Limit Price - Simple Example

Simple Example

In a simple case, suppose industry demand for good X at market price P is given by:

Suppose there are two potential producers of good X, Firm A, and Firm B. Firm A has no fixed costs and constant marginal cost equal to . Firm B also has no fixed costs, and has constant marginal cost equal to, where (so that Firm B's marginal cost is greater than Firm A's).

Suppose Firm A acts as a monopolist. The profit-maximizing monopoly price charged by Firm A is then:

Since Firm B will never sell below its marginal cost, as long as, Firm B will not enter the market when Firm A charges . That is, the market for good X is an effective monopoly if:

Suppose, on the contrary, that:

In this case, if Firm A charges, Firm B has an incentive to enter the market, since it can sell a positive quantity of good X at a price above its marginal cost, and therefore make positive profits. In order to prevent Firm B from having an incentive to enter the market, Firm A must set its price no greater than . To maximize its profits subject to this constraint, Firm A sets price (the limit price).