Revenue Management and Pricing

1. Revenue Management and Pricing Chapter 4 Price Differentiation

2. Price Differentiation • Price differentiation refers to the practice of a seller charging different prices to differentcustomers, either for exactly the same good or for slightly different versions of the samegood. • Price differentiation is a powerful way for sellers to improve profitability. • It also addsa new level of complexity to pricing, often creating a need to use analytical techniques toimprove the calculation and updating of prices over time. • We use the term price differentiation to refer to the ways that additional profit can beextracted from a marketplace by charging different prices.

3. Price Differentiation • Tactics for price differentiationinclude • charging different prices to different customers (or groups of customers) for exactlythe same product, • charging different prices for different versions of the same product, and • combinations of the two. • The term price discrimination is used in the economics literatureto refer to much the same thing. • However, we also want to stress that price differentiation includesnot only charging different prices to different customers for the same product (group pricing), but also the less controversial strategies of product versioning, regional pricing, and channel pricing.

4. Price Differentiation • There is both art and science to price differentiation. • The art lies in finding a way to dividethe market into different segments such that higher prices can be charged to the highwillingness-to-pay segments and lower prices to the low-willingness-to-pay segments. • Thereis no one way to segment customers that applies to all possible markets. Instead, there is avariety of techniques that can be applied in different ways, depending on the characteristicsof a market, the competitive environment, and the character of the goods or services beingsold. • The science lies in setting and updating the prices in order to maximize overall return from all segments.

5. Price Differentiation • Observe that 10,000 customers are willing to paysome amount greater than zero • 5,000 are willing to pay $6.25 or more, • 3,000 are willing to pay $8.75 or more (the contribution-maximizing price), • and 1,200 are evenwilling to pay $11.00 or more.

6. Price Differentiation • The marketing department might see an opportunity to improveprofitability. After all, there are 2,000 customers willing to pay $10.00 or more whoare purchasing at $8.75. • This is a good deal for these customers, but it is also at least $1.25in additional revenue “left on the table” from each sale. • Furthermore, 3,000 customers arewilling to pay more than the production cost ($5.00) but less than $8.75—the sales price.Each of these is a potentially profitable sale lost because the price is too high. • What if theseller could determine the maximum amount that each customer would be willing to payand could charge that amount to everyone willing to pay more than the per-unit cost of$5.00? • This would be pricing nirvana—the ultimate in “one-to-one” pricing.

7. Price Differentiation

8. Price Differentiation • With a single price, the widget maker will charge $8.75 per unit and realizea total profit of ($8.75 - $5.00) * 3,000 = $11,250. This is the area of regionA in Figure4.1. • “Perfect” price differentiation would enable the seller to charge each customer willingto pay more than $8.75 per unit her exact willingness to pay. This would provide theadditional revenue in regionB in the figure. • There is an additional opportunity to sell widgetsto customers who are willing to pay more than $5.00, the unit production cost, but lessthan $8.75. This potential profit is shown as regionC in the figure. • The sum of the three regionsis the total contribution that the widget maker would realize if he were able to chargeevery potential customer exactly at her willingness to pay. This is an upper bound on whatcould possibly be realized under any price differentiation program. • Charging every customerexactly her willingness to pay is known as third-degree price discrimination in the economics literature.

9. Price Differentiation • Assume that thewidget maker finds he can divide his market into two segments. • One segment consists of allcustomers willing to pay more than $7.00 for widgets. The other segment consists of all thecustomers willing to pay $7.00 or less. The corresponding price-response curves are: • where d1(p1) is the price-response curve for customers with a high willingness to pay andd2(p2) is the price-response curve for customers with the lower willingness to pay.

10. Price Differentiation • The sum of these two curves is the originalprice-response curve • The difference is that now we can offer adifferent price to each of the two segments. • We assume for this example that the widgetmaker can perfectly identify customers as belonging to one group or the other and can thenoffer each customer the appropriate price, without any opportunity for resale or arbitrage between the two groups.

