If You Could Read My Mind: First-Degree Price Discrimination Strategies
Readers are probably a step or two ahead of me. Why, one may ask, does Wendy have to charge all four clients the same price? Can’t she negotiate prices with each client individually? Indeed, she probably can. If she does, Wendy is engaging in price discrimination. Price discrimination is the practice of charging different prices to different customers. Before we elaborate, let’s first identify what would not constitute price discrimination. In our simplified example, we assumed the cost of each job was identical. In the context of interior design, this isn’t a very realistic assumption. Some clients will want more elaborate design jobs than others. Consequently, one can reasonably expect that the price Wendy charges each client will be based on the cost of the job. This would not constitute price discrimination because the price variations across customers are based on cost differences across customers. Price discrimination exists when the price differences are unrelated to cost differences; that the firm charges different prices to different customers because of differences in their willingness to pay. In essence, price discrimination is based on what we saw in Figure 4.1: that under a single price strategy, some consumers are willing to pay more than the profit-maximizing price. Hence, these customers walk away with consumer surplus that the firm cannot capture with a single price. Price discrimination is an attempt to capture some or the entire consumer surplus.
The most extreme form of price discrimination is first-degree price discrimination (sometimes called perfect price discrimination). Under first-degree price discrimination, each unit is sold for the highest price the market will bear. We can examine first-degree price discrimination by looking at the numbers in Table 5.1. We already determined that one of Wendy’s clients would have been willing to pay as much as $1,300 for the job, a second would have been willing to pay $1,200, a third would have been willing to pay as much as $1,100 for the work, and a fourth was willing to pay no more than $1,000. Quite obviously, then, rather than to charge each client $1,000, she should negotiate with each buyer individually and extract the highest price each person is willing to pay. Instead of bringing in $4,000 in revenue, Wendy would collect $4,600, and her profits would rise from $300 to $600.
Table 5.1. First-Degree Price Discrimination
In fact, using a first-degree price discrimination strategy, Wendy’s profits would increase by much more than $600. To illustrate, let’s go back to the single-price strategy exhibited earlier. Recall that Wendy opted to charge a price of $1,000 and take on no more than four jobs. Why did she decide against the fifth job? Because, as Table 4.1 indicated, the marginal cost of the fifth job ($550) exceeded the marginal revenue ($500). If she decided to go with the fifth job, her profit contribution would decrease by $50. But is this still the case?
Let’s go back to Table 4.1 and re-examine the marginal revenue from the fifth job. Recall that the marginal revenue was composed of the output effect and the price effect. The output effect consisted of the revenue generated by that specific job. In this instance, the job could be performed at a price of $900. The price effect refers to the foregone revenue from the other four jobs owing to the price cut. If Wendy took on four jobs, the price charged to each of the four clients would have been $1,000. By taking on five jobs, the price charged to those clients falls to $900. Therefore, the price effect is –$100 times four jobs, or –$400. By taking on five jobs instead of four, Wendy’s revenue increases by $500 (the sum of the output and price effects), which is not sufficient to cover the marginal cost of $550.
But note how this changes with first-degree price discrimination. Because Wendy negotiates with each client individually, she can lower the price to $900 for the fifth client without reducing it for the other four clients. In other words, with first-degree price discrimination, there is no price effect. Put another way, with first-degree price discrimination, the marginal revenue of each job is equal to the price charged for that job. Therefore, Wendy will be willing to take on the job if the price is sufficient to cover the cost of the job.
Let’s re-produce Wendy’s demand schedule and make the necessary adjustments to show the full ramifications of first-degree price discrimination. Recall that with the single-price strategy, Wendy took on four jobs, charged a price of $1,000, earned a profit of $300, but was unable to capture consumer surplus totaling $600.
With first-degree price discrimination, Wendy will take on every job for which the price is sufficient to cover its cost. As the table indicates, all six jobs carry price tags that exceed the cost of the work. Consequently, Wendy will opt to do all six jobs and increase her profits from 300 to $1,500. In fact, because the table is truncated at six jobs, Wendy could probably increase her profits well beyond $1,500. In effect, she will take on every job that she can price above $550.
Let’s compare Tables 4.1 and 5.1 to see why Wendy is willing to take on more jobs with first-degree price discrimination. Under a single-price strategy, she was not willing to perform the fifth job because the marginal revenue ($500) was less than the marginal cost of the job ($550). Note, however, that the fifth job, in and of itself, could have been performed at a profit. The cost of the job is $550 and the client was willing to pay her $900 for the work. The only reason Wendy declined to perform it was due to the price effect; despite the fact that the job could have turned a profit, she wasn’t willing to take it on if it was going to require her to drop her price from 1,000 to $900 for the other four clients.
