentage of price. Its value ranges from 0, in case of a perfect competition, to 1, in case of a pure monopoly.

One of the most important difference between perfect competition and monopoly lies in the relationship between price and marginal cost. A perfectly-competitive firm can’t afford to set its price higher than its marginal cost. It is because it faces a horizontal demand curve which means that if it attempts to charge a price higher than its marginal cost, it will have zero revenue because all its customers will switch to its competitors. A monopolist on the other hand faces a downward-sloping demand curve which means that it can charge a price higher than its marginal cost. One way of finding out the extent of monopoly power is to work out the difference between price and marginal cost of the monopolist. This is exactly what the Lerner Index does.

## Formula

Lerner Index is essentially the firm’s markup over its marginal cost. If price is P and marginal cost is MC,

Lerner Index L is given by the following equation:

L = | P − MC |

P |

In perfect competition, since P and MC are equal, Lerner Index is 0. A pure monopolist, on the other hand, can theoretically charge an infinite markup which leads us to L value of 1.

## Lerner Index and Elasticity of Demand

The higher the price elasticity of demand of a firm’s product, the lower its Lerner Index. It is because a high elasticity of demand means that any increase in the price of the product will cause customers to switch to substitute goods. This reduces the monopolist’s ability to sell its products at a higher markup. There is an inverse relationship between Lerner Index and elasticity of demand as given by the equation below:

L = | -1 |

E_{d} |

## Example

Fill the blank spaces in the following table:

Industry | Price | Marginal Cost |
Elasticity of Demand |
Lerner Index |
---|---|---|---|---|

A | 10 | 0.4 | ||

B | 30 | -2 | ||

C | 40 | 30 |

**Industry A**

Since L = -1/E_{d} and E_{d} = -1/L; therefore, elasticity of demand for Industry A is -2.5. We can use the Lerner Index value to work out marginal cost (MC) of the firm as follows:

0.4 = | 10 − MC |

10 |

MC = 10 − 4 = 6

**Industry B**

From Ed value of -2, we find that Lerner Index is 0.5. If Price is $30 and L is 0.5, MC must be 15.

MC

= P − P × L

= 30 × 30 × 0.5

= 15

**Industry C**

At price of $40 and marginal cost (MC) of $30, Lerner Index is 0.25 [=($40−$30)÷$40] and E_{d} must be -4 [=-1÷0.25].

by Obaidullah Jan, ACA, CFA and last modified on