Chapter 6

Allowing Buyers to Self-Select By Willingness to Pay: Second-Degree Price Discrimination Strategies

Quantity Discounts

The obvious limitation of first-degree price discrimination is the level of consumer-specific information needed to extract the buyer’s consumer surplus. An alternative to first-degree price discrimination is second-degree price discrimination. Here, the firm has an awareness of the distribution of consumer preferences in aggregate and a sense that different market segments exist. The goal of second-degree price discrimination, therefore, is to design a pricing scheme that causes buyers to self-select based on their willingness to pay. In doing so, the firm is able to extract some, albeit probably not all, of the buyers’ consumer surplus.

One form of second-degree price discrimination is quantity discounts. This pricing practice implicitly recognizes the law of diminishing marginal utility. According to the law, each additional unit provides the consumer will less additional satisfaction. Therefore, the consumer’s willingness to pay decreases with each successive unit.

To illustrate, Disney World allows patrons to buy tickets to any of its four Florida theme parks at a price of $85. Suppose each visit provides less additional utility. Let us assume that Marsha’s willingness to pay for each park visit is indicated in Table 6.1. If Marsha’s demand schedule is typical, note that the revenue-maximizing price is $85. (We will assume all costs are fixed; this implies that the revenue-maximizing price is also the profit-maximizing price). At this price, Marsha will visit parks on two days, for revenues totaling $170. We can also calculate Marsha’s consumer surplus under the single-price strategy as equal to $35.

Marsha would not be willing to visit the park on the 3rd day because the value she places on the experience ($50) is less than the price ($85). But under the 2011 Disney pricing policy, Marsha can opt to visit parks on three days for a package price of $231.99, or an average of $77.33 per day. At first glance, one might conclude that this would not make a difference because the price of the third day still exceeds the value she places on the third day. But Disney is not charging $77.33 for each day; rather, it is offering a package of three days for a price of $231.99 (or an average of $77.33 per day). Is the package worthwhile? According to Table 6.2, Marsha values three days of park visits at $255, so the three-day package seems to be quite a good value. As a result, Marsha pays $231.99 instead of $170. With the three-day package, Marsha’s consumer surplus is $255 – $231.99, or $23.01.

Why did the package induce Marsha to go for an extra day? Under a single pricing strategy, Marsha weighs the value of each individual visit against its price. She values the first day at $120, but only has to pay $85. Hence, the $35 in consumer surplus is uncaptured by Disney. Disney captures the entire consumer surplus on the second day, but cannot entice her to spend a third day at the parks because the value she derives from a third day is less than the price. Although the package deal is promoted at an average price of $77.33/day, Table 6.2 shows the actual ramifications of the package deal.

The package deal effectively captures Marsha’s consumer surplus for the first two days. The remaining expenditure ($26.99) is less than the price of a ticket for the third day, so Marsha sees the overall value of the three-day package as worth the price.

Figures 6.1 and 6.2 illustrate the quantity discount graphically. Under the single-price strategy, the revenue-maximizing price is $85. Marsha attends Disney parks on two days, with uncaptured consumer surplus totaling $35. Under the three-day package, Disney captures the consumer surplus from the first two visits, generates additional revenue from a third visit, while leaving uncaptured consumer surplus equal to $23.01.

But if the three-day package generates more revenue than the single-price strategy, why does Disney offer both? Let’s create a slightly different demand schedule for Derek, another prospective visitor. Derek’s willingness to pay is the same as Marsha’s for every visit except the first. As indicated in Table 6.3, note that the revenue-maximizing price is still $85. Under the single-price strategy, Derek attends two parks, spends $170, with $5 in uncaptured consumer surplus. However, unlike Marsha, Derek’s valuation of three visits is only $225, which is not sufficient to induce him to buy the $231.99 three-day package.

This example illustrates the benefits from offering the three-day package and the single pricing strategy simultaneously. Second degree price discrimination does not require the firm to know each person’s demand schedule. Instead, it offers a pricing policy that allows consumers to self-select.

Frequent shopper programs are also a form of second-degree price discrimination. Here, the buyer gets credit for each purchase. Once the buyer accumulates sufficient credits, he gets his next order for free or for a significant discount.

Quality Choices

Another form of self-selection is to offer quality choices. In this case, the firm offers two different versions of the same product. The higher priced version offers a higher quality product than the lower priced version. However, the profit margin on the higher priced version is greater than that on the lower quality version. This allows buyers to naturally self-select based on price sensitivity. Presumably, the more price sensitive consumers will choose the lower priced, lower quality version whereas the less price sensitive buyers will opt for the higher price, higher quality version.

