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,

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**

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

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,

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

$-0.4E_d=1$

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

$E_d=-2.5$

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