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.[1][page needed][2][page needed]

Derivation of the markup ruleEdit

Mathematically, the markup rule can be derived for a firm with price-setting power by maximizing the following expression for profit:

Q = quantity sold,
P(Q) = inverse demand function, and thereby the price at which Q can be sold given the existing demand
C(Q) = total cost of producing Q.
  = economic profit

Profit maximization means that the derivative of   with respect to Q is set equal to 0:

P'(Q) = the derivative of the inverse demand function.
C'(Q) = marginal cost–the derivative of total cost with respect to output.

This yields:


or "marginal revenue" = "marginal cost".

A firm with market power will set a price and production quantity such that marginal cost equals marginal revenue. A competitive firm's marginal revenue is the price it gets for its product, and so it will equate marginal cost to price.

By definition   is the reciprocal of the price elasticity of demand (or  ). 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 (where   and  ). 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 (because demand is inelastic at the starting point) and a decrease in costs (because output has decreased); thus the original point was not profit-maximizing.


  1. ^ Roger LeRoy Miller, Intermediate Microeconomics Theory Issues Applications, Third Edition, New York: McGraw-Hill, Inc, 1982.
  2. ^ Tirole, Jean, "The Theory of Industrial Organization", Cambridge, Massachusetts: The MIT Press, 1988.