Perhaps the most obvious example of quality choice-based price discrimination is first-class versus coach seats on an airplane. The cost of the seats to the airlines is nearly identical; the only real cost difference is the higher quality food and drinks available to first-class ticket buyers. The seats offer more elbow room and first-class patrons have the privilege of boarding and deplaning before the coach passengers, but these are perquisites that cost nothing to the airline, aside from the obvious opportunity cost of using up space that could go toward a few more paying customers. Of course, the opportunity cost is hardly nominal. If four first-class seats in a row replace six coach seats that would otherwise have been occupied, the airline must be able to charge a price that is at least 1.5 times higher than the price of a coach seat to make the venture worthwhile. Yet first-class seats are often 4–5 times higher than the price of an economy seat, thereby far exceeding the actual cost of servicing a first-class passenger relative to other passengers.

Similarly, Quicken offers a number of different products, from Quicken Starter Edition to Quicken Deluxe to Quicken Premier to Quicken Home and Business. Although the latter is priced three times higher than the Starter edition, it is higher unlikely that the cost of the Home and Business product is three times higher than the cost of producing the Starter edition.

We will use a numerical example to show how this works. Suppose a software company had but one standard version for which the marginal cost of each unit was $10. Market demand is illustrated in Table 6.4.

As the table indicates, the firm’s profit contribution ($495) is maximized by charging a single price of $65.

Suppose instead of a single, standard version, the firm manufactures two versions: the Starter version and the Deluxe version. The marginal costs are similar: each unit of the Starter version can be manufactured for $9 and each unit of the Deluxe version can be produced at a cost of $11. Market demand for each version at each price is shown in Table 6.5. (Note that the quantities demanded at each price sum to the totals shown in Table 6.4).

As the table indicates, the profit-maximizing prices are $65 for the Deluxe version and $45 for the Starter version. By creating two versions, the firm’s profit contribution rises from $495 to $504. The underlying assumption is that consumers will self-select to the product that reflects their willingness to pay.

Figure 6.3 illustrates the strategy. Rather than to charge the profit-maximizing price for the standard version, the firm produces two versions and prices them in accordance with the buyers’ willingness to pay.

Bundling

Pricing Individually Versus Pure Bundling

Another strategy that bears resemblance to quantity discounts and quality choices is bundling. Bundling exists when the firm offers multiple products as a “bundle” that differs from the sum of the prices of the two products purchased individually.1 Bundling has become extremely popular in telecommunications. Customers may choose between mobile phone coverage, high-speed Internet service, and landline phone service, or some combination of the three at a price that is less than the sum of the individual prices.

The firm seeking to maximize profits can choose to either price its products individually, combine them into a bundle and offer only the bundle to customers (pure bundling), or offer the customers the choice of either the individual products or the bundle (mixed bundling). Our purpose is to determine which of these strategies is most profitable.

In the telecommunications industry, where bundling opportunities are widespread, the cost structure is heavily weighted toward fixed costs. Variable, or marginal costs, are minimal. Thus, to simplify the analysis, we will assume marginal costs are zero. If so, a firm that maximizes revenues will also maximize profits. We will later release this assumption. Suppose a telecommunications firm offers monthly mobile service, high-speed Internet, and landline phone service.

Assume we have three prospective customers: Archie, Byron, and Crystal. Table 6.6 shows their willingness to pay for each of the three products.

We will begin by assuming that the firm will price each product individually. According to the table, if mobile service is offered at a price of $100, only Archie will buy the service, generating $100 in revenue. If the firm charges $80 for mobile service, Archie and Byron will buy the service, which yields $160 in revenue. If the service is offered at a price of $70, all three consumers will purchase the service, which brings revenues totaling $210. Hence, the firm will charge $70 to maximize revenues.

The same analysis can be applied to the high-speed Internet and landline phone service (Table 6.7).

Pricing the three products individually will generate revenues equal to $350.

Suppose that instead of pricing the products individually, the firm offered only bundles. Table 6.6 shows that Archie would be willing to spend up to $220 for the bundle, Byron would be willing to spend $145, and Crystal would be willing to spend up to $100. Based on this information, Table 6.8 summarizes the firm’s revenue if the bundle were to be priced at $220, $145, or $100.

As the table illustrates, revenues would be maximized by charging $100 for the bundle. Notice that the profit-maximizing bundle price generates only $300, whereas the sum of the profits from charging the individual profit-maximizing prices is $350. Thus, the firm would be more profitable offering each product separately instead of the bundle.

If we look at Table 6.6, we will see why. As the table exhibits, Archie values all three services more than either Byron or Crystal. Likewise, Byron values all three services more than Crystal. Because the relative valuation of the products does not differ across prospective customers, the firm cannot price a bundle that is more profitable than pricing each product individually.

