Many firms produce several different products, or at least several different models in their product lines. And, service firms frequently offer various lev- els or combinations of services: basic, premium, ultra, and so on. As you will recall from our discussion of economies of scope, many industries are com- posed primarily of multiproduct firms because cost-savings from multiproduct production can be substantial. We start this section by showing you how to make profit-maximizing pricing decisions if you are managing a firm that sells multiple products or services that are related in consumption—as either sub- stitutes or complements.8 As it turns out, you must incorporate the interrela- tions between the demand for each of the firm’s products and the prices of the rest of the firm’s products to find the profit-maximizing prices and quantities of multiple goods or services. Although this can be a computationally chal- lenging process, we will show you that the fundamental principle of setting marginal revenue equal to marginal cost continues to provide the key to mak- ing optimal pricing decisions. Then we will examine a very common pricing tactic that involves bundling two or more individual products or services as a
“package.” We will explain why bundling can increase profit and what kinds of products and services can be profitably bundled.
Now try T echnical Problems 7–8.
8In this section, we will examine multiproduct pricing for goods that are related in consumption.
However, goods may also be related in production. The rules making pricing decisions when goods are related in production are set forth in Online Topic 3: Pricing Multiple Products Related in Production.
Pricing Multiple Products Related in Consumption
Recall that the demand for a particular commodity depends not only on the price of the product itself but also on the prices of related commodities, incomes, tastes, and so on. For simplicity, we ignore the other factors and write one demand f unction as
QX = f (PX, PY)
where QX is the quantity demanded of commodity X, PX is the price of X, and PY is the price of a related commodity Y—either a substitute or complement.
In the discussion so far in the text, we have treated PY as if it were given to the firm. That is, we assumed PY to be a parameter determined outside the firm. Thus the firm would maximize its profits by selecting the appropriate level of produc- tion and price for X. If, however, the firm in question produces both commodities X and Y, the price of the related commodity Y is no longer beyond the control of the manager.
To maximize profit, the levels of output and prices for the related commodi- ties must be determined jointly. For a two-product firm, the profit-maximizing conditions remain the same
MRX = MCX and MRY = MCY
However, the marginal revenue of X will depend on the quantities sold of both X and Y, as will the marginal revenue of Y. The interdependence of the two marginal revenues, MRX and MRY, requires that the marginal conditions set forth earlier must be satisfied simultaneously. (Note that in this case the products are not related in production, so MCX and MCY depend only on, respectively, the output of X and the output of Y.) When products are used together, consumers typically buy them together, and these kinds of goods are complements in consumption. A different situation, substitutes in consumption, arises when a firm sells multiple products that are substitutes. Then buyers would purchase only one of the firm’s products.
In both cases, marginal revenues are interdependent.
Principle When a firm produces two products, X and Y, that are related in consumption either as sub- stitutes or complements, the manager of the multiple-product firm maximizes profit by producing and selling the amounts of X and Y for which
MRX = MCX and MRY = MCY
are simultaneously satisfied. The profit-maximizing prices, PX and PY, are determined by substituting the optimal levels of X and Y into the demand functions and solving for PX and PY.
To show how a manager would maximize profit under these circumstances, we will use another hypothetical example. In this example we will look at a firm that produces products that are substitutes in consumption, but exactly the same tech- nique applies for products that are complements in consumption.
Consider Zicon Manufacturing, a firm that produces two types of automobile vacuum cleaners. One, which we denote as product X, plugs into the cigarette
complements in consumption Products that are used together and purchased together.
substitutes in consumption
Products are substitutes and buyers purchase only one of the firm’s products.
I L L U S T R AT I O N 1 4 . 3 Computer Printers and Replacement
Cartridges: Pricing Multiple Products That Are Complements
When a firm sells two (or more) products that are related in consumption, as either substitutes or complements, the price of each good affects the de- mand for the other good. Therefore, a manager must account for this interdependence by choosing prices that result in equalization of marginal revenue and marginal cost for both goods simultaneously. While you may have found our discussion of this rule a bit tedious because of the messy algebra required to solve marginal conditions simultaneously, we want you to see that, messy or not, the rule can offer a manager a way to make sizable profits. Gillette, the manufacturer of razors and blades, understood this pricing relation and made a fortune nearly a half-cen- tury ago by setting a low price for razors to stimulate demand for its high-profit-margin blades.a Today, many multiproduct firms still can increase profits by making pricing decisions that account for product complementarities.