Notice how this changes under first-degree price discrimination. Because there is no price effect, Wendy is not concerned that by dropping her price for the fifth client, she will have to lower her price for the other four. As long as that job can be priced at a profit, the job is worth accepting.
Beyond leading to a greater number of jobs and increased profits, one can see the effect of price discrimination on consumer surplus. Under a single-price strategy, $600 worth of consumer surplus went uncaptured. With first-degree price discrimination, each customer pays the highest price that he is willing to bear; consequently, consumer surplus is equal to zero. No consumer surplus goes uncaptured.
Figure 5.1 illustrates the effects of first-degree price discrimination graphically. Since there is no price effect, the marginal revenue is the same as the price of the good. Therefore, unlike with the single-price strategy, there is no marginal revenue curve that lies below the demand curve. Rather, the marginal revenue curve and the demand curve are one and the same.
Figure 5.1. Graphical representation of first-degree price discrimination.
Notice that in Figure 5.1, the marginal revenue of all six units exceeds their marginal cost. This is because each of the six units can be sold at a profit. Wendy would be willing to take on all six jobs, and more: Q* represents the profit-maximizing quantity. Note also that because each consumer is charged the highest price he is willing to pay, there is no consumer surplus. Instead, the entire area that lies between the demand curve and the marginal cost curve constitutes her profit contribution, shown as the shaded area in the more generic graph in Figure 5.2.
Figure 5.2. First-degree price discrimination and the profit-maximizing output.
Figure 5.3 shows a generic graph that contrasts first-degree price discrimination with the single price strategy. As the figure indicates, the profit-maximizing output is greater with first-degree price discrimination (QPD) than under the single price strategy (QSP). The dark shaded area represents consumer surplus that is not captured under the single price strategy, but is transferred to the firm with first-degree price discrimination. And whereas the lined area represents the profit contribution using the single price strategy, the profit contribution with first-degree price discrimination is the sum of the shaded, striped, and dotted areas.
Figure 5.3. Comparing the single-price strategy and first-degree price discrimination.
Now that we’ve examined first-degree price discrimination from a theoretical perspective, let’s translate it into practical application. Note my choice of examples: an interior designer. I used this example for several reasons. First, Wendy gets to decide how many jobs she wants to perform. In contrast, most manufacturers make production decisions in lot sizes or batches. Few can make production decisions one unit at a time.1 Second, Wendy is in a position to negotiate the price of each job individually with her clients if she wishes to do so. In a standard production environment, each unit that appears on the shelf of the retailer will carry the same price tag, although prices may vary somewhat across retailers. Third, Wendy is likely to have at least some semblance of market power. The tastes and skills are likely to vary across interior designers. If clients are “brand loyal” to Wendy, she need not have to match the price offered by her competitors. She does, however, have to be cognizant of the prices charged by the competition. If she asks too much, even the most loyal of customers might go elsewhere. The demand curve used in the exercise was based on the assumption that the clients’ willingness to pay Wendy factored in the degree of substitutability across designers and the prices charged by the others.
We often see attempts at first-degree price discrimination practiced at car dealerships. Although each car has a sticker price, most buyers are aware than they can bargain with the salesperson for a better price. Because the salesperson receives a commission on the sale of a car, he attempts to gauge each buyer’s willingness to pay. The more the buyer gushes over how much he loves the car, the better the price the salesperson is likely to extract. If the prospective buyer demonstrates knowledge of the invoice price, the availability of similar cars in the region, and most importantly, the degree to which he considers vehicles at other dealerships to be an adequate substitute for this model at this particular dealership, the better the price the consumer is likely to get. In any event, a dealer may sell ten identical models to ten different customers at ten different prices.
The University of Alabama athletic department implements a unique form of first-degree price discrimination. A common practice among college athletic departments is to offer special perks, such as priority seating or personalized parking, for persons who donate to the department. Typically, the perks associated with specific donation amounts are publicized in a brochure or web site. But Alabama’s Tide Totals program ups the ante. Donors receive points based on various categories associated with dollar donations and the longevity of such donations. Each year, the donors are ranked in points from highest to lowest, with the priorities in divvying out perks based on points. So how much must one donate to assure one’s self first dibs for a ticket to a major bowl game involving the Crimson Tide? Answer: more than anyone else. By substituting a point system for perks tied to fixed dollar donations, the athletic department pits fan against fan, competing for the top priorities. In doing so, the department is able to recoup quite a bit of consumer surplus. In fact, according to its website, the Crimson Tide athletic department attracted more than $20 million in donations when it first instituted the program in 2006.2
Private colleges also engage in first-degree price discrimination. The posted tuition and fees are the equivalent of a sticker price on a new car. The high price is used to signal a higher quality product. Financial aid budgets to determine “merit-based aid” are, in fact, student-specific price discounts based on the applicant’s inferred willingness to pay. An estimated 60% of private colleges and universities use statistical formulas to determine financial aid offers.3 Some schools “strongly recommend” a campus visit, use the visits to infer interest and commitment, and then extend less generous aid offers to those students. Many private colleges offer an “early admission” program. The application is fast-tracked through the admissions process with the proviso that the student will not choose another school if admitted. This effectively eliminates price competition and can result in lower financial aid offers. Some schools even determine aid based on the student’s planned major. A student at Johns Hopkins University learned that he would have received a more generous aid offer if he had indicated a desire to major in the humanities rather than premed.4 In most cases, prospective students can appeal the financial aid offer, but this is rarely advertised up front. Applicants who claim to have received better offers elsewhere are usually requested to fax the proof before the appeal is heard.
