Price Differentiation

Transcription

1 Price Differentiation Page Outline Price Differentiation: Limitations and Tactics Volume Discounts Pricing with Arbitrage and Cannibalization Consumer Welfare Based on Phillis (005) Chater 4

2 Price differentiation: Different rices for different customers Price Differentiation For exactly the same roduct For a slightly different roduct By customer grou» UTD students vs. staff By roduct version» Older version vs. newer version By geograhy» US rices vs. international By distribution channel» E-commerce vs. brick & mortar E-cigarette or non E-cigarette section? Page For $ extra, would you like us to make it look like the one in the hotograh? Price differentiation requires segments What are the segments? How do they differ from each other? Do they remain the same over time? Are there customers switching segments? Cannibalization Can a roduct sold to a segment end u in another? Arbitrage How can we create barriers between segments?

3 Price Differentiation: À la Carte Consider lunches at Nazar restaurant in Addison. Suose that the demand function d()=00-8 and the cost c=$5 er lunch. The total contribution (rofit) [ =(-5)(00-8)] maximizing rice solves [-6+40=0] and it is $8.75=$40/6. The demand at = 8.75 is [30=00-8*8.75], the rofit is $.5. Page 3 00 d() 30 $.5 30 or more eole are willing to ay >$

4 Price Differentiation: Lunch Buffet and À la Carte Demands Nazar restaurant divides its market into two: those aying below and above $7. The restaurant offers a lunch buffet for low willingness to ay customers. [44=00-8*7] eole are willing to ay more than $7. Market size for high-ayers is 44 and for low-ayers is 56. w() /.5 D(-W()) Lunch Buffet 7 7 À la Carte.5.5 d ( ) D ( W ( )) d ( 7) min{44,(00 8 ) 00-8 for 7 ( ) D ( W 56 ( )) for 0 44 (8 56).5; } for 0 (56 8 ) 7; ignore ignore art of.5 for 0 7. we write x 7. number.5 Toindicate the ositive x Page 4 max{0, x}.

5 Lunch Buffet and À la Carte Demands via Pictures Page 5 w() /.5 Lunch Buffet À la Carte D(-W()) Lunch Buffet 7.5 À la Carte 7.5

6 00 56 Lunch Buffet and À la Carte Demands Segment Demands via Pictures 56 Lunch 44 Buffet 44 0 À la À la Lunch Carte Carte Buffet Demand functions from above d = 00 8 for 7.5 and d = 56 8 for 0 7 Page 6.5 Before segmentation w(x) 7 Lunch Buffet After segmentation w l (x) 5.5 w a (x) À la Carte 0 WTP=x WTP l = x 7 7 WTPa = x.5 Remark: If you know about conditioning in robability, note that segmentation is conditioning of random variable WTP: WTP l [WTP WTP 7] and WTP a [WTP WTP 7]

7 Price Differentiation: Lunch Buffet at $6 and À la Carte at $8.75 Nazar restaurant continues to charge an average of $8.75 for à la cart service. Still d (=8.75)=30 eole are willing to ay more than $8.75 and bring a rofit of.5=30(8.75-5) er lunch time. Suose that the restaurant rices the lunch buffet at $6. Then the buffet demand turns out to be d (=6)=8 eole. This brings in an additional rofit of 8=8(6-5) er lunch time. The rofit increases from $.5 to $0.5 er lunch time. This difference can draw the fine line between success and bankrutcy in the restaurant business. Page 7 00 d()= Lunch buffet $8 À la Carte $

8 Price Differentiation: Lunch Buffet at $6.5 and À la Carte at $9 With $9 for à la cart service, demand is d (=9)=8 which brings a rofit of =8(9-5) er lunch time. With $6.5 for lunch buffet, demand is d (=6.5)=4 which brings a rofit of 6=4(6.5-5) er lunch time. These rices under rice differentiation increase the rofit to 8 from.5 under no differentiation. Note that lower rices on the revious age yielded higher total rofit. Some rices under differentiation are better than others. Page 8 00 d()= Lunch buffet $6 À la Carte $

9 Price Differentiation: Lunch Buffet at $5.5 and À la Carte at $8.5 With $8.5 for à la cart service, demand is d (=8.5)=3 which brings a rofit of =3(8.5-5) er lunch time. With $5.5 for lunch buffet, demand is d (=5.5)= which brings a rofit of 6=(5.5-5) er lunch time. These rices increase the rofit from.5 to 8 while a rofit of 0.5 is ossible with rices of $6 and $8.75. Price differentiation alone (without otimization) is a rofitable strategy. Page 9 00 d()= Lunch buffet $6 À la Carte $

