CHAPTER 10 • Market Power: Monopoly and Monopsony 363 A Rule of Thumb for Pricing We know that price and output should be chosen so that marginal revenue equals marginal cost, but how can the manager of a firm find the correct price and output level in practice? Most managers have only limited knowledge of the average and marginal revenue curves that their firms face Similarly, they might know the firm’s marginal cost only over a limited output range We therefore want to translate the condition that marginal revenue should equal marginal cost into a rule of thumb that can be more easily applied in practice To this, we first write the expression for marginal revenue: MR = ⌬(PQ) ⌬R = ⌬Q ⌬Q Note that the extra revenue from an incremental unit of quantity, ⌬ 1PQ2 > ⌬Q, has two components: Producing one extra unit and selling it at price P brings in revenue (1)(P) ϭ P But because the firm faces a downward-sloping demand curve, producing and selling this extra unit also results in a small drop in price ⌬P> ⌬Q which reduces the revenue from all units sold (i.e., a change in revenue Q[⌬P> ⌬Q]) Thus, MR = P + Q Q ⌬P ⌬P = P + Pa ba b ⌬Q P ⌬Q We obtained the expression on the right by taking the term Q 1⌬P> ⌬Q2 and multiplying and dividing it by P Recall that the elasticity of demand is defined as Ed = 1P>Q2 1⌬Q> ⌬P2 Thus 1Q>P2 1⌬P> ⌬Q2 is the reciprocal of the elasticity of demand, 1/Ed, measured at the profit-maximizing output, and MR = P + P(1/Ed) Now, because the firm’s objective is to maximize profit, we can set marginal revenue equal to marginal cost: P + P(1/Ed) = MC which can be rearranged to give us P - MC = P Ed (10.1) This relationship provides a rule of thumb for pricing The left-hand side, (P - MC)/P, is the markup over marginal cost as a percentage of price The relationship says that this markup should equal minus the inverse of the elasticity of demand.4 (This figure will be a positive number because the elasticity Remember that this markup equation applies at the point of a profit maximum If both the elasticity of demand and marginal cost vary considerably over the range of outputs under consideration, you may have to know the entire demand and marginal cost curves to determine the optimum output level On the other hand, you can use this equation to check whether a particular output level and price are optimal The elasticity of demand is discussed in §§2.4 and 4.3