The airline industry has turned first-degree price discrimination into a near art form. Until 1978, airfares were regulated by the Civil Aeronautics Board (CAB). The fare for a given route was set by the CAB. After the Airline De-Regulation Act passed in 1978, the airlines were free to set their own prices, and quickly recognized the benefits of first-degree price discrimination. By and large, the costs associated with a given flight are fixed. The cost for fuel and flight staff are the same regardless of how many passengers are on the plane. The variable cost associated with the number of passengers is negligible (i.e. the cost of a soft drink, napkin, small package of pretzels, etc.). Under a single-price strategy, the airline had to determine the one price that would maximize profits. If the plane had 125 seats, it might be worthwhile to sell tickets to 75 customers if lowering the price to fill the plane caused overall profits to fall (i.e. if the price effect resulting from lowering the price on the first 75 seats exceeded the output effect of selling 50 additional tickets). But airline de-regulation eliminated any legal restriction on ticket prices. If the airline had sold 124 tickets, it could lower its price to sell the remaining ticket without having to lower the price for the remainder of the passengers. Once the plane took off, an empty seat represented foregone profit. In 1998, the New York Times reported that 27 different fares were charged to 33 customers on the same plane flying from Chicago to Los Angeles. The prices ranged from a low of $87.21 to a high of $1,248.51.5
In a New York Times Magazine article, Laurence Zuckerman explained how the airlines accomplished such a feat, more commonly referred to as yield management. Armed with sophisticated statistical software, computers review historical bookings, cancellations, and fares to determine how many tickets to release for sale, and at what price. Zuckerman broke yield management for an American Airlines flight from Phoenix to Dallas-Fort Worth into the following stages:
1. Six months prior to departure: The computer organizes the airfares into several categories, each with a different price. The number of discounted seats available for sale is limited to allow sales to last-minute premium buyers.
2. 48 days prior to departure: By now, 41 seats have been reserved for sale at steep discounts. Agents have been authorized to sell 154 seats, which exceeds capacity by 29 seats. No reservations have been taken in first class.
3. 13 days prior to departure: 21- and 14-day advance ticket sales have been closed. One-hundred-and-one seats have been booked. Airfares to Dallas have risen from $220/roundtrip to $448/roundtrip. Agents are authorized to overbook by 21 seats. There are still no reservations for first class.
4. Four hours prior to departure: The price of a roundtrip ticket is up to $1,142. Although the flight is already overbooked by 11 passengers, the agents are authorized to book three more tickets. The first-class cabin is now filled, largely by frequent flier passengers.
5. Five minutes before departure: The flight is overbooked by 13 passengers, but three took an earlier flight and the remainder is composed of no-shows, resulting in a full plane.
The final tally of paying customers is as follows:
1. 52 passengers purchased 21-day or 14-day advance tickets at prices between $220 and $420
2. 25 passengers purchased tickets with seven-day discounts
3. 35 passengers paid full fare for their tickets
4. 13 redeemed frequent flier credits
5. 2 passengers paid full fare for first-class seats
6. 12 passengers redeemed frequent flier tickets to obtain first-class seats.
Another industry that routinely implements yield management is the hotel industry. Hotels face a market that is quite similar to the airline industry. Like the airline, the number of rooms available for rent is pre-existing. Also similar to the airline, the marginal cost of filling a room for the night is quite small (washing towels, replacing soap, etc.). Consequently, it’s better for the hotel to fill each room than it is to leave a few empty. If first-degree price discrimination was not possible, the hotel would determine the profit-maximizing price, which would likely lead to empty rooms. But if they can rent out rooms at discounted rates, while still renting other rooms at higher rates, they can add to their profits.
Priceline and HotWire are firms that assist hotels in price discriminating. Both firms use “opaque” models through which hotels can dump unsold rooms at discount prices without sacrificing revenues from their advertised retail prices. The firms negotiate with brand-name hotels for unlisted discount prices. Buyers, without knowing the names of the hotels, bid prices based on location and hotel class. If the bid price matches or exceeds the unlisted discount, the consumer is charged for the room at the bid price.