Let’s change the relative valuations between the three consumers and see how this affects the strategy. In Table 6.9, we changed the buyers’ willingness to pay such that Archie values mobile service the most, Byron values high-speed Internet more than either Archie or Crystal, and Crystal exhibits the greatest willingness to pay for landline service.

Because we used the same willingness to pay figures (but attributed them to different consumers), the revenue-maximizing prices for separate mobile, Internet, and landline services are still $70, $50, and $40, respectively, and generate revenues of $210, $100, and $40, respectively. Thus, by pricing each product separately, the firm can earn a maximum of $350.

According to the figures in Table 6.9, Archie would be willing to spend up to $150 for the bundle, Byron would be willing to spend $175 on the bundle, and Crystal would spend up to $140 to obtain the bundle. Table 6.10 illustrates the revenue ramifications associated with bundle prices of $175, $150, and $140. As the Table indicates, charging $140 will yield revenues totaling $420.

Notice that the bundle is now more profitable than the maximum profit earned from pricing the goods separately. When the relative valuations did not differ between consumers (i.e. Archie was willing to pay the most for all three products and Byron was willing to pay the second most for all three goods), bundling did not increase the firm’s revenue. However, when the relative valuation of the three goods differed between customers, bundling was a more profitable option than pricing each good separately.

Because a firm may potentially sell to many consumers, let’s find a way to generalize the implications. To allow for a two-dimensional graph, we will limit the choices to mobile service and high-speed Internet. Suppose we have the following list of prospective customers for the two goods. The maximum price that each of 20 consumers is willing to pay for the respective goods, including the bundle (called the reservation prices) is shown in Table 6.11.

If we sort the prices from high to low, we can determine the revenue-maximizing price for each good, as shown in Table 6.12. The table shows that the revenue-maximizing prices for mobile service and high-speed Internet are $50 and $45, respectively.

The scatterplot for the reservation prices appears in Figure 6.4. If we draw a line through the corresponding revenue-maximizing prices (the vertical line at $50 is the price of mobile service and the horizontal line at $45 is the price of Internet service), we can visualize the ramifications for pricing each good separately. If priced separately, consumers in quadrant I would buy only the high-speed Internet because their reservation price for high-speed Internet exceeds $45 whereas they would not be willing to pay $50 for mobile service. The opposite is true for consumers in quadrant IV. They would be willing to pay $50 or more for mobile service, but they would not be willing to pay $45 for high-speed Internet. Consumers whose reservation prices place them in quadrant II would buy both goods and persons in quadrant III would not purchase either product.

To see the implications for bundling, let’s rank the reservation prices from high to low and determine the profit-maximizing bundle price (Table 6.13). As the table indicates, the revenue-maximizing bundle price is $95.

If we reproduce Figure 6.4 and draw a line through every combination of products whose prices sum to $95, we can visualize every consumer who would be willing to buy the bundle (Figure 6.5). Specifically, every consumer to the right of the bundle line would purchase the bundle at a price of $95. This can be readily seen by glancing back at Table 6.11. According to the table, only two consumers (H and N) would not be willing to pay $95 for the bundle. These two individuals are represented graphically as the two points that appear to the left of the $95-line.

Figure 6.5 allows us to see the impact of bundling. When the goods are priced separately, consumers in quadrant II buy both products whereas consumers in quadrants I and IV only purchase one of the two goods. By offering a bundle at the revenue-maximizing price of $95, all consumers in quadrant II buy the bundle, but this generates no additional revenue for the firm because they would have bought both services for a total of $95 anyway.2

However, if each product was priced separately, consumers in quadrants I and IV would have only purchased one of the two goods. Notice that by offering the bundle, the firm can induce five of these consumers to buy the bundle. For quadrant I, the difference between $95 and their willingness to pay for high-speed Internet is the increased revenue for the firm. For customers in quadrant IV, the increased revenue is represented by the difference between $95 and their willingness to pay for mobile service.

We can refer to Table 6.11 to see numerical examples. Consumer C is willing to spend $70 for mobile service and $30 for high-speed Internet. Priced separately at $50 and $45, respectively, consumer C will only buy the mobile service. But C values mobile service and high-speed Internet collectively at $100. Therefore, C is willing to pay $95 for the bundle. The firm collects $95 from C instead of $70. Consumer E values mobile service and high-speed Internet at $40 and $55, respectively. This individual (who appears in quadrant I in Figure 6.5) would only purchase high-speed Internet if the products were sold separately. But the bundle is worth $95 to him. Therefore, by offering the bundle, consumer E spends $95 for both services instead of $55 for high-speed Internet only.

Let’s rearrange the reservation prices. This time, the same set of prices are rearranged (Table 6.14) such that consumer A is willing to pay the most for both mobile service and high-speed Internet, consumer B is willing to pay the second-most for each product, and so on. Without reproducing the arithmetic, the revenue-maximizing prices for high-speed Internet, mobile service, and the bundle are the same as in the previous exercise.

