Markup rule

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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[edit]

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".

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 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.

References[edit]

  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.