Because it’s rare for a firm to have the kind of comprehensive information about customers that it needs to practice perfect price discrimination, a firm can’t generally capture all of the market surplus using price discrimination. But it can still earn more profit than a regular monopoly by using a pricing strategy called segmenting (or third-degree price discrimination, charging different prices to different groups (segments) of customers based on the identifiable attributes of those groups.1

For this kind of pricing strategy to work, the company must be able to directly identify groups of customers—students, for example—who have systematically different demands than other buyers. This group-level demand identification is typically much easier to determine than figuring out every individual customer’s willingness to pay.

Think about a company that sells a clothing line emblazoned with your school logo. If the company knows that students typically don’t have a lot of money and tend to be bargain hunters while their parents are less price-sensitive, the firm will want to charge students a lower price for clothing and parents a higher price. To do this, the company needs to be able to identify the groups directly. It must be able to tell before the sale which customers are students and which are parents, as well as prevent parents and faculty from pretending to be students to get the discount. One way the company can do this is to make showing a student ID a condition of the lower price.

As with all forms of price discrimination, however, the company must be able to prevent resale. They can’t sell school sweatshirts at a student discount just to have the students then turn around and sell them to visiting parents for less than the higher price these groups would be charged. As a practical matter, if such resales became a problem, the company could institute a quota that would limit the number of sweatshirts a student could buy. Limiting resale is critical to price discrimination.

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If a firm is able to engage in segmenting, how different should the prices be across the groups, and how much does the company stand to gain by price-discriminating compared to the standard one-price monopoly strategy?

To answer these questions, let’s consider an example with two consumer groups, the market for entry into the prestigious Ironman 70.3 Cozumel Triathlon. This triathlon is a race that comprises a 1.2-mile swim, a 56-mile bike ride, and a 13.1-mile run. It may seem like a masochistic pursuit, but people pay serious money to enter this race.

There are two kinds of people who want to enter the Ironman Cozumel: people who live near Cozumel, and people who fly in from somewhere else. The two groups’ demand curves for entering the race are shown in Figure 10.4. Panel a shows the demand (D_T) for the participants traveling to Cozumel for the competition. The travelers mostly come from the United States; have high incomes and expensive triathlon equipment; and will have to pay for a plane ticket, a hotel room, food, and a rental car. They don’t care if the price of their registration for the race is a bit higher, because it’s a small share of the total cost to them. In other words, the demand curve for the traveling participants is fairly inelastic.

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Panel b of the figure shows the local group’s demand curve, D_L. The local residents’ demand is more price-sensitive because they have many other activities they can pursue if the price of entering the race is too high. Thus, their demand curve is flatter and more elastic.

Preventing resale won’t be a problem for the firm organizing the race as long as it can tell which athletes are from out of town and which are not. This is easy because out-of-town athletes have to pay their entrance fees with some form of identification that gives their address, and they have to prove who they are when claiming their bib numbers on race day.

The fundamental economic idea of segmenting is simple. If a firm can directly identify groups that have different demands and charge different prices to each, it can essentially treat each group as a separate market. The firm then sets its profit-maximizing quantity for each one of these “markets” where MR = MC and sets the corresponding single-price profit-maximizing price according to each market’s demand curve.

Let’s see how the organizers of the Ironman Cozumel competition follow the segmenting strategy. The organizers have identified these two different demand curves and treat each as a separate market. From the demand curve of out-of-town entrants (travelers) D_T, the organizers compute marginal revenue, labeled MR_T in panel a of Figure 10.4. Then from the point at which MR_T equals marginal cost MC, the organizers determine the optimal quantity of entries to sell to out-of-towners (Q_T = 600). At that quantity, the entry fee is P_T = $220.

The organizers go through the same process for the local entrants. These entrants’ demand curve D_L in panel b implies a marginal revenue curve MR_L. The optimal number of entries for the organizer to offer to locals is Q_L = 700, the quantity at which marginal revenue from locals equals marginal cost. (The marginal cost is the same for either type of racer. It amounts, basically, to the cost of a bib, some extra Gatorade, some water, a finisher’s medal, and a race T-shirt.) The price, determined from the locals’ demand curve, is P_L = $170, significantly lower than the $220 price for traveling entrants.

