Markup rule


A markup rule is the pricing practice of a producer with market power, where a firm charges a fixed mark-up over its marginal cost.

Derivation of the markup rule

Mathematically, the markup rule can be derived for a firm with price-setting power by maximizing the following expression for profit:
Profit maximization means that the derivative of with respect to Q is set equal to 0:
This yields:
or "marginal revenue" = "marginal cost".
By definition is the reciprocal of the price elasticity of demand. Hence
Letting be the reciprocal of the price elasticity of demand,
Thus a firm with market power chooses the output quantity at which the corresponding price satisfies this rule. Since for a price-setting firm this means that a firm with market power will charge a price above marginal cost and thus earn a monopoly rent. On the other hand, a competitive firm by definition faces a perfectly elastic demand; hence it has which means that it sets the quantity such that marginal cost equals the price.
The rule also implies that, absent menu costs, a firm with market power will never choose a point on the inelastic portion of its demand curve. Intuitively, this is because starting from such a point, a reduction in quantity and the associated increase in price along the demand curve would yield both an increase in revenues and a decrease in costs ; thus the original point was not profit-maximizing.