11. Price Differentiation • The widget maker can determine the optimal prices for each segment by solving the price optimization problem twice—once for each segment. • The results (along with a comparison to the unsegmentedcase) are shown in Table 4.1. • It is interesting to note that customers benefit as well. The same3,000 customers who would buy under a single price at $8.75 still get to buy at $8.75. Inaddition, 800 additional customers get to purchase at the new low price of $6.00. These800 customers are priced out of the market if the seller can only charge a single price. • In thiscase, price differentiation is a win-win situation since the seller is certainly better off and allof the buyers are at least as well off as before. However, price differentiation is not alwayssuch a boon for consumers.

12. Limits to Price Differentiation • Imperfect segmentation:The brain-scan technology required to determine the precisewillingness to pay of each customer has not yet been developed. The best thatcan be done is to create market segments such that the average willingness to pay is different for each segment. • Cannibalization:Under differential pricing, there is a powerful motivation for customersin high-price segments to find a way to pay the lower price. In the widgetexample, there is a strong motivation for high-willingness-to-pay customers whoare being charged $8.75 per widget to “masquerade” as low-willingness-to-paycustomers and pay only $6.00 per widget. • Arbitrage:Price differentials create a strong incentive for third-party arbitrageurs tofind a way to buy the product at the low price and resell to high-w.t.p. customersbelow the market price, keeping the difference for themselves. Ex: Assume that the widget seller has segmented his market and is charging the twoprices as $8.75 and $6.00. If 300—that is 10%— of the high-willingness-to-paycustomers are able to find a way to purchase widgets at the lower cost of $6.00,it would totally eliminate the benefits of price differentiation.

13. Tactics for Price Differentiation • Group pricing:tactic of offering different prices to different groups of customers forexactly the same product. • The idea is to offer a lower price to customers with a low willingnessto pay and a higher price to those with a high willingness to pay. • In practice, “pure”group pricing requires determining whether or not a prospective buyer belongs to a particulargroup and using that information to determine which price to charge. • Examples of pure group pricing include: • Student discounts • Senior citizen discounts • “Ladies’ Night” specials • Family specials • Discounts for favored customers • Favorable terms offered by manufacturers or wholesalers to large retailers suchas Wal-Mart • Lower prices offered to government, educational, and nonprofit organizations by suppliers

14. Tactics for Price Differentiation 1. Group pricing: Four criteria must hold for group pricing to be successful. • There must be an unambiguous indicator of group membership. Examples of suchindicators include a student ID card or a driver’s license that lists age. Furthermore,it must be difficult or impossible for members of one group to masquerade asmembers of another. Otherwise, cannibalization could easily reduce or destroythe benefits of price differentiation. • Group membership must strongly correlate with price sensitivity. Senior citizen discountsare predicated on the belief that senior citizens, as a whole, are more pricesensitive than the public in general. • The product or service should not be easily traded or exchanged among purchasers.This is necessary to avoid arbitrage—in which customers with access to low pricesresell to customers who are quoted higher prices. • The segmentation must be both culturally and legally accepted. While group pricingon the basis of age is broadly accepted, differentiating prices on the basis of othercharacteristics, such as race and gender, are controversial or illegal.

15. Tactics for Price Differentiation 1. Group pricing: • Puregroup pricing is relatively rare indirect consumer sales. • It is most common in services. Services are often sold directly by thesupplier so that Disneyworld, for example, can check a customer’s age before selling a child’sticket. • Furthermore, many services, such as health care and haircuts, are intrinsically nontransferable,so arbitrage is not an issue. • Airlines originally began checking passenger identificationnot for security reasons but to prevent arbitrage. • Pure group pricing is also common in business-to-business sales. Customized pricing in business-to-business sales is often combinedwith some form of product versioning, particularly in industries where individualorders are very complex and/or configurable.