That’s all there is to the strategy. As long as a seller can keep people from sneaking into the lower-price group or keep those in the lower-price group from reselling to the higher-price group, it can use segmenting to treat each group like a separate market and set the monopoly price for each market.

A firm following this pricing strategy will not earn as much producer surplus as one using perfect price discrimination (which would allow it to take the entire surplus from the market). However, it will earn more surplus than if it acted like a regular monopoly and charged the same price to everyone, because the strategy gives the firm some ability to charge a higher price to consumers with relatively inelastic demand and lower prices to consumers with relatively elastic demand.

Figure 10.5 shows the total Ironman Cozumel demand and marginal revenue that would face a monopolist forced to set only a single price. As in Chapter 5, we calculate the market demand as the horizontal sum of the participants’ demand curves—in this case, the sum of the traveling and local participants’ demands. This results in a kink in the market demand curve at $240, the demand choke price for local participants. At prices above $240, no locals purchase tickets, so the market demand curve is just the traveling racers’ demand curve.2

A single-price monopolist race organizer sets the quantity of entries where its marginal cost equals marginal revenue, and charges the price corresponding to the total market demand curve. This quantity, 1,300 racers, is shown in Figure 10.5, and the corresponding price is $186.67 per entry. Notice how this price falls between the two prices ($170 and $220) that the organizers charge the segments when price-discriminating. Although it might not be obvious from looking at the figure, the producer surplus for the single-price monopolist is considerably smaller than the surplus the monopolist would earn by segmenting the market. (We see that this is indeed the case when we calculate the benefits from segmenting in the next section.)

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To do the same analysis of segmenting using mathematics, we start with the two distinct demand curves for the Ironman Cozumel. The demand curve of the traveling participants is given by Q_T = 1,700 – 5P_T, and the locals’ demand curve is Q_L = 2,400 – 10P_L. Note that, in accordance with our story, the locals’ quantity demanded is more sensitive to price than the travelers’ quantity demanded: A $1 increase in the entry fee reduces the number of local entrants by 10, while it only decreases the number of traveling entrants by 5. We assume the marginal cost to the organizer of adding another triathlete to the race is a constant $100, no matter how many entrants there are.

The mathematical analysis of segmenting is done using the same steps as in the graphical analysis above. If the race organizers can identify the separate groups and prevent resale, they can compute the marginal revenue curves for each segment and solve for the monopoly prices separately for each group.

We can follow the methods discussed in Chapter 9 to find the marginal revenue curves from linear demand curves. First, we determine the inverse demand curves by rearranging the demand function to express price in terms of quantity demanded. Doing so gives us the following equations:

Next, we know that the marginal revenue curve will look like the inverse demand curve, but the coefficient on quantity will be twice as large. The marginal revenue curves for the two segments are

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The organizers want to sell the quantities at which marginal cost ($100, the same for both groups of triathletes) equals its marginal revenue. Setting each marginal revenue equation above equal to marginal cost tells us the optimal number of entrants from each group:

The last step is to find the entry fees that correspond to these quantities by plugging the quantities back into the inverse demand curve:

Therefore, in a segmentation strategy, the race organizers sell 600 entries to out-of-towners for $220 each and 700 entries to locals at $170 each.

The total producer surplus the organizers earn is the difference between the price and the marginal cost for each segment times the number of entries sold to that segment. In Figure 10.4, those surpluses are rectangles PS_T for the segment of nonlocal triathletes and PS_L for the local triathletes. Using the results we computed above, we have

for a combined producer surplus of $121,000 to the race organizer.

In our graphical analysis, we contended that the price-discriminating monopolist earns more producer surplus than the single-price monopolist. This makes intuitive sense, because a firm that segments the market can charge higher prices to more price-inelastic customers and capture more of their consumer surplus. But how can we show this algebraically?

