Markup rule
A markup rule refers to the pricing practice of a producer with market power, where a firm charges a fixed mark up over its marginal cost.[1][2]
Derivation of the markup rule
Mathematically, the markup rule can be derived for a firm with price-setting power by maximizing the following equation for "Economic Profit":
- where
- 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 (Economic) Cost of producing Q.
- = Economic Profit
Profit maximization means that the derivative of with respect to Q is set equal to 0. Profit of a firm is given by total revenue (price times quantity sold) minus total cost:
- where
- Q = quantity sold,
- P'(Q) = the partial derivative of the inverse demand function.
- C'(Q) = Marginal Cost, or the partial derivative of Total Cost with respect to output.
This yields:
or "Marginal Revenue" = "Marginal Cost".
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 quantity at which the demand 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 believes which means that it sets price equal to marginal cost.
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.