This chapter examines a number of popular pricing practices. It becomes apparent that, when studied in detail, the methods commonly employed by successful firms reflect a careful appreciation of the use of marginal analysis to derive profit-maximizing prices.

• Many firms derive an optimal pricing policy using a technique called markup pricing, whereby prices are set to cover all direct costs plus a percentage markup for profit contribution. Flexible markup pricing practices that reflect differences in marginal costs and demand elasticities constitute an efficient method for ensuring that MR = MC.

• Markup on cost is the profit margin for an individual product or product line expressed as a percentage of unit cost. The numerator of this expression, called the profit margin, is the difference between price and cost. Markup on price is the profit margin for an individual product or product line expressed as a percentage of price, rather than unit cost.

• During peak periods, facilities are fully utilized. A firm has excess capacity during off-peak periods. Successful firms that employ markup pricing typically base prices on fully allocated costs under normal conditions but offer price discounts or accept lower margins during off-peak periods when substantial excess capacity is available.

• The optimal markup-on-cost formula is OMC* = -1/(eP + 1). The optimal markup-on-price formula is OMP* = -1/eP. Either formula can be used to derive profit-maximizing prices solely on the basis of marginal cost and price elasticity of demand information.

• Price discrimination occurs whenever different market segments are charged different price markups for the same product. A market segment is a division or fragment of the overall market with essentially different or unique demand or cost characteristics. Price discrimination is evident whenever identical customers are charged different prices, or when price differences are not proportional to cost differences. Through price discrimination, sellers are able to increase profits by appropriating the consumers' surplus. Consumers' surplus (or customers' surplus) is the value of purchased goods and services above and beyond the amount paid to sellers.

• The extent to which a firm can engage in price discrimination is classified into three major categories. Under first-degree price discrimination, the firm extracts the maximum amount each customer is willing to pay for its products. Each unit is priced separately at the price indicated along each product demand curve. Second-degree price discrimination involves setting prices on the basis of the quantity purchased. Quantity discounts that lead to lower markups for large versus small customers are a common means for second-degree price discrimination. The most commonly observed form of price discrimination, third-degree price discrimination, results when a firm separates its customers into several classes and sets a different price for each customer class.

• Multiple-unit pricing strategies have also proved an effective means for extracting consumers' surplus for the benefit of producers. In general, a firm can enhance profits by using two-part pricing comprised of a per-unit fee equal to marginal cost, plus a fixed fee equal to the amount of consumers' surplus generated at that per-unit fee. If you have ever purchased a 12-pack of soft drinks, a year's supply of tax preparation services, or bought a "two-for-the-price-of-one" special, you have firsthand experience with the bundle pricing concept. As in the case of two-part pricing, the optimal level of output is determined by setting price equal to marginal cost and solving for quantity. Then, the optimal bundle price is a single lump sum amount equal to the total area under the demand curve at that point.

• A by-product is any output that is customarily produced as a direct result of an increase in the production of some other output. Profit maximization requires that marginal revenue be set equal to marginal cost for each by-product. Although the marginal costs of by-products produced in variable proportions can be determined, it is impossible to do so for by-products produced in fixed proportions. Common costs, or expenses that are necessary for manufacture of a joint product, cannot be allocated on any economically sound basis. • A vertical relation is one where the output of one division or company is the input to another. Vertical integration occurs when a single company controls various links in the production chain from basic inputs to final output. Transfer pricing deals with the problem of pricing intermediate products transferred among divisions of vertically integrated firms. When transferred products cannot be sold in competitive external markets, the marginal cost of the transferring division is the optimal transfer price. When transferred products can be sold in perfectly competitive external markets, the external market price is the optimal transfer price. When transferred products can be sold in imperfectly competitive external markets, the optimal transfer price equates the marginal cost of the transferring division to the marginal revenue derived from the combined internal and external markets.

Throughout the chapter, it has been shown that efficient pricing practices require a careful analysis of marginal revenues and marginal costs for each relevant product or product line. Rule-of-thumb pricing practices employed by successful firms can be reconciled with profit-maximizing behavior when the costs and benefits of pricing information are properly understood. These practices add tremendous value to the managerial decision-making process.

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