The Wall Street Journal recently reported that manu- facturers of computer printers are enjoying exceptional profitability despite dramatically falling prices for computer printers.b Managers at companies such as Hewlett-Packard, Seiko-Epson, and Canon have ex- ploited the multiproduct pricing rule for complements, discussed in this chapter, to make huge profits in the market for replacement printer cartridges—both inkjet cartridges and laser toner cartridges. Computer printers enjoy nearly the same popularity as personal comput- ers: More than 100 million of them are in use world- wide. In the Wall Street Journal article John B. Jones, Jr., an analyst at Salomon Brothers, estimated that H-P, which has about half of the entire printer market, earned an astonishing $3.4 billion worldwide on sales of ink-jet and laser replacement cartridges.
The strategy for making the replacement car- tridge market enormously profitable is a straightfor- ward application of some of the tools developed in managerial economics. First, because the two goods, printers and replacement cartridges, are comple- ments produced by the multiproduct firms, the
printer firms lower prices on the printers and raise prices on replacement cartridges. The Wall Street Journal reported that the profit margin on printers is just 30 percent while the profit margin on replacement cartridges is a whopping 70 percent. One H-P official, commenting on the firm’s pricing policy for replace- ment cartridges, was quoted as saying, “We just charge what the market will bear.” Of course this is true of any firm with market power, but H-P has clev- erly boosted “what the market will bear” by lowering prices of its printers, the complement good.
A second part of the strategy for exploiting profits in the printer–replacement cartridge business involves securing profits over the long run by slowing or block- ing entry of rivals into the replacement cartridge mar- ket. The large printer manufacturers now design their printer cartridges so that they are not simply plastic boxes with ink or toner in them. Purposely, engineers design the cartridges to include some or all of the printer-head technology required to make the printer work. In so doing, the printer cartridge can be covered by patents to prevent other companies from produc- ing “clone” replacement cartridges. Clearly, this sec- ond part of the strategy is just as important as the first part, at least if long-run profitability is the manager’s objective.
It is interesting to note that H-P, Canon, and Seiko- Epson are all suing Nu-Kote Holding, a Dallas sup- plier of generic replacement cartridges, for patent infringement. Nu-Kote, in turn, is suing the three manufacturers for allegedly colluding to keep replace- ment cartridge prices artificially high. It seems to us that Nu-Kote would be smart to spend its litigation resources winning the patent infringement case and let any alleged pricing conspiracy continue to prop up prices of its product.
aKing Gillette invented the disposable razor blade but did not make much profit selling it. He sold the patent and the name, and it was the new owner who devised the strategy of setting a low price for razors and a high price for the blades.
Using this now widely used pricing strategy, the new owner of Gillette was enormously successful.
bLee Gomez, “Industry Focus: Computer-Printer Price Drop Isn’t Starving Makers,” The Wall Street Journal, August 16, 1996.
lighter receptacle; the other, product Y, has rechargeable batteries. Assuming that there is no relation between the two products other than the apparent substitut- ability in consumption, the manager of Zicon wanted to determine the profit- maximizing levels of production and price for the two products.
Using the techniques described in Chapter 7, the demand functions for the two products were forecasted to be
QX = 80,000 − 8,000PX + 6,000PY and QY = 40,000 − 4,000PY + 4,000PX
Solving these two forecasted demand functions simultaneously for PX and PY, the manager obtained the following inverse demand functions in which each price is a function of both quantities9
PX = 70 − 0.0005QX − 0.00075QY and PY = 80 − 0.001QY − 0.0005QX
The total revenue functions for each product are
TRX = PXQX = 70QX − 0.0005 Q X 2 − 0.00075QYQX
and
TRY = PYQY = 80QY − 0.001 Q Y 2 − 0.0005QXQY
The (grand) total revenue from both products is obtained by adding the revenues from both products: TR = TRX + TRY. The associated marginal revenue functions for each product are10
MRX = 70 − 0.001QX − 0.00125QY and MRY = 80 − 0.002QY − 0.00125QX
The production manager obtained estimates of the total cost functions TCX = 7.5QX + 0.00025 Q X 2 and TCY = 11QY + 0.000125 Q 2 Y The marginal cost functions associated with these total costs are
MCX = 7.5 + 0.0005QX and MCY = 11 + 0.00025QY
9One way to solve these two equations simultaneously is to use the method of substitution. First, solve one demand function for PX in terms of QX and PY and the other demand function for PY in terms of QY and PX. Then substitute the equation for PY into the equation for PX, and vice versa. These two equations can then be solved for PX and PY in terms of QX and QY. The mathematical appendix at the end of this chapter shows how to use matrix algebra to find equations for linear inverse demand curves.