Does yield management work? American Airlines and Delta Airlines credit yield management with adding $500 million and $300 million per year, respectively, to their revenues.6 Marriott attributes $100 million per year in revenues to yield management techniques.7
What does it take to make first-degree price discrimination work? Can anyone do it? To begin with, we need to recognize that extracting all consumer surplus is very difficult. Take the car salesman’s attempt to price discriminate. His goal is to extract all that the prospective buyer is willing to pay to get the car. But he doesn’t know what the person is willing to pay, and it behooves the buyer not to disclose the figure. The car dealer may succeed in obtaining some of the surplus, and maybe even all of it, but given that consumers have a vested incentive in concealing their willingness to pay, it would be very difficult for the dealer to extract the entire surplus from every consumer. Hence, the scenario depicted in Figure 5.3 represents perfect price discrimination. In real-world situations, firms that implement price discrimination strategies do so imperfectly; they are able to extract some, but not all consumer surplus.
Beyond that clarification, when is first-degree price discrimination most likely to work? Going back to Wendy’s interior design business, one reason she was in a position to price discriminate was because clients with a lower willingness to pay were not able to purchase her work and re-sell it to clients with a greater willingness to pay. Suppose Wendy sold artwork rather than interior design. As with the interior design business, she has the ability to choose how many paintings she wants to sell, and she believes she can negotiate a price with each customer. Assume Dave is willing to pay as much as $5,000 for a painting, whereas Paul is not willing to pay more than $200. According to theory, Wendy charges Dave and Paul $5,000 and $200 for their paintings, respectively. But what if Paul buys his painting for $200 and then offers it to Dave for $4,000? For price discrimination to work, Wendy has to come up with a way to keep Paul from buying her work for a low price and re-selling it at a higher price. Obviously, this is not an issue for her interior design business. If she fixed up Paul’s living room, he’s not in a position to sell it to Dave.
For price discrimination to succeed, firms must subvert the potential for re-sale. This is not nearly as difficult as one might think. An athletic department at a major university, for example, may offer discount prices to students, based on the assumption that students have less income and, hence, a lower willingness to pay than working adults. In this scenario, the potential for re-sale is obvious: the students buy up a few hundred discounted tickets and then sell them at prices that are less than the face value of the regular tickets. With the Internet, creating efficient re-sale markets is comparatively easy. How do athletic departments keep this from happening? First, students often are required to buy their tickets in person. In this manner, the university can assure that only students who present their college IDs can purchase a ticket. To subvert the possibility of re-sale, each student ticket is often printed with a “Student Ticket” label. If a 40-year old shows up at the gate with a “Student Ticket,” the ticket-taker is in a position to demand to see proof that the individual is, indeed, a college student.
Savvy readers may have noticed something about the dynamics of price discrimination. When an airline or hotel implements yield management, it does so by pricing the buyer with a lesser willingness to pay into the market without having to lower the price for the buyers with a greater willingness to pay. That’s why it’s a smart idea for the airline to sell every seat and for the hotel to rent out every room. But in most industries, the firm does not need to lower the price to suit the low-demand buyer; it can simply store the inventory to sell another day and exclude the low-demand buyer entirely. But the plane cannot store unused seats in inventory and sell them another day. Neither can the hotel do the same with its empty rooms. Once the plane takes off, the empty seat represents revenue foregone. Likewise, once dawn breaks the following day, an empty hotel room is a room that could have had a paying customer. For this reason, price discrimination works best when the product is perishable and cannot be stored to re-sell another day.
There is another common bond among the airline and hotel industries. In both cases, variable costs are negligible. Filling a seat or hotel room brings in revenue while having little or no impact on costs. Price discrimination can be successfully practiced when variable costs are higher. However, given that the goal is to price the more price sensitive buyers into the market, the firm has significantly more pricing flexibility when unit costs are low.
Summary
• First-degree price discrimination is the practice of charging each customer the maximum he is willing to pay.
• Successful first-degree price discrimination allows the firm to extract all of the consumer’s surplus, thereby maximizing revenues.
• It is difficult to extract all consumer surplus because consumers have an incentive to disguise their willingness to pay.
• Because the firm does not have to charge the same price to all customers, the firm will maximize profits by producing each unit that can be sold at a price above its marginal cost. This will allow the firm to profitably sell more units than it would under a single price strategy.
• To successfully price discriminate, the firm must have some degree of market power and limit the ability of customers to re-sell the units at a higher price.
• First-degree price discrimination is often referred to as yield management and is widely practiced by airline and hotel rooms because variable costs are minimal and each seat/room that sits empty represents lost revenue that cannot be stored in inventory and re-sold on another day.