WHAT IS LERNER INDEX

Abba P. Lerner, a Russian-British economist, formalized the term "Lerner index" in 1934.

The Lerner index is a measure of the market power possessed by a firm.

It is a measure of the percentage markup that a firm can charge above its marginal cost.

That is, it measures the difference between the price and marginal cost of a firm and then divides the result by the price received by the firm.

Mathematically, the Lerner index is represented as:

$$\text{Lerner index}=\frac{P-MC}{P}$$

Where P is the price of the good set by the firm and MC represents the marginal cost of the firm.

The Lerner index ranges from 0 to 1, with 0 being the lowest and 1 being the highest.

A perfectly competitive firm has a Lerner index of zero because the price it charges is equal to its marginal cost.

A monopolist charges a price greater than its marginal cost. As a result, a monopolist's Lerner index is greater than 0.

An oligopolist also charges a price greater than its marginal cost. Hence, its Lerner will be greater than one.

From the foregoing, we can conclude that a Lerner index of 0 indicates that the firm has no market power (as is the case with the perfectly competitive firm) and a Lerner index of 1 indicates that a firm has high market power.

It should be noted that the Lerner index must not exceed one.

The Lerner index is influenced by three major factors, namely; Price elasticity of demand, interaction with competition and the degree of regulation.

1. Price elasticity of demand: Generally, the less elastic the demand, the greater the value of the Lerner index.

2. Degree of regulation: The more actively a state pursues an anti-trust policy, the lower the value of the Lerner index.

3. Interaction with competition: The large the competition, the less the company's ability to maximize profits and the smaller the value of the Lerner index.

The Lerner Rule or Lerner Condition states that if a firm wants to maximize profits, it must set its price so that the Lerner Index equals -1 over the firm's elasticity of demand (which is not always the same as the market elasticity of demand).

That is,

$$\frac{P-MC}{P}=\frac{1}{-E_d}$$

One limitation of the Lerner Index is that while it is reasonably easy to obtain a firm's prices, measuring its marginal costs is extremely complex.

This is the reason why most times, the average cost is used as a rough estimate.

Perhaps the best way to understand the Lerner curve is with an example.

Example 1

Given that a firm receives €10 for every unit of a good sold and given that the firm marginal cost is €6. determine:

1. Lerner index

2. The elasticity of demand at the profit-maximizing point.

3. If the firm is perfectly competitive

Solution

1. As noted earlier, the Lerner index is simply

$$\text{Lerner index}=\frac{P-MC}{P}$$

Accordingly, 

$$\text{Lerner index}=\frac{10-6}{10}=0.4$$

2. Earlier, I told you that a Lerner condition, which can be expressed as:
$$\frac{P-MC}{P}=\frac{1}{-E_d}$$

From no 1, we know that the value of the right hand is 0.4, therefore,

$0.4=\frac{1}{-E_d}$

$-0.4E_d=1$

$E_d=\frac{1}{0.4}$

$E_d=-2.5$

3. The Lerner index is not equal to zero, hence, the firm is not perfectly competitive.
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