10As noted several times, the marginal revenue curve associated with a linear demand curve has the same intercept and is twice as steep as linear demand. In this case of interdependent demand curves, an additional term must be included in each marginal revenue function to reflect the effect of selling another unit of one good on the price of the other good. The intercepts for MRX and MRY are, respectively, (70 − 0.00075QY) and (80 − 0.0005QX). The additional terms reflecting the interdepen- dence of MRX and MRY are, respectively, −0.0005QY and −0.00075QX. Thus
MRX = (70 − 0.00075QY) − 2(0.0005)QX − 0.0005QY = 70 − 0.001QX − 0.00125QY
and
MRY = (80 − 0.005QX) − 2(0.001)QY − 0.00075QX = 80 − 0.002QY − 0.00125QX
The mathematical appendix at the end of this chapter provides the general algebraic solution for linear demands and marginal revenues for the case of two goods.
To determine the outputs of each product that will maximize profit, the manager of Zicon equated MR and MC for the two products
70 − 0.001QX − 0.00125QY = 7.5 + 0.0005QX
80 − 0.002QY − 0.00125QX = 11 + 0.00025QY
Solving these equations simultaneously for QX and QY (following the approach in footnote 8), the profit-maximizing outputs were found to be Q*X = 30,000 and Q*Y = 14,000. Using these outputs in the price functions, the manager of Zicon found that the profit-maximizing prices for X and Y were
P *X = 70 − 0.0005(30,000) − 0.00075(14,000) = $44.50 and
P Y* = 80 − 0.001(14,000) − 0.0005(30,000) = $51
The total revenue from selling the optimal amounts of X and Y was $2,049,000, which was the sum of TRX and TRY
TRX + TRY = $44.50(30,000) + $51(14,000) = $2,049,000
The total cost of producing the optimal amounts of X and Y was $628,500, which equals the sum of TCX and TCY
TCX + TCY = 7.5(30,000) + 0.00025(30,000)2 + 11(14,000) + 0.000125(14,000)2 = $628,500
The manager expected Zicon Manufacturing to earn profit of $1,420,500 (= $2,049,000 2 $628,500).
Bundling Multiple Products
One very common pricing practice employed by multiproduct firms involves bundling two or more products and selling the bundle of goods or services at a single price. For example, Disney World makes you buy one ticket for admission, which allows you to ride all of the rides, rather than separately selling individual tickets for each ride. Most computer manufacturers sell computer bundles that include the computer, some software, and a monitor. And, software companies offer “office suites,” which are bundles of office programs that might include word processing, spreadsheet, database, and presentation tools. Bundling is not always profitable, however. Recently, some airlines decided to “unbundle” their flight and baggage services, charging separate fees for baggage service.
When a multiproduct firm only allows consumers to purchase their different products in a bundle, the practice is called, more precisely, pure bundling. Frequently, however, multiproduct firms offer several products in both a bundle and separately, a practice known as mixed bundling. With mixed bundling, then, consumers get to buy
Now try T echnical Problem 9.
bundling
Selling a bundle of two or more products at a single price.
the bundle or instead purchase one or more of the products separately.11 Both types of bundling can increase profit by capturing consumer surplus in a fashion similar to price discrimination. As it turns out, when price discrimination is possible, charging different prices to different buyers can generate even greater profit than bundling.
However, price discrimination is not always possible, as we explained earlier in this chapter. Bundling, then, provides a way to capture greater consumer surplus when it is not possible to identify and separate consumers with high and low levels of willing- ness to pay and charge them different prices. For bundling to increase profit, certain conditions on demand must be met. We will explain these conditions shortly.
