Profit Maximization - Markup Pricing

Markup Pricing

In addition to using methods to determine a firm's optimal level of output, a firm that is not perfectly competitive can equivalently set price to maximize profit (since setting price along a given demand curve involves picking a preferred point on that curve, which is equivalent to picking a preferred quantity to produce and sell). The profit maximization conditions can be expressed in a "more easily applicable" form or rule of thumb than the above perspectives use. The first step is to rewrite the expression for marginal revenue as MR = ∆TR/∆Q =(P∆Q+Q∆P)/∆Q=P+Q∆P/∆Q, where P and Q refer to the midpoints between the old and new values of price and quantity respectively. The marginal revenue from an "incremental unit of quantity" has two parts: first, the revenue the firm gains from selling the additional units or P∆Q. The additional units are called the marginal units. Producing one extra unit and selling it at price P brings in revenue of P. Moreover, one must consider "the revenue the firm loses on the units it could have sold at the higher price"—that is, if the price of all units had not been pulled down by the effort to sell more units. These units that have lost revenue are called the infra-marginal units. That is, selling the extra unit results in a small drop in price which reduces the revenue for all units sold by the amount Q(∆P/∆Q). Thus MR = P + Q(∆P/∆Q) = P +P (Q/P)((∆P/∆Q) = P + P/(PED), where PED is the price elasticity of demand characterizing the demand curve of the firms' customers, which is negative. Then setting MC = MR gives MC = P + P/PED so (P - MC)/P = - 1/PED and P = MC/. Thus the optimal markup rule is:

(P - MC)/P = 1/ (- PED)

or

P = ×MC.

In words, the rule is that the size of the markup is inversely related to the price elasticity of demand for the good.

The optimal markup rule also implies that a non-competitive firm will produce on the elastic region of its market demand curve. Marginal cost is positive. The term PED/(1+PED) would be positive so P>0 only if PED is between -1 and -∝ —that is, if demand is elastic at that level of output. The intuition behind this result is that, if demand is inelastic at some value Q₁ then a decrease in Q would increase P more than proportionately, thereby increasing revenue PQ; since lower Q would also lead to lower total cost, profit would go up due to the combination of increased revenue and decreased cost. Thus Q₁ does not give the highest possible profit.