The scatterplot exhibiting the reservation prices and the revenue-maximizing product/bundle prices appear in Figure 6.6. Note that the reservation prices follow a pattern that is upward-sloping. Note also that every consumer lies in either quadrant II or quadrant III. Thus, by offering the bundle, the firm sells to all of the consumers who would have bought both products anyway, but cannot entice anyone to buy the bundle who would have only purchased one service otherwise. We can see this by examining Table 6.14. Consumers A through K (depicted in quadrant II in Figure 6.6) would be willing to buy each product separately because each has a willingness to pay for mobile service and high-speed Internet that exceeds $50 and $45. Therefore, the firm would collect $95 from each of these customers if the services were priced separately. The same individuals will buy the bundle for $95. Hence, the firm collects no additional revenue from these individuals.

If we examine consumers L through M (depicted in quadrant III in Figure 6.6), we can see that none of them would be willing to pay $95 for the bundle. Thus, bundling the services does not entice anyone to buy more services collectively than if the products were available individually. Figure 6.5 revealed that the bundle enticed some individuals (those in quadrants I and IV) who would have only purchased one of the services to buy the bundle. But Figure 6.6 reveals that there are no consumers in either of these quadrants.

Relating this to the “real-world” is easy. Suppose an individual is willing to spend up to $80 for mobile service, but no longer owns a landline. If a telecommunications firm offers mobile service for $75 and landline service for $30, the consumer will buy the mobile service because he places no value on landline service. Offer the bundle for a discounted price of $85 (less than the combined prices) without an opportunity to buy either one separately and the same consumer will not buy the bundle. By only offering the bundle, the firm loses $75.

Figures 6.5 and 6.6 help illustrate the ramifications for bundling. The lesser is the variation in relative valuations across prospective customers (i.e. the more highly correlated the rank order of preferences for each good), the lesser is the opportunity to gain by bundling. In contrast, the more negatively correlated the relative valuations across prospective customers (i.e. the person willing to pay the most for one good is willing to pay the least for the other good), the greater the potential gains from bundling.

Pure Bundling Versus Mixed Bundling

The previous analysis discussed the potential benefits of pricing a bundle rather than setting individual prices for each good. An alternative is to offer the consumer a choice of either the bundle or the individually priced goods (mixed bundle). Figure 6.5 shows the ramifications of mixed bundling. If only offered the bundle for $95, 13 consumers would make the purchase. Two consumers have bundle reservation prices below $95 (i.e. graphically, they lie to the left of the bundle line) and would not buy the bundle. However, one consumer values mobile service at a price of $50 and another values high-speed Internet at a price of $45. Thus, when offered the opportunity to either buy the bundle or an individual product, these two persons (consumers H and N from Table 6.14) would buy the mobile and Internet service, respectively, adding $95 to the firm’s total revenue.

Thus far, we relied on an analysis in which all costs were assumed to be fixed; hence, the price that maximized revenues also maximized profit contribution. Let’s return to the simple example of Archie, Byron, and Crystal to see the implications. Table 6.15 reproduces each person’s set of reservation prices.

Let’s assume the marginal cost of mobile service is $75, the marginal cost of high-speed Internet is $40, and the marginal cost of landline phone service is $10. The marginal costs were rigged such that at least one consumer has a reservation price that is below marginal cost. For example, Crystal is only willing to pay $70 for mobile service. Because the service carries a marginal cost of $75, the firm cannot fashion a price that would suit her. If we limit the choice of individual prices to the reservation prices that would generate a profit, we can see that the profit-maximizing mobile, Internet, and landline phone service prices are $100, $80, and $40, respectively, as shown in Table 6.16. At these prices, each consumer would buy exactly one product and the firm’s total profits would be equal to $95.

The marginal cost of a bundle is the sum of the individual marginal costs, or $125. Using the sum of each person’s reservation prices to indicate their willingness to pay for a bundle, we can see the price that will maximize profits.

As Table 6.17 indicates, the bundle is less profitable than pricing the goods individually. However, suppose the firm offers the consumers a choice of either the bundle or the individual goods. If the bundle is priced at $175, Byron will buy the bundle, Archie will purchase mobile service for $100, and Crystal will buy landline service for $40. Collectively, the mixed bundling strategy will generate profit contribution equal to $105.3

As we apply theory to the real world, which bundling option is likely to be most profitable? As we noted, if the reservation prices across consumers are positively correlated, bundling will not be more profitable than individual pricing. Often, however, firms offer products that have substitutable traits. An individual with a high reservation price for mobile service is unlikely to have an equally high reservation price for landline phone service, as one tends to substitute for the other. Moreover, often the available products cater to individual tastes. Cable/satellite companies tend not to offer a la carte programming because their customers have varying tastes. One prospective customer is likely to place a high value on sports-related programming whereas another will prefer channels that offer programs on home improvement. Moreover, because the time available for watching television is fixed, an individual with a high preference for some types of programming must have a relatively low preference for other programming. Thus, in most cases in which bundling may be considered, it is unlikely that reservation prices for individual products are positively correlated.