16. Tactics for Price Differentiation 2. Channel pricing:the practice of selling the same product for different prices through differentdistribution channels. • Barnes and Noble sells books for different prices online than through its outlets. • Special “Web-only” fares for airline tickets are available through the Internet but not through travel agencies. • Many fashion and home furnishing merchants offer lower prices for merchandisethrough mail-order catalogs than for the same merchandise sold through retail outlets. • As with other price differentiation schemes, there can be more than one reason whya seller might charge different prices through different channels. One is cost—for manycompanies, selling through the Internet is cheaper than selling through traditional channels.Continental Airlines calculated that distribution costs for a $325 ticket are about $43when the ticket is sold through a travel agent versus only $18 when the same ticket is soldthrough Continental’s Web site. This difference in itself would be sufficient reason for Continentalto charge lower prices on its Web site.

17. Tactics for Price Differentiation 2. Channel pricing: • However, it is also the case that customers arriving via different channels have differentprice sensitivities. For personal loans, it has been shown that customers inquiring throughthe Internet are more price sensitive than those contacting a call center, who are in turnmore price sensitive than those who apply for a loan at a retail branch. • Furthermore, Internetcustomers who access a consolidator Web site or use a shopping ’bot tend to be moreprice sensitive than those who go directly to a bank’s Web site. • This is not surprising giventhe characteristics of the channels—it is generally easier and more convenient to shop andcompare prices during a single Internet session than by making many phone calls. Thus differentialwillingness to pay is also a motivation for channel pricing.

18. Tactics for Price Differentiation 3. Regional pricing: • McDonalds sells hamburgers for higher prices in wealthy neighborhoods than in poorer ones. • A roundtrip New York–Tokyo ticket purchased in Japan will usually cost morefor many airlines than the same ticket purchased in the United States. • A glass of beer costs more at an airport bar than at the corner bar. • In each case, the price difference is based on the supplier’s desire to exploit differences inprice sensitivity between locations. After all, travelers at an airport are essentially a captivemarket and have few alternatives.

19. Tactics for Price Differentiation 4. Couponing and Self-Selection:It is often muchmore convenient to differentiate prices in ways that allow customers to self-select. • In a self-selectionapproach, both the list price and a discounted price are available to all customers,but it takes additional time, effort, or flexibility to obtain the discounted price. • The idea isthat those willing to make the additional effort to get the discount are generally more pricesensitive than those who are not. • Retailers commonly offer discount coupons through newspapers, direct mail, and magazines. • Retailers often offer mail-in rebates for purchasers of a good. • Movie theaters charge lower prices for a weekday matinee than for a Saturday night show. • Brand-name retailers operateoutlet stores in somewhat out-of-the-way locations in which merchandise is available for a substantial discount.

20. Tactics for Price Differentiation 4. Couponing and Self-Selection: • The common thread among these examples is that the seller has chosen a mechanism thatallows customers to self-select, depending on the value they place on time or flexibility. • Any customer can obtain an item at a discount if she is willing to take some additional effort. • Research has shown that users of coupons are more price sensitive than nonusers ofcoupons. • Locating outlet stalls away from large cities segments the market between thosewho are willing to spend additional time shopping and those who aren’t. • Peak-load, day-of-week, and time-of-day pricing segments the market between those who have the flexibilityto change their plans in order to save some money and those who are not willingto do so. • Since these mechanisms are based on self-selection, they are far more acceptableto most consumers than mechanisms in which the seller unilaterally selects customers to receive discounts.

21. Tactics for Price Differentiation 5. Product Versioning: Designingor developing products (either virtual or real)that may have only minor differences but enable the seller to exploit differences in price sensitivityamong customer segments. • This can involve developing an “inferior” variant and/ora “superior” variant of an existing product. • Inferior goods: • Well-known international brand names such as Mobil /Exxon and Shell sell excessgasoline in bulk at low prices to so-called “off-brand” independent dealers whoresell it under their own brands. • A well-known premium wine producer sells some of its production under a differentlabel at about half the price. • Brand-name vegetable canners sell their products under their own brand but alsosell to retailers who sell the product to consumers as a “house brand” or a generic brand. • The motivation on the part of the seller in each case is thesame—a desire to sell a product cheaply to customers with lowerwillingnessesto pay withoutcannibalizing sales of the full-price product. This is achieved in each case by creating aninferior version of the “standard product.”

