ABC Firm in Industry Alpha has MC of production = $100 and they know from past experience that their Lerner index is 0

ABC Firm in Industry Alpha has MC of production = $100 and they know from past experience that their Lerner index is 0.3. XYZ firm in Industry Beta has MC of production = $35 and Lerner index is 0.55.

a. Determine optimal price both firms should be charging.

Lerner index is measured by the difference between the output price of a firm and its marginal cost divided by the output price. The formula is given by;

Let us begin by determining selling price of ABC Firm in Industry Alpha.

The firm has a Lerner index of;

And a marginal cost of production equal to;

Substituting L and MC into the Lerner index formula;

Multiplying both sides of the equation by P;

Collecting the like terms;

Dividing both sides of the equation by 0.7;

The optimal price for firm ABC Firm in Industry Alpha is

In the same way, let us determine the optimal price charged by XYZ firm in Industry Beta.

The firm has a Lerner index of;

And am marginal cost of production equal to;

Substituting the Lerner index and the marginal cost of production in the Lerner index formula;

Multiplying both sides of the equation by P;

Collecting the like terms;

Dividing both sides of the equation by 0.45;

The optimal price charged by XYZ firm in Industry Beta is

b. Which firm is likely to earn more profits in the long run? Explain why the connection between Lerner index and industry concentration made you reach this conclusion.

Firm XYZ in Industry Beta and firm ABC in Industry Alpha will earn equal profits in the long run.

The price-cost margin for firm ABC in Industry Alpha is;

The price-cost margin for firm XYZ in Industry Beta is;

Although the two firms have different Lerner indices, they have the same price-cost margins. This means that the firms will earn equal profits in the long-run. This implies that Lerner index is a measure of market power and not profitability.