The Lerner index, formalized in 1934 by Abba Lerner, is a measure of a firm's market power. It is defined by: where P is the market price set by the firm and MC is the firm's marginal cost. The index ranges from 0 to 1. A perfectly competitive firm charges P = MC, L = 0; such a firm has no market power. An oligopolist or monopolist charges P > MC, so its index is L > 0, but the extent of its markup depends on the elasticity of demand and strategic interaction with competing firms. The index rises to 1 if the firm has MC = 0. The Lerner Rule or Lerner Condition is that if it is to maximize its profits, the firm must choose its price so that the Lerner Index equals -1 over the elasticity of demand facing the firm : A drawback of the Lerner Index is that while it is relatively easy to observe a firm's prices, it is quite difficult to measure its marginal costs. In practice, the average cost is often used as an approximation. The Lerner index can never be greater than one. As a result, if the firm is maximizing profit, the elasticity of demand facing it can never be less than one in magnitude. If it were, the firm could increase its profits by raising its price, because inelastic demand means that a price increase of 1% would reduce quantity by less than 1%, so revenue would rise, and since lower quantity means lower costs, profits would rise. Put another way, a monopolist never operates along the inelastic part of its demand curve.
Derivation
The Lerner Rule comes from the firm's profit maximization problem. A firm choosing quantity Q facing inverse demand curve P and incurring costs C has profit equalling revenue minus costs: Under suitable conditions and C, we can find the maximum by taking the derivative of profit with respect to Q and getting the first-order-condition: which gives the standard rule of MR = MC. To get the Lerner Rule, switch to the notation dC/dQ = MC and rewrite as Divide by P to get using the derivative definition of elasticity.