First, we can see that the marginal cost curve intersects demand at the part of the demand curve below the kink—the portion of the demand curve that is the sum of the local and nonlocal demand:

Q = 1,700 – 5P + 2,400 – 10P = 4,100 – 15P

The inverse demand curve at this intersection is then , and the marginal revenue curve has twice the slope, or . We set MR equal to the marginal cost to solve for the optimal number of participants under the single-pricing strategy:

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Note that 1,300 is exactly the sum of the local and traveling participants under the previous pricing system. Single-price monopolists and those who segment differ in the prices they set, but not always in the quantity they provide. That doesn’t mean the firm would be selling to the same group of individuals, however. The new price will be lower than the segmented price for travelers (inducing more to buy than in the segmented case) and higher than the segmented price for locals (excluding some locals from buying). Just what is the price in this instance? Plug the quantity into the inverse demand curve:

Thus, although locals face a slightly higher price, the travelers get a bargain relative to the segmented outcome.

To calculate the producer surplus, we find the area of the rectangle A in Figure 10.5:

PS = (186.67 – 100) × 1,300

= 86.67(1,300) = $112,671

If the monopolist organizers segment the market for triathlon entries, they earn $121,000 in producer surplus; if they must charge a single price, they earn $112,671. Just by segmenting the market, the monopolist organizers can increase their producer surplus by $8,329, or about 7%.

Because the standard market power pricing rule applies in each segment, it also means that the Lerner index, the basic markup formula we derived in Chapter 9, applies in each market. Recall that this formula relates the price elasticity of demand to the markup of price over marginal cost:

If the firm sells the same good to both segments of the market, the marginal cost of producing for each segment is the same. In this case, the only reason to charge different prices to customers in different segments is because they have different demand elasticities. To see what the Lerner index implies for the ratio of the prices in the two segments (label them 1 and 2), first solve the Lerner index for price in each segment:

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Likewise,

Now, we can compute the ratio of these prices:

As the demand in Segment 1 becomes less elastic relative to Segment 2 (i.e., E₁^D becomes smaller than E₂^D in absolute value), the ratio P₁/P₂ will rise. That is, the greater the difference in price sensitivities between the segments, the greater should be the ratio in their prices.

Returning to our Ironman Cozumel example, suppose we know that the elasticity of demand for travelers is –1.83 and the elasticity for locals is –2.43.3 We can immediately determine what the ratio of prices should be by plugging these elasticities into the formula:

In other words, the race organizer should set the price travelers face to be almost 1.3 times (i.e., 30% higher than) the price for locals. This is, in fact, the ratio between the $220 and $170 optimal entry fees we computed earlier.

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There are many ways firms directly identify customer segments for the purposes of price discrimination. Here are some of the most common ones.

By Customer Characteristics Firms sometimes price according to customer characteristics such as age (e.g., senior citizen discounts at the movies or child discounts at a hotel), gender, or whether the customer is a student or local resident. The basic idea remains to identify the more price-sensitive customers and charge them less. Firms need to be careful when pricing based on consumer characteristics in certain countries because in some cases this may be prohibited by laws against discrimination based on age, gender, race, physical disabilities, and so on.

Segmenting can even be based on the user’s species. Doctors and veterinarians sometimes use the same medicines. Drug makers recognize that Grandma’s willingness to pay for the arthritis medication Lodine probably well exceeds someone’s willingness to purchase Lodine for her arthritic dog Rover (and not only because Grandma’s savings are larger than Rover’s collection of buried rawhides). This difference in willingness to pay probably explains why a congressional investigation found that the price of Lodine for humans was almost three times higher than for dogs. Indeed, it determined that manufacturers priced almost every comparable medication significantly higher for people than for animals.4

Customer characteristics can also apply to firms or other corporate organizations in business-to-business transactions. Academic journals, for example, know that individuals are much more price-sensitive to subscription prices than libraries, so the publishers charge significantly more for institutional subscriptions than for individual ones. Elsevier, for example, one of the largest publishers of academic journals, charges individuals $134 for a year’s subscription to the International Journal of Industrial Organization (don’t all rush to order it at once), but the publisher charges libraries $2,139 for the same subscription.