10 Perfect Price Differentiation is an Utoia Page 0 There are limitations to achieve erfect rice differentiation Imerfect segmentation: Are you willing to ay high or low? This is hard to answer on your own. Your willingness to ay can change deending on various factors, some are objective (such as income) and other are subjective (such as mood).» Tactics to identify and segment the customers are very imortant. Cannibalization: Customers with high willingness to ay may discover the low cost alternative and urchase that alternative. All of the À la Carte customers at Nazar restaurant may buy the lunch buffet. Then the lunch buffet demand d (=6)=44 due to high aying customers and the lunch buffet demand d (=6)=8 due to low aying customers. Or 44+8=5=00-8*6. This gives a rofit of only 5=5(6-5) which is far below the original rofit of.5 without rice differentiation.» Tactics to identify and segment the customers are very imortant. Arbitrage: Third arty arbitrageurs buy the roduct at low rice and sell it to high willingness to ay customers.» Tactics to identify and segment the customers are very imortant. When segmentation fails due to customer effort, it is cannibalization. When it fails due to third arty effort, it is arbitrage.

11 Tactics to Segment Customers Grou ricing: Student discounts Need Unambiguous indicator of grou membershi: UTD-ID card Exerience Dallas Program of Comet Center High correlation between grou membershi and willingness to ay Difficult to trade of roduct/services among customers to avoid cannibalization and arbitrage. Services are difficult to trade. Legally and culturally acceted grouing: Lower health care remiums for nonsmokers? Higher health care remiums for re-existing condition of a subscriber. Page Channel ricing Low cost distribution in some channels like Internet Tablet users are imulse buyers who buy in large quantities. Tablet users conversion rate (=# of urchases/# of visits) = 4-5%. Traditional PC users conversion rate=3%. Tablet users lace 0-0% larger orders than PC users. ipad uses as but not Flash software when browsing. Source: Tablets: Ultimate Buying Machines by D. Mattioli in WSJ, Se 8, 0. Customer s channel choice indicates willingness to ay: Outlet stores. Regional ricing Costs are higher in affluent areas so are the rices. Willingness to ay are higher in affluent areas so are the rices.

12 Tactics to Segment Customers Page Couoning and Self-Selection Those willing to make an extra effort to get the discount are rice sensitive Manufacturer issued mail-in discount/rebate couons Not everybody mails the couon Sometimes no rebates are given even after couon is mailed in make the effort Versioning Using minor differences between version of roducts to exloit rice sensitivity Adding minor features to create a suerior good from an inferior one Proctor -Silex iron ready button Deleting minor features to create an inferior good from a suerior one Disabled math rocessor of Intel 486DX rocessor Creating roduct lines Software with basic-ro-remier-enterrise editions Time-based differentiation Faster delivery costs more

13 Volume Discounts Page 3 Per unit rice of an item decreases when many more items are urchased. Why to discount? Cost based ricing: Cheaer to roduce/transort items in big quantities. o Recall Millie s cider sho and allocation of rent to cider bottles. If Millie sells more ciders, she allocates less of her rent to a single cider bottle. Value based ricing: Marginal utility decreases for the customer. o First glass of the water is the most valuable when you are thirsty. Indicator of rice sensitive customers: These customers buy in big quantities. o Costco customers are more rice sensitive than Target customers.

14 Two Discounting Schemes Page 4 Cost/Unit Total Cost $3 $.96 $.9 All-unit quantity discount Discount is alied to every unit 5,000 0,000 5,000 0,000 Purchase Quantity Purchase Quantity Cost/Unit Total Cost $3 $.96 $.9 Marginal-unit quantity discount, or Incremental quantity discount Discount is alied to additional units 5,000 0,000 5,000 0,000 Purchase Quantity Purchase Quantity Other uses of discounting schemes are in OPRE 6366 Suly Chain Management.