22. Tactics for Price Differentiation 5. Product Versioning: • A particularly extreme example of inferior goods is the category of so-called damagedgoods. This is a term coined to refer to the situation in which a manufacturer or supplier createsan inferior good by damaging, degrading, or disabling a standard good. • Since this process starts with the standard good, the supplier is actually payingmore to create the inferior good it will sell at a lower price. • One example is the 486SXprocessor developed and sold by Intel Corporation.The 486SX processor of Intel Corporation was initially produced in a curious way.Intel began with a fully functioning 486DX processor, then disabled the math coprocessor,to produce a chip that is strictly inferior to the 486DX but more expensive to produce. • Nevertheless, in 1991, the 486DX sold for $588, and the 486SX for $333, a little over halfthe price of the chip that is less expensive to produce.

23. Tactics for Price Differentiation 5. Product Versioning: • Complex application software packages such as supply-chain software or enterpriseresource planning (ERP) software are often sold at different prices, depending on the numberof features purchased by a customer—the more features purchased, the more expensivethe license. • In many cases, the software is configured for a particular customer by startingwith the complete package and then disabling the features that the customer did not purchase. • The concept of “damaging” a good in order to create an inferior good to be sold at a lowerprice may initially seem somewhat bizarre. However, it is really only a special case of themore general category of “inferior” goods. • There can be a tremendous gain from offering aninferior good at a lower price, even if the supposedly inferior product is more expensive toproduce. Starting from a standard product and then paying to have it “damaged” is only aspecial case of this more general principle.

24. Tactics for Price Differentiation 5. Product Versioning: • Superior goods:This is the obviouscomplement to the inferior-good strategy: creating a superior good in order to extracta higher price from less price-sensitive customers. • An example of the superior-good strategy was employed by Proctor-Silex. In 1985,Proctor-Silexpriced a top-of-the-line iron at $54.95, while their next best model was pricedat $49.95. The only difference between the two was that the top model had a small light indicatingwhen the iron is ready to use. The difference in manufacturing cost between thetwo models was only $1.00, yet Proctor-Silex was able to maintain a $5.00 price differencebecause, as a Proctor-Silex marketing manager put it, “There is a segment of the market thatwants to buy the best, despite the cost.” By creating a “superior” product, Proctor-Silexenabledthe less price-sensitive segment of the market to self-select and extracted an additional$4.00 in contribution margin from each high-end buyer. • In some ways, a superior-goodstrategy is safer than an inferior-good strategy because it does not threaten cannibalizationof existing sales.

25. Tactics for Price Differentiation 5. Product Versioning: • Product lines:Establishing a product line is the natural extension of creating inferior orsuperior products. A product line is a series of similar products serving the same generalmarket but sold at different prices. • For our purposes, we will consider vertical product lines,where almost all customers would agree that a higher-priced product is superior to a lower-pricedone. • This applies, for example, to a hotel that charges more for an ocean-view roomthan a parking-lot-view room • It also applies to personal computers offered by Dell, where each productin the line has higher performance (faster CPU, more memory, etc.) than the product justbelow it in the line. • This can be contrasted to horizontal product lines, where different customerswould prefer different products within the line, even at the same price. • Coca-Colaoffers a horizontal profit line with “Classic” Coke, Diet Coke, Coke Zero, etc. This is a horizontal product line because none of the products is unambiguouslyhigher quality or more desirable thananother.

26. Tactics for Price Differentiation 5. Product Versioning: • Product lines: An example of a vertical product line is shown in Table 4.2, which gives prices for fourversions of the QuickBooks financial software offered by Intuit. The software comes in four“editions,” ranging from the Basic Edition, which costs $199.95, to the Enterprise Solutions,which costs $3,500. In between are the Pro Edition, which is described as including “all thefeatures of Basic plus advanced tools and customization options to boost efficiency and accuracy”and the Premier Edition, which includes “all the features of Pro and comprehensivetools for greater insight into your business.” The top-of-the-line Enterprise Solutions packageis described as “Our most comprehensive business management tool for growing businesses,with all the features of Pro and Premier.”