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By Past Purchase Behavior Consumers reveal a lot about their willingness to pay when they buy other products, and many sellers use that information to segment customers. In industries like auto insurance or direct-broadcast satellite TV, where people don’t like switching companies once they decide on a provider, existing customers tend to be less price-sensitive than potential new customers. As a result, it is common for firms in these industries to give special discounts to new customers, such as reduced premiums during the first policy period or the first three months of a subscription free. These are ways to price-discriminate based on whether the customer has bought the product before.

For some other products, the price sensitivity of new customers is lower than that of past purchasers. For example, it is notoriously difficult to convince people to upgrade their software to a new version. When Microsoft releases a new version of Windows, the price of upgrading an older version is typically much lower than buying the new version outright. With this low price, Microsoft is trying to entice the more price-sensitive customers to purchase the new version.

By Location Customers living in one area may have a hard time getting to another to take advantage of a lower price, or they might not even have knowledge of the prices in other locations. This often allows sellers to charge different prices in different locations, depending on the price sensitivity of local demand. For example, chain restaurants often charge higher prices at their airport locations than at their other stores, at least in part because travelers in a hurry, in an unfamiliar city, and (often) on an expense account tend not to be price-sensitive in their food and drink purchases.

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Over Time One way to price-discriminate in certain markets is to take advantage of the different kinds of people who buy a product at different times. When a new generation of computer CPUs first hits the market, for example, the new CPUs usually sell at a substantial premium, sometimes hundreds of dollars more than the last generation’s chips. Yet only a few months later, they are available for a fraction of their original price. Maybe marginal cost fell that much, you say? Perhaps. But how about movies in first-run theaters that cost $10 but then cost only $4 when the same movie runs at a discount movie house several weeks later? Or hardcover books that cost $26.95 while their paperback versions cost only $10.95, when the actual difference in production cost is only about a dollar? These are all cases in which the kinds of people who want the latest, greatest, most current version of a product—PC gamers, big movie fans, and active readers—tend to be less sensitive to price than the folks who enter the market later.

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In other cases, demand can become less price-sensitive (more inelastic) over time, and price discrimination will lead to price increases over time. Many goods and services with initially uncertain quality have this feature. For example, tickets to a new play or musical that hasn’t been reviewed are often relatively inexpensive. But once local reviewers have given the play a “thumbs up,” demand can become much more inelastic and the producers raise their price accordingly.

In either situation, a firm that prices the same good differently in two different time periods applies the basic segmentation rules and uses the standard monopoly pricing rule as it applies to the state of demand in each period.

However, there is one complication in pricing across time that is worth keeping in mind. Technically, pricing across time is only segmenting if the seller directly assigns customers to a given time period. That is, in segmentation strategies, the seller is effectively saying, “You buyers over here, this is your price. You buyers over there, you have a different price.” Buyers are stuck paying the price designated for their group (assuming again as we have throughout this chapter that the seller can prevent resale). With time-based segmentation, however, if customers are forward-looking, meaning that they consider what the seller might do in the future even as they decide whether to buy today, then the seller is not actually directly segmenting its customers. The seller cannot prevent its customers from changing groups; the buyers choose when to buy. So, for example, if buyers believe that the seller is charging a high price today but will reduce the price in the future, they might consider waiting to purchase, even if they had the type of relatively inelastic demand that the seller was trying to take advantage of with the high current price. In cases like this, the seller needs to consider how the different prices it plans to charge over time will affect the consumer’s decision of when to buy.

For instance, Intel might want to initially price its fast new CPU at an extremely high level to take advantage of a segment of high-horsepower PC gamers with really inelastic demand, while making deep discounts thereafter. But if gamers realize Intel is likely to do this, they might be willing to trade off waiting to purchase the new CPU in exchange for enjoying the deep discount. This potential response will limit Intel’s ability to segment the market in the first place. It could lead to Intel having to charge a lower initial price than it would have otherwise, and perhaps also reduce the discount applied to that price later.

The more forward-looking consumers are, the more segmenting across time actually becomes something known as indirect price discrimination, the pricing strategy we discuss next.