Price Differentiation

Transcription

1 Price Differentiation Page Outline Price Differentiation: Limitations and Tactics Volume Discounts Pricing with Arbitrage and Cannibalization Consumer Welfare Prof. Metin Çakanyıldırım used various resources to reare this document for teaching/training. To use this in your own course/training, lease obtain ermission from Prof. Çakanyıldırım. If you find any inaccuracies, lease contact for corrections. Udated in Fall 08

2 Price differentiation: Different rices for different customers / segments 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» Comuter vs. comuter; see next age 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? 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 Product Pick-u Location: SFO Time: 3:30, May 0, 8 Return Location: SFO Time: 6:00, May 3, 8 Standard SUV Channel Deendent Pricing Avis Car Rental Channel deendent deiction of booking stes Page 3 Booking Time: 40 hours in advance Channels:. Mac &. Windows Simultaneous booking Channels & yield base rates of $85.60 $67.04 Any other content difference? Channel deendent deiction of booking stes Ultimate question: Cheaer channel?

4 On May 5, 08 $9 A B C D 3 G H J K L Q R $7 $9 $30 6 $50 $94 $30 $30 W X Violins Piano 4 Center Line 5 0 Cellos $9 Version Deendent Pricing Dallas Symhony Product: Scheherazade Concert June 9, 08 Versions: Locations on Orchestra Floor Data from htts:// Price based quality deduction Acoustics: Cheaest rice on the sides & front Staged back rows: W,X highest rice at $30 Inconsistent rices. Center is