27. Tactics for Price Differentiation 5. Product Versioning: • Product lines: In all likelihood, there is only a tiny difference (if any) in the marginal cost of producingand delivering the four different versions of QuickBooks software. Yet the Enterprise Solutionspackage is priced more than 15 times higher than the Basic Edition. The rationale forthe product line and the broad difference is market segmentation—very small businessesthat need less functionality and have fewer users are presumably more price sensitive thanlarger businesses with more users. The establishment of a series of products allows Intuit tosegment its market via self-selection on the part of its customers.

28. Tactics for Price Differentiation 5. Product Versioning: • Product lines: Table 4.3 shows the one-dayrates on display for a Hertz one-day rental from the Seattle airport ona midweek day in May. • By providing a menu of alternativesat different prices Hertz allows customers to self-select. • The range of rates is not driven by cost differences.Life-cycle costs do not vary much among models. There is little orno difference in the daily incremental cost to Hertz from renting out an economy or aluxury car. The spread in daily rates is driven almost entirely by Hertz’s desire to segmentits market and charge different prices to different segments.

29. Tactics for Price Differentiation 5. Product Versioning: • Product lines: For service companies like Hertz, creation of a product line has an important sidebenefit—it creates opportunities for upgrading. • A rental car company or a cruise line has theability to oversell lower-quality car types and upgrade customers into higher-quality types. • Not only does this provide the company with greater flexibility to manage its inventory, butbeing upgraded is usually viewed favorably by customers. • An important advantage of pricingdifferentiation by establishing a product line is that consumers perceive it as fair. • Thepricing menus offered by Hertz and Intuit are openly communicated and available to allcomers. • Consumers get to choose among the alternatives, and the concept of “paying moreto get more” is widely accepted. This makes product-line pricing more acceptable thangroup pricing in most customers’ minds.

30. Tactics for Price Differentiation 6. Time-Based Differentiation: • Amazon offers 5-to-9-day “Super-saver” shipping free while charging $3.97 for “standard shipping.” • Passenger airlines offer discount rates to customers who book a week or more prior to departure. • Software- and hardware-support contracts charge more for “two-hour response” than for “two-day response.” • Fashion goods cost more during the beginning of the season and are marked downtoward the end of the season. • In each of these cases, companies have created differentiated products that allow customersto self-select. In the case of Amazon, customers who are willing to wait for delivery can payless. For passenger airlines, customers who have the flexibility to book earlier can pay less.Of course, it may be that the higher price charged by Amazon for early delivery exactlymatches the incremental cost. But it is highly likely that Amazon is also using time of deliveryas a segmentation variable, relying on the fact that some of their customers will willinglypay a premium in order to have the product in their hands sooner.

31. Tactics for Price Differentiation 6. Time-Based Differentiation: • Time-based differentiation plays a very important role at passenger airlines, hotels, andrental car companies, in which time of booking and other factors, such as willingness toaccept a Saturday night stayover, are used as indicators of whether or not a potential customeris traveling for leisure purposes or business purposes. • Those traveling for leisure purposesare presumed to be more price sensitive than those traveling for business. • This segmentationis the foundation of revenue management in those industries, and we will discuss itin detail in Chapter 6. The willingness of some customers to wait in order to purchase fashiongoods at a discount is the basis of markdown management, which we will treat in detail in Chapter 10.

32. Tactics for Price Differentiation Product Versioning or Group Pricing? • In reality, there is no clear line separating the two approaches and many price differentiationstrategies contain elements of both. • For example, consider the classic airlineexample of a roundtrip ticket from San Franciscoto Chicago costing $250 if purchased a week in advance and including a Saturday stayoverversus $750 if purchased at the last minute without restrictions. Is this group pricing orproduct versioning? • Disgruntled customers might argue that it is simply group pricing,since different customers are paying different amounts for exactly the same service, namely,a roundtrip coach seat San Francisco–New York. This is the “Why am I paying $500 morethan the person sitting beside me for exactly the same flight?” objection. • The airline wouldreply that the two types of tickets are distinct products and that the added cost of the fullfareticket is fully justified by the flexibility of being able to purchase late and return withoutstaying over a Saturday night.