The best opportunities for bundling occur as the reservation prices become increasingly negatively correlated. The notion of a perfect inverse correlation (the consumer who values one good the most values the other good the least) would seem rather unlikely. However, to the extent that a negative correlation between reservation prices is more likely than a positive correlation, bundling can be the more profitable alternative. In general, mixed bundling is best when individual prospective customers have reservation prices that are less than the marginal cost of the good. Again, this would seem to be a very likely scenario for most firms.

There are ample examples of bundling beyond choosing between mobile service, cable, and landline phone service. Cable/satellite companies usually offer mixed bundling alternatives. DirecTV, for example, offers several bundles (Choice, Choice Extra, Choice Ultimate, and Choice Premier). In addition to the bundles, subscribers can add individual paid channels such as HBO or a sports package such as NFL Sunday Ticket. Auto manufacturers also offer mixed bundling or pure bundling packages. Many manufacturers allow for mixed bundling in which several models of a car are available in which the standard equipment increases with various price levels. In addition to the models, consumers can add options that suit their preferences. Other manufacturers offer pure bundling alternatives by packaging the options as standard equipment. Fast food restaurants offer mixed bundles. Diners can pick and choose between individual menu items or they can buy a bundle (i.e. burger, fries, and a drink) for a price that is less than the sum of the individual menu prices. Note that the bundled menu items offer larger portions than the individually priced items. Although McDonald’s offer small drinks and fries as individual menu items, the Extra Value Meals only offer medium or large drinks and fries.

Tying

Related to bundling is the concept of tying. Tying occurs when the seller requires the buyer to purchase a different product. The difference between bundling and tying is that, with the former, the consumer can obtain enjoyment through the purchase of only one good. For example, the buyer of mobile service can enjoy the benefits of a cell phone without purchasing landline service. In the case of tying, the consumer cannot obtain the benefits of the first good without the benefits of the second good.

Many tying requirements have been pronounced an illegal restraint of trade by the Supreme Court. The monopolist’s incentive to tie purchases together was established in the IBM v. United States court case. IBM required entities that leased their mainframe computers to also buy the paper cards used by the machines by IBM. Although IBM had no direct information on the lessee’s willingness to pay, it extracted consumer surplus indirectly by charging relatively high prices for its cards. Hence, the greater the willingness to pay (based on machine usage), the more the lessee paid.

Another example of illegal tying was block booking by movie studios. This practice required exhibitors to purchase a below-quality film they did not want in order to buy the movie they did want. The practice was deemed illegal twice: once in 1948 (United States v. Paramount Pictures, Inc.) and again in 1962 (United States v. Loew’s, Inc.).

Allegations of illegal tying were also made when Apple released the iPhone in 2007. The iPhone was sold through exclusive contracts with AT&T. The iPhone came with a special software lock that made it inoperable with any other carrier than AT&T. If the buyer wanted to use the iPhone with another carrier, the individual had to pay a $175 termination fee to unlock the software.

Legal tying can exist when manufacturers create a product that requires a manufacturer-specific complementary good. As an example, in 2011, Dell Computers offered its V515w printer at a price of $74.99. However, it requires model-specific color and black ink cartridge replacements that retail for $19.99 and $15.99, respectively. Consequently, the consumer will pay for the equivalent of a new printer after only two refills.

Similarly, the Gillette web site revealed that its Fusion Power razor could be purchased online from WalMart for $9.47. The Fusion Power requires its own product-specific razor blades. According to the WalMart website, an eight-pack of replacement blades cost $29.57, roughly three times as much as the razor itself. In Chapter 2, we noted the relationship between the price of one good and the demand for a complementary good. By lowering the price of one good, the demand for its complement increases.