15 Decreasing Marginal Value of Number of CPA Certified Emloyees CPA is a common accounting certification. A community college offers CPA classes for comanies at the remises of the comanies. This is convenient for the ersonnel of the comanies. A certain bank has 50 emloyees at the level of associate, manager and senior manager, assistant director who consider taking the CPA classes if they are offered at the bank s remises. The accounting ersonnel at the level of director and above already have a CPA. The utility of the CPA class for emloyees are not the same. An assistant director requires a CPA to be romoted to be a director so the utility of the CPA class is high for him/her. Associates can be romoted all the way u to an assistant director over time without a CPA so the utility of the CPA class is low for them. The community college estimates the utility of the class to range uniformly over $0-$500 for the emloyees. Using the number of emloyees interested in CPA and its utility estimate, the community college forecasts the demand to be D()=50(-/500)=50-/50. Revenue R()=50- /50 so the revenue maximizing rice is found from solving 50-/5=0 and it is $50. Page 5

16 Cost of CPA Class by an Marginal-unit Discounting Page Revenue $350 Revenue $350 D()=50-/50 50 D()=50-/ With the rice of $50 er emloyee, 5 bank emloyees take the CPA class. Community college makes a revenue of $3,50 by offering classes at the remises of the bank. For the community college, the cost of offering class to 5 or to 30 eole is identical. The college comutes that if the rice were $000, 30 eole would take the course. This gives a revenue of only $30,000. To obtain more than the revenue of $3,50 and to enroll 30 eole, the college offers a volume discounting scheme: Each of the first 5 eole ay $50 Each additional erson ays $000. This discounting scheme rovides the bank with an additional revenue of $5000, reresented by the red box on the left.

17 Market Segmentation vs. Volume Discounting Page 7 Pictures that have boxes reresenting revenue/rofit underneath the demand curve are common in market segmentation and volume discounting. Each box indicates some more revenue. D() If all we are doing with both market segmentation and volume discounting is inserting boxes under the demand curve, can we aly both in the same buyer-seller context? Either you say yes, Or you say no and exlain the difference(s) between the contexts.

18 Calculating Differentiated Prices by Eliminating Arbitrage Page 8 Arbitrage haens when a lower riced roduct i is transorted to be sold as a higher riced roduct j a ij j transortation cost a ij ugraded to be sold as a higher riced roduct j i a ji ugrade cost a ij stocked to be sold as a higher riced roduct j inventory holding cost a ij Arbitrage can be eliminated with constraints j i + a ij on the rice decision variables. and i j + a ji Constraints are called arbitrage elimination constraint. The constraint makes the cost of using arbitrage i + a ij higher than the rice i.

19 Motivating Examle of Chis Page 9 Intel chis are sold both in US (country ) and in Brazil (country ). The demand functions are given by d ) a b and d ( ) a b ( The transortation cost er chi is $0.08 between these countries. With the constant sloe demand curves (lines), the revenue maximizing rices are given as a.54 and a b b Since the constraint is not satisfied, an arbitrageur can buy chis in Brazil and transort them to US to sell them in US. We need to jointly otimize rices in US and Brazil to eliminate arbitrage rather than searately as we have done above. but 0 a

20 Quadratic Program Formulation to Eliminate Arbitrage Page 0 When we have linear demands d i ( i ), the rofit ( i -c i )d i () is a quadratic function (it is a olynomial of degree ). Summing these rofits over N regions, we still have a quadratic objective for the joint otimization roblem: max... N N i i j ( subject to i c ) d ( ) i i a ij i for i j 0 for i N i N This is a quadratic rogramming roblem and it can be solved efficiently with algorithms similar to those used to solve linear rogramming roblems.

21 Solving Quadratic Program for N= When there are two regions (US and Brazil), N= and we can solve the quadratic rogram without a software. max, subject to ( a, b 0 a ) and ( a If the searately found rices satisfy the arbitrage eliminating constraints, they are otimal and we sto. Else let the region with higher rice be and the other be, we have b ) a Page 0 0 a and 0 In the otimal solution, the violated constraint must be satisfied as an equality, so we can let a and for some that weshall find next This rearameterization reduces the number of decision variables to one and hence simlifies the solution rocedure. 0 a

22 Solving Quadratic Program for N= After rice rearameterization, the constraints will hold and we focus on the objective max a b ( a a ( a a )( a ) a b a b ( a b b b )) 0 ( a b ) which yields this can be shown tobe nonnegative by using the violated constraint a This argument also leads whose derivative is to Page Plugging in the arameters of US-Brazil ricing roblem, we obtain a a b (0.08) b a b and.457

23 Calculating Differentiated Prices by Incororating Cannibalization Market segmentation often assumes that markets are erfectly segmented in that higher wt (willingness to ay) customers do not buy at lower rice. Recall Nazar restaurant, some à la cart customers can buy lunch buffet so cannibalization can haen. Suose that 0 α ercentage of high wt buy at lower rice. Page 3 wt Buy à la cart -α Buy à la cart if rice is aroriate Customer wt >7 α Buy buffet wt < Do not buy from Nazar Cannibalization alters the demands from d d ( ) min{44,(00 8) ( ) (56 8) } to d ( ) ( ) min{44,(00 8) d ( ) (56 8) 44 }

24 Calculating Differentiated Prices by Incororating Cannibalization Page 4 The otimal rice for à la cart service is found by maximizing ( 5)( ) min{44,(00 8 } ( The otimal rice satisfies ( )(40 6 ) 5)( )(00 8 ) 0, so ) for 7.5 The otimal rice for lunch buffet is found by maximizing ( 5)((56 8 ) 44 ) ( The otimal rice satisfies ( )( ) ) 0, so for 0 7 min{7,6.75 }.