33. Tactics for Price Differentiation Product Versioning or Group Pricing? • The reality is, of course, that airline pricing—like many successful examples of price differentiation—includes elements of both group pricing and product versioning. • The airlinesconsciously created restricted discount fares as an inferior product. They did so, however,as a way to enable them to offer different fares to different customer groups: lower fares toleisure travelers, who are more price sensitive but more flexible; and higher fares to businesstravelers, who are less price sensitive but less flexible. • Viewed one way, we could say that theairlines created an inferior product as the most efficient and least controversial way to institute group pricing. • The airline example illustrates a very important point. Pure group pricing is very difficultto pull off in consumer markets. There are few cases in which consumers canunambiguously be identified as belonging to a particular group.

34. Tactics for Price Differentiation Product Versioning or Group Pricing? • Airlines have no reliableobjective marker to tell them whether a particular customer is flying for business orfor pleasure. • In the absence of such a marker, they rely on the very imperfect criterionof whether or not a customer can book early. This works well enough, but it is imperfect. • For example, there are plenty of highly price-sensitive leisure customers who would loveto book late. Furthermore, the airlines have lots of empty seats they would like to fill withthese customers even at a very low price. But, at least until recently, there has been nosystematic way to sell to these customers without cannibalizing the full-fare business customers.

35. Tactics for Price Differentiation 7. Volume Discounts: “Buy more to save more” isa common motto. • A six-pack of beer purchased from the supermarket costs less than six times the costof a single bottle, and a case (12 bottles) usually costs less than two six-packs. • Larger boxes of laundry detergent cost less per ounce than smaller boxes. • Verizon offers residential long-distance plans in which the cost per minute declineswith the number of minutes. • Volume discounting is as prevalent, if not more prevalent, in wholesale and business-to-businessselling. Table 4.4 shows that the sellers offersignificantly lower unit prices to customers who are buying more units.

36. Tactics for Price Differentiation 7. Volume Discounts: • There are at least three reasons why companies offer volume discounts: • Transaction or order costs. If there are substantial costs associated with fulfilling anorder independent of size, the order cost per unit will decrease as the size of theorder increases. Therefore, it may make sense for the seller to charge a lower price per unit for large orders. Ex:A software seller has a fixed cost of $1,000 per installation and a variable costof $40 per user. His total cost for an installation with 10 users is $1,400, or$140/user, compared with a total cost of $5,000, or only $50/user, for aninstallation with 100 users. Even if large users and small users have the sameprice sensitivity, it will make sense to charge less per user to large users.

37. Tactics for Price Differentiation 7. Volume Discounts: 2. Decreasing marginal utility: In many cases, the marginal utility to a buyer decreasesas the number of units purchased increases. A hot and thirsty customer walkinginto a convenience store places more value on the first can of cold soft drink thanshe does on the second. Decreasing marginal utility is also often seen in business-to-business sales. Ex: A company wants to purchase copies of a financial analysis software package forits employees to use. The company isable to determine that there are 500 employees who would use the package andthat the value to the company from their access is uniformly distributed between0 and $250 per year. This means that the software vendor is essentiallyfacing a “demand curve” of d(p)=500-2p for the number of copies it can sellat a single annual license fee to this company. The vendor can set a single annuallicense fee of $125 and sell 250 copies for total revenue of $31,250—themaximum revenue from a single price. However, if it adopted a two-tier pricingscheme and licensed the first 250 copies for $125 each but dropped the priceto $75 for each additional sale, it will sell an additional 100 copies at $75 for additional revenue of $7,500.

38. Tactics for Price Differentiation 7. Volume Discounts: 3. Increasing price sensitivity: Customers purchasing larger amounts are often moreprice sensitive than customers purchasing smaller amounts. Corporate purchaserswho buy large volumes are likely to be following a formal procurement process inwhich they carefully compare alternatives. A contractor who spends millions of dollarson galvanized pipe annually is much more likely to spend time and effort findinga good deal than a homeowner who is buying a length of pipe at the hardware store.Volume discounting is one way that a seller can differentiate among large-volume,highly price-sensitive buyers and smaller-volume, less price-sensitive buyers.