To illustrate the benefits of product bundling, let’s consider an example: Crystal Channel Inc. is the local monopoly provider of digital cable television for a small community. Marketing analysis of the community served by Crystal Channel reveals two types of cable television viewers: family-oriented viewers and adult-oriented viewers. The family-oriented viewers are primarily interested in cable TV channels providing G- and PG-rated movies, educational programming, and some sports cov- erage, and also occasionally enjoy viewing some adult-oriented channels. The adult- oriented viewers are primarily interested in channels showing “films” with mature plots, news analysis programs, and comprehensive sports coverage, and also occa- sionally enjoy watching some family-oriented channels. The market study estimates there are 2,000 family-oriented viewers and 2,000 adult-oriented viewers in the lo- cal market for cable television. Unfortunately for Crystal Channel, the market study offers no means of identifying the type of viewer, which would then make price discrimination possible. (Note: You will see in Technical Problem 10 that when it is possible to identify and separate family- and adult-viewer types, price discrimina- tion can generate more profit than bundling the family and adult channel packages.) To keep things as simple as possible, let’s suppose Crystal Channel’s total variable costs are zero, so that all of its costs are fixed costs. Consequently, the manager of Crystal Channel maximizes economic profit by maximizing total revenue.
Table 14.1 shows demand prices for each type of viewer. As you can see from the table, family-oriented viewers are willing to pay at most $100 per month for the fam- ily package of channels and at most $50 per month for the adult package of channels.
Thus, for family-oriented viewers, the demand price for a bundle of both packages is equal to the sum of the two demand prices, $150 (= $100 + $50) per month.12
11In this text, we will limit our analysis of bundling to the case of pure bundling, because analysis of mixed bundling is a bit more complicated and would take more space than we wish to allocate to bundle pricing. You can find a complete treatment of pure and mixed bundling in Lynne Pepall, Daniel J. Richards, and George Norman, Industrial Organization: Contemporary Theory and Practice, third edition, Thomson/South-Western, 2005.
12We are assuming that the willingness to pay for family and adult packages are independent, which means the maximum willingness to pay for a bundle is computed by adding the two demand prices. When family and adult packages are either complements or substitutes for a viewer, then the demand price for the family and adult bundle will be, respectively, greater or less than the sum of the two demand prices. For example, if the two packages “overlap” or contain some of the same chan- nels, then the demand price for the bundle of both packages would, of course, be less than the sum of the two demand prices for the family and adult packages.
Adult-oriented subscribers are willing to pay at most $100 per month for the adult package of channels and at most $25 per month for the family package of channels.
For adult-oriented subscribers, then, the demand price for a bundle of both packages is $125 (= $100 + $25) per month.
In order to increase profit through bundling multiple goods or services, the individual demands for the goods or services must satisfy two requirements.
First, different consumer types must possess differing tastes for the multiple products, which has the effect of creating different demand prices across con- sumers for each of the multiple goods. You can see from Table 14.1 that family- oriented viewers and adult-oriented viewers do indeed possess different demand prices for family and adult channel packages. Second, the demand prices for the two products or services must be negatively (or oppositely) corre- lated with consumer types. In this example, the consumer type that most highly values one package must place the lowest value on the other package. In Table 14.1, you can see the required negative correlation between demand price and viewer type: Family-oriented viewers hold the highest demand price for the family package of channels ($100) and the lowest demand price for the adult package of channels ($50). Adult-oriented viewers hold the lowest demand price for the family package of channels ($25) and the highest demand price for the adult package of channels ($100).
The reason these two demand conditions make bundling profitable—when price discrimination cannot be implemented—is best explained by viewing bun- dling as a means of capturing consumer surplus. Recall from our discussion at the beginning of this chapter that the closer you can set the price of a good or service to its demand price, the greater will be the amount of consumer surplus that you can capture or transform into profit. When consumer tastes differ, de- mand prices will differ for the multiple goods. Bundling goods together reduces the (proportionate) variability in demand prices across buyers, and, in so do- ing, makes it possible to set price closer to the bundle’s demand price for every consumer, thereby capturing more consumer surplus than separate prices can capture. As you can see in Table 14.1, it is not possible to set one price for either the family package or the adult package that will capture all consumer surplus because demand prices differ across consumer types. For the family package, the difference in demand prices is $75 (= $100 − $25), and for the adult package, the difference is $50 (= $100 − $50). Notice, however, that when the two packages are bundled, the difference in demand prices is reduced to just $25 (= $150 −
$125). By simple arithmetic, bundling reduces the difference or variability in de-
Number of
viewer type Type of viewer Family package
only Adult package
only Family and
adult bundle 2,000
2,000
Family-oriented Adult-oriented
$100 25
$ 50 100
$150 125 T A B L E 14.1
Demand Prices for Family and Adult Channel Packages (Monthly Subscription Fees)