25 Effect of Cannibalization on Total Profit Page 5 Suose α=0., rofit from à la cart service is (8.75-5)(-0.)(00-8(8.75))=0.5 Then the rofit from the lunch buffet is (6.75-5)(60.4-8(6.75))= Profit with otimal segment rices under cannibalization α=0. is 4.55 The same rofit without cannibalization is 0.5 and without segmentation is.5. Suose α=0., rofit from à la cart service is (8.75-5)(-0.)(00-8(8.75))=90 Then the rofit from the lunch buffet is (6.55-5)(64.8-8(6.55))=9. Profit with otimal segment rices under cannibalization α=0. is 09.. Profit of 09. is less than.5 obtained without segmentation. Cannibalization can quickly wash away the benefits of segmentation. Should the cannibalization deend on the rice differential -?

26 Best Segmentation Nazar restaurant divided its market into two: those aying below and above $7. Is this value of v=7 the best rice to segment the market? We need to generalize our revious analysis. Page 6 w() /.5 D(-W()) Lunch Buffet v À la Carte.5 d ( ; v) D ( W ( )) d.5 v ( v) v 8(. 5-) for v.5 ( ; v) D ( W ( )) v v 8( v-) for 0 v v.5

27 Best Segmentation Page 7 Formulation of the segmentation roblem max max( v 5)(00 8 v ) max( 5)(8 8 ) for v.5 and 0 For a fixed v, the otimal rices are max{ v,8.75} and min{ v,( v Since v>5, =(v+5)/. The objective then is 5)/ } v max (max{ v,8.75} 5)(00 8max{ v,8.75}) (min{ v,( v 5) / } 5)(8v 8min{ v,( v 5) / }). v This objective can be evaluated in Excel for different values of v to find otimal v. See best_segmentation.xlsx on the course web site. The otimal segmentation haens with v=$0.

28 Consumer Surlus Page 8 For each consumer, the ositive art of the difference between wt and the roduct rice is the surlus: (wt-) +. Summing this u for all consumers, we find total consumer surlus. Grahically, D() Consumer Surlus More Consumer Surlus Less Consumer Surlus l h Consumer surlus is ositive only for the consumer buying the roduct. It can be increased by selling to more customers with a lower rice; see the middle figure above. It can be decreased by selling to the same number of customers with a higher rice; see the figure on the right above.

29 Price Differentiation Page 9 Summary Price Differentiation: Limitations and Tactics Volume Discounts Otimal Pricing with Arbitrage Cannibalization Market segmentation Consumer Welfare

30 Legally Eliminate Arbitrage Page 30 For each emty beverage container Michigan State offers 0 cents Other states do not offer as much: New York State offers 5 cents. It is temting to collect containers in other states to bring them to Michigan and to deosit them for 0 cents in grocery stores such as Save Plus Suerstore in Pontiac, The Larosa Market in Sylvan Lake and Value Foods in Ysilanti, The Farmer John, Savemart Food Center and Americana Foods, the last three in Detroit. Can smuggling across states is illegal as it frauds Michigan Bottle Deosit Fund set u for environmental clean u. A o-can smuggling ring has been arraigned in Michigan. 5 man ring face charges that include maintaining a criminal enterrise (0 year felony) and fraud (5 year felony). Susects Arraigned In Po Can Smuggling Ring, Se 6, 007. htt:// On a lighter side, watch a 996 eisode of Seinfeld: The Michigan Deosit Bottle Scam from You Tube htt:// Gist of the scam: Newman, who has sent days trying to calculate a rofit to the deosit scheme, realizes that there will be a surge of mail the week before Mother s Day (the "mother of all mail days") to be sorted in Saginaw, Michigan. He tells Kramer that he signed u for a mail truck that would carry sillover mail from the other four main trucks, leaving lenty of sace left over in theirs for bottles and cans to refund in Michigan. Kramer realizes that by avoiding truck rental fees, Newman has found a loohole and they set off collecting cans and bottles around the city. For the info, thanks to Seinfeld fan Osman Kazan, DemReMan 0 Teaching Assistant.