39. Tactics for Price Differentiation 7. Volume Discounts: • There are numerous schemes for volume discounting, many of which are often groupedunder the general category of nonlinear pricing. • Thenonlinear refers to the fact that the totalprice paid is not a linear function of the number of units ordered as it would be with a singleprice. • Figure 4.3 shows how the total order price for St. Louis Commerce Magazine varieswith the number of copies ordered.

40. Tactics for Price Differentiation 7. Volume Discounts: • The sharp downward jumps are at the price-points whendeeper and deeper discount levels kick in. Without the volume discounts, the total costwould be a linear function of the number ordered. • This type of discounting has the well-knowndrawback that the price-jumps can create a situation in which a buyer can actuallypay less money by purchasing more units. Thus, an order of 250 copies would cost $562.50while an order of 260 copies would only cost $455.00. In essence, the magazine is paying thebuyer almost $9.00 apiece to take an additional 10 copies. Despite this seemingly irrationalaspect, this type of volume discount is extremely common in practice. • Volume discounts can either be applied to an entire order, or incrementally. • In incremental discounting, additional discounts areonly applied to additional units—not to the entire order. A common example is:“Buy one, get the second at half price.” In this case,the discount is applied only to the second unit purchased, not to the first. • Incremental discountsavoid the downward price jumps seen in Figure 4.3. However, they can also beharder to communicate to buyers.

41. Tactics for Price Differentiation 7. Volume Discounts: • Volume discounts are often applied based on total volume of business over some period,rather than on size of a single order. • This is often accomplished in consumer markets by “frequentbuyer” schemes such as the airlines’ frequent-flyer programs. • Somelocal coffee shopkeeps track of thepurchases and gives every 10th cup free. The stated purpose of suchprograms is to reward loyal customers, but they also serve the purpose of lowering the realprice seen by frequent purchasers, who are likely to be more price sensitive. • This practice isextremely common in business-to-business sales, in which discounts are often applied basedon sales volume in a quarter or other period.

42. Tactics for Price Differentiation 7. Volume Discounts: • A manufacturer (suchas Hewlett-Packard) selling through the distributor will offer a progressive end-of-quarterrebate based on how much of their product the distributor has sold during the quarter. Forexample, Acme Electronics might offer a 0.5% rebate if the distributor sells between $1 millionand $1.499 millionworth of Acme products during the quarter, a 0.75% rebate if the distributorsells between $1.5 million and $1.999 million, and a1%rebate if the distributor sellsover $2 million. • In freight transportation, a carrier will often offer a higher discount if a shippercommits to a higher volume of business over some future period. • Combining different terms and discount structures can lead to an extremely wide varietyof volume discount schemes. All of these schemes are designed to exploit the decreasing marginal valueof purchasers and/or the higher price sensitivity of large purchasers.

43. Tactics for Price Differentiation 7. Volume Discounts: • Like any market segmentation scheme, volume discounts provide opportunities for arbitrage. • For example, an enterprising arbitrageur could purchase50 copies of Opera software at $33.00 and then resell them at $38.00, undercutting thesingle-copy list price of $39.00. • Software companies often require users to register to receivefuture support and maintenance, in part to avoid the possibility of such arbitrage. • In other cases, bulk-and-volume-purchasers are required to signa contract that prohibits them from reselling for profit. • Wholesalers suchas the St. Louis Commerce Magazine should presumably be largely indifferent to arbitragesince they are using volume discounts to encourage the largest number of sales possible.

44. Calculating Differentiated Prices • If market segments are completely independent (i.e., no cannibalization) and the seller facesno capacity constraints, then calculating differentiated prices is quite simple—the sellersimply finds the contribution-optimizing price for each segment. • This is the right approachwhether the underlying differentiation is based on channel, geography, or pure group pricing. Ex:An electronics distributor sells portable MP3 players through its exclusive retailoutlets and on its Web site. The unit cost for each MP3 player is $200. The additionalcost per sale through the Internet is $35.00, including shipping, but $70through the retail stores. Through price testing, the distributor has discoveredthat price elasticity is 2.5 for Internet customers versus 2.2 for retail customers. The distributor calculates the contribution-maximizingprice as: (2.5/1.5) *($200 +$35) =$392 for Internet sales and (2.2/1.2) *($200 +$70) =$495 for retail sales.