The economic advantages of tying can be illustrated graphically. Suppose we have two types of computer printer users: one who prints extensively and one who prints occasionally. Figure 6.7 shows the ink cartridge demand schedules for the light user (DL) and the heavy user (DH). Assume the printer manufacturer is considering producing a printer that can use any generic ink cartridge that can be sold at the market price PG. Because the printer is worthless without ink cartridges, the highest price the firm can charge for a printer and still attract both customers is equal to the consumer surplus of the light user. Let’s take a moment to explain why this is true. At the inkjet price of PG, each buyer’s consumer surplus represents the uncaptured value from printing. The consumer surplus of the heavy user will necessarily be greater than that of the light user. If the price of a printer is less than the consumer surplus of the light user, both consumers will buy the printer, print the number of copies that corresponds to PG (which will be greater for the heavy user) and still have uncaptured consumer surplus. If the price of the printer exceeds the light user’s consumer surplus, the light user will not buy the printer at all because the price exceeds the surplus value that he places on printing. But even if the light user doesn’t buy the printer, the heavy user will purchase it as long as the printer price is less than his consumer surplus. Therefore, if the price of the printer exceeds the consumer surplus of the light user, all of the profits will come from the heavy user. If the price of the printer is set equal to the light user’s consumer surplus, both consumers will buy the printer and all of the light buyer’s consumer surplus will be captured.

If we assume that both users will purchase the manufacturer’s own ink cartridges as long as the price is competitive with the other generic producers, the firm’s total profit will be double the low-demand buyer’s consumer surplus (both the heavy and light user buy the printer) plus the profits from the ink cartridges (graphically, it is represented by the dark area between the generic price of ink cartridges and the total quantity of ink cartridges purchased by the heavy and light user at that price (QT).

Now let us change the printer to allow for tying. The implicit assumption is that the firm will be able to charge a higher price for the ink cartridges (PI) because they cannot be substituted by generic brands. Figure 6.8 shows the implications. Note that the higher price of ink cartridges reduces the consumer surplus of the light user. This implies that the firm will have to lower the price of the printer to entice both consumers to buy the printer.

Figure 6.9 allows one to see the net benefits from tying. The light shaded area shows the increased profit contribution from charging a higher price for the model-specific ink cartridges. The striped area shows the reduction in profit contribution because the higher priced ink cartridges give the user an incentive to reduce printer consumption. Note that the reduction in printer price is more than offset by the increased profit contribution from the model-specific ink cartridges. Therefore, as the figure illustrates, tying is more profitable as long as the light shaded area (the increased profits from the model-specific ink cartridges) exceed the striped area (the lost profits from deterring usage due to more expensive ink cartridges).

Two-Part Tariffs

A two-part tariff exists when the buyer is required to pay an upfront fee to purchase the product and subsequent fees for each unit consumed. As we will see, the analysis bears a great deal of similarity to tying. Consider, for example, a state fair. Typically, the patron pays an entrance fee, but must pay additional fees for each ride or concession. Examples of two-part tariffs abound. Country clubs charge membership fees while charging additional fee for each round of golf or use of the tennis courts. Professional sports franchises often require fans to purchase a personal seat license (often for thousands of dollars) for the right to purchase season tickets. Costco and Sam’s Club require patrons to pay a membership fee as a condition to shop at their stores. Cell phone services also employ two-part tariffs. Subscribers pay a monthly base fee, which allows a fixed number of minutes, text messages, etc., and then pay additional fees for each minute or text message over that allotment.

The theory underlying the two-part tariff is fairly simple. Suppose we have a large number of consumers with identical tastes. The law of diminishing marginal utility creates a downward-sloping demand curve, such as that which is illustrated in Figure 6.10. The figure depicts the profit-maximizing price and quantity and the level of consumer surplus. The entry fee is set equal to the level of consumer surplus. Note that because the entry fee is a sunk cost, and is equal to consumer surplus, it has no impact on the number of units purchased.

Of course, consumers are unlikely to have identical tastes. To expand theory to allow for differing tastes, assume we have two consumers: one with a high demand for the good and another with a low demand (similar to what we did with tying). This is depicted in Figure 6.11. Note that the consumer surplus for the high-demand buyer will be larger at any given price than that of the low-demand buyer. If the usage fee was set equal to marginal cost and the entry fee was equal to the consumer surplus of the high-demand buyer, the low-demand buyer would not pay the entry fee. On the other hand, if the entry fee was equal to the consumer surplus of the low-demand buyer, both the low- and the high-demand buyer would pay the entry fee. Hence, the entry fee revenues would be equal to twice the size of the low-demand buyer’s consumer surplus shown in Figure 6.11.

Figure 6.11 does not, however, depict the entry and usage fees that will maximize profits. By setting the usage price equal to marginal cost, the firm only profits from the entry fees. If the firm raises its price above marginal cost while keeping the entry fee the same, the low demand buyer will not purchase the entry fee (because its consumer surplus at the usage price is now less than the entry fee, as shown in Figure 6.12).

If the firm was to charge a usage fee equal to P1 and an entry fee equal to the consumer surplus of the low-demand buyer, the total profit would be twice the entry fee (paid by both consumers) and the shaded area between the price and marginal cost for all QT units consumed (the usage profit contribution from the high- and low-demand buyers).