45. Optimal Pricing with Arbitrage • Unfortunately for sellers, perfect price differentiation is usually impossible • Cannibalizationis likely whenever customers cannot be perfectly segmented according to willingness to pay. • Arbitrage is likely whenever a third party can purchase the product at a low price and resellit at a high price. • Regional pricing is subject to arbitrage whenever a product can be purchasedin a low-price region and transported cheaply to be resold at a higher price elsewhere. • For this reason, global companies often set price bands for various markets to avoidresales from low-price countries that would cannibalize sales in higher-price countries. Ex:A computer chip manufacturer finds that the contribution-maximizing pricesfor his chips are $2.54 in the United States and $2.43 in Brazil. However, if itcosts $0.08 per unit to ship chips from Brazil to the United States, he will not beable to charge those prices due to the potential for arbitrage between the twocountries. He needs to set prices for both countries that do not vary by more than $0.08.

46. Optimal Pricing with Arbitrage • The regional pricing problem with arbitrage can be formulated as a constrained optimizationproblem. • Assume that a manufacturer is selling a common product to n differentlocations. These could be cities or regions, but for purposes of discussion we will considerthem to be countries. • The delivered cost (including transportation) in country i is ci. • The cost of an arbitrageur to transport the product from country i to country j is aij. • Toavoid arbitrage, the supplier needs to set prices such that pj ≤pi+ aijfor each i and j. Otherwise,the supplier faces the possibility that an arbitrageur will purchase product in countryi, transport the product to country j, and sell it for a price pˆj. If pˆj< pjand pˆj> pi+ aij,then the arbitrageur can undercut the supplier in country j while still turning a profit. • It isclear that a contribution-maximizing supplier would usually like to avoid this situation. • Let pibe the price in country i and di(pi) be the price-response curve faced by the supplierin country i. Then the problem of optimizing international prices under the possibilityof arbitrage can be formulated as:

47. Optimal Pricing with Arbitrage

48. Optimal Pricing with Cannibalization • To analyze differentiatedpricing with cannibalization, let’s return to the case in which we divided widget customersinto those with w.t.p.≥$7.00 and those with w.t.p. < $7.00. • We assumed before that the companycan perfectly distinguish between those customers willing to pay more than $7.00 and thosewilling to pay less than $7.00 and can charge the optimal price to each group. • What if someof the higher-willingness-to-pay customers find a way to buy at the lower price? • Let α be thecannibalization fraction—the fraction of higher-willingness-to-pay customers who find away to buy at the lower price. • α=0 corresponds to the case of perfect differentiation—none of the high-w.t.p. customers buy at the lower price—while α=1 corresponds to nodifferentiation—all of the customers buy at the lower price. • Values of α between 0 and 1represent different segmentation efficiencies.

49. Optimal Pricing with Cannibalization • Given a value of α, the price-response curvesfor each of the two segments are given by: • The second term in the equation for d2(p2) reflects the fact that there are 4,400 total customerswith a w.t.p. greater than $7.00 and that a fraction a of them will find a way to buyat the lower price, p2. • To find the values of p1 and p2 that maximize total contribution, we need to solve the optimization problem:

50. Optimal Pricing with Cannibalization • The prices that maximize total contribution in this case are: • When α=0 (no cannibalization), p*2=$6.00. • As α increases, cannibalization increases andp*2 increases as well. • This corresponds to intuition—the more our low-price product is cannibalizingour high-price product, the higher we need to price the low-price product tomaximize total contribution. • When α=0.36 (i.e., 36% of the high-w.t.p. customers find away to pay the lower price), the optimal low price has risen to $7.00. At this point, none ofthe low-w.t.p. customers are buying any more (since their w.t.p. is less than $7.00) and theonly low-price customers are cannibalized high-w.t.p. customers.