The implications from the two-consumer illustration can be extrapolated to many consumers. From the decision-maker’s perspective, the notion that a firm has sufficient information to replicate the fees shown in Figure 6.12 is unrealistic. The figure does, however, illuminate the trade-offs inherent in two-part tariffs. First, as the entry fee becomes larger, the number of entrants decreases. This causes the firm to lose out on the usage profit contribution from each excluded patron. Raising the usage price increases the profit contribution from each patron, but it also necessitates lowering the entry fee to avoid losing customers.

To illustrate, consider a movie theater. The movie theater generates profits from two sources: ticket purchases and concessions sales. Therefore, the theater owner has to determine two sets of prices: one for ticket prices and another for concessions. In setting the corresponding prices, the owner knows that whereas all concessions customers will buy movie tickets, not all ticket buyers will purchase concessions. Moreover, no one buys a movie ticket simply to gain access to the concessions. From this perspective, it would make no sense to offer cheap concessions and high ticket prices. Instead, the owner has an incentive to hold ticket prices down to increase the number of prospective concessions customers, and then to raise concessions prices as a way to segment the buyers.

Implementing a two-part tariff does not come without costs. Prior to 1980, Disney theme parks offered a “passport” that included admission and a predetermined number of rides. Tickets for additional rides could be purchased at five different price tiers; the more popular the ride, the higher the price. Because the cost of administering the system was relatively high, the two-part tariff was discarded in favor of the simpler single admission fee policy in 1980.

Intertemporal Price Discrimination

Intertemporal price discrimination is the practice of charging different prices at different points in time as a means of reaching different market segments. In marketing literature, it is associated with price skimming. The strategy is widely practiced in electronics. When a new gadget hits the marketplace, some consumers, anxious to be the “first guy on the block” to own one, are willing to pay a relatively high price for the good. Once this segment of the market has been saturated, the firm lowers the price to attract the more price sensitive customers.

Many years ago, the movie theater industry was composed of first- and second-run movie houses. The first-run movie houses featured the latest films at higher prices. Once the movies had made their run at the first-run theaters, they would disappear briefly and then reappear at the second-run movie houses at discount prices. Nowadays, the market segment served by second-run movie houses has largely been replaced by the movie rental market. Consumers who were unwilling to pay the first-run prices are able to download or rent the same films several months later at lower prices.

From a theoretical perspective, here is how intertemporal price discrimination works. The firm realizes that it has two market segments that vary by price sensitivity. The firm cannot identify the market segments directly, but can use price skimming to allow them to self-select. Figure 6.13 shows the two market segments: the demand curve on the left (DNow) is the less price sensitive group that is willing to pay a higher price to get the good soon after it becomes available. The demand curve on the right (DLater) is more price sensitive that is willing to defer buying the good until the price is right. To capitalize on the two segments, the firm sets the profit-maximizing price and quantity for the less price sensitive segment and then, at a later date, the firm lowers the price to attract the more price sensitive segment.

Although the timing of price decreases is rarely the subject of controversy, Apple drew the ire of its customer base when the iPhone was first introduced. The iPhone was released to much fanfare in September 2007. It was priced at $599. Only 69 days later, Apple dropped the price by $200. The early adopters were enraged by the rapid and significant price decrease, causing Apple CEO Steve Jobs to offer a $100 store credit to early adopters.

In addition to the risks of alienating the customer base by cutting prices too quickly, the firm has to consider the response of potential rivals. By setting its prices relatively high initially, the firm enjoys greater profits. However, in doing so, it invites competition to create a lower priced alternative. For this reason, some firms forego the skimming strategy in favor of a penetration pricing strategy. In this case, the firm enters the market with the price that seeks to maximize long-term profits. Here, the firm may even set a price that is below marginal cost and then raise it later on. The assumption is that the firm can reach a broad customer base immediately, and ideally, establish brand loyalty before rival firms enter the market.

Microsoft used a penetration strategy when it introduced its Windows Live OneCare antivirus package in 2006. With an average price below $30, the package vaulted to #2 in terms of market share in its debut month.4

The penetration strategy is illustrated in Figure 6.14. The firm hopes to penetrate the market quickly by its introductory price that is below marginal cost (PNow). By creating a customer base quickly, the firm hopes to instill brand loyalty, which will cause the demand for the firm’s good to increase in the future (DLater). After demand increases, the firm can increase the price to its long-run profit-maximizing level (PLater).

The penetration strategy works best when the firm is producing a good that is repurchased frequently. The assumption is that by establishing a sense of brand loyalty, the consumer will continue to purchase the product in the future. The strategy is most suitable when product demand is relatively elastic. The market should be large enough that the firm can effectively supply a large number of buyers at the introductory price. The strategy is particularly useful if significant economies of scale exist in production. Economies of scale occur when unit costs decrease over the long haul as production increases. Hence, by pricing low, unit sales are sufficiently large that the firm can profitably produce at a relatively low unit cost.

Firms should be wary of the possible consequences of the penetration strategy. Although the purpose is to attract buyers early on and establish brand loyalty, the plan could backfire if its only effect is to draw price sensitive buyers who will switch to another brand as soon as the price rises. This implies that firms choosing this strategy should work to develop product-specific attributes to keep their customers once they attract them.

Peak-Load Pricing

Peak-load pricing refers to the practice of setting different prices for “peak” and “off-peak” periods of demand. The purpose of peak-load pricing is to redistribute demand. Prior to the proliferation of cell phones, consumers may recall that the rates charged for long-distance phone calls were significantly cheaper after 11 PM. The telephone companies’ switching capacity (i.e. its ability to connect one caller to another) is fixed, but phone usage tends to be greatest during the day. Thus, the marginal cost of providing phone service is high during peak periods but is much lower during off-peak hours when much of the switching capacity goes unused. By charging a lower rate for off-peak usage, the phone company redistributes demand away from peak usage toward nonpeak usage.

Figure 6.15 provides a graphical illustration of peak-load pricing. The figure shows two levels of demand: peak demand (DP) and off-peak demand (DO). The upward-sloping marginal cost curve corresponds to the firm’s higher variable costs during peak usage. As opposed to setting a single profit-maximizing price, the firm sets two separate prices that correspond to peak (PP) and off-peak demand (PO).

Hotels and resorts deal with peak- and off-peak demand in a similar fashion. As with the telephone industry, capacity is fixed over the short-term and cannot be increased quickly. Therefore, if hotel rates never changed, the hotel may find itself turning away customers during periods of peak demand while exhibiting low occupancy rates during off-peak periods. An individual hoping to check into the Portofino Bay Hotel outside the Universal Studios resort during the week of Christmas would pay $404/night. Three weeks later, when children return to school and the resort is well into its off-peak period, the same room could be booked for only $279/night.5

London developed an innovative peak-load pricing system to deal with congestion in its central business district in 2003. Private vehicles in London’s central district between 7 AM and 6:30 PM on weekdays must pay an £8 congestion fee. A network of video cameras records the license plates of vehicles and imposes a fine of £80 to those who have not paid the congestion fee. Roughly 110,000 drivers per day pay the fee. After the fee was introduced, the percentage of private vehicle traffic flowing into the central district declined by 20%, or by 20,000 vehicles. As a result, congestion delays decreased by 30%, while bus ridership and subway usage increased by 14% and 1%, respectively.6

Summary

• Second degree price discrimination is the practice of offering pricing alternatives that cause buyers to self-select based on their willingness to pay.

• Quantity discounts exploit the law of diminishing marginal utility by creating a package that entices the consumer to buy more than he would have otherwise.

• Quality choices allow the buyer to self-select according to quality, as with the choice between first-class or coach seats on a plane.

• Bundling will be more profitable than pricing goods separately if the relative valuations of prospective consumers differ. Because consumer tastes tend to vary between goods (John is willing to pay more for mobile service than Mary, but Mary is willing to pay more for landline service than John), bundling will generally be more profitable than pricing goods separately.

• Mixed bundling, which refers to offering consumers the option of either the bundle or the individual goods, will be more profitable than pure bundling when some consumers’ willingness to pay is less than the unit cost of one of the goods. Requiring a consumer to buy a bundle when he has minimal interest in buying one of the goods may cause him not to buy at all.

• Tying can increase profits by enticing the consumer to buy one good at a relatively low price, and making up for it with a higher price margin on the complementary good. Examples include razors/razor blades and printers/ink cartridges.

• A two-part tariff involves an entry fee and a separate usage fee. An example would be a fair that charges an admission fee and separate prices for rides and concessions. Because the firm does not want to price the more price sensitive consumer out of paying for admission, two-part tariffs involve a trade-off between the admission fee and the usage fee. In general, the higher the usage fee, the lower the admission fee.

• Intertemporal price discrimination refers to charging different prices at different points in time. Price skimming refers to introducing a good at a relatively high price to attract consumers who want to be “the first one on the block” to own one. Once this market is tapped, the firm lowers the price to attract the more price sensitive buyer. In a penetration strategy, the firm starts with a low price to attract customers and build brand loyalty, only to raise the price later on. The benefit of the penetration strategy is that it makes it harder for competition to enter the market due to the low price. The potential disadvantage is that the low price will attract price sensitive buyers who will leave once the price rises.

• Peak load pricing is charging different prices to redistribute demand. It is useful if the alternative is to incur significant costs to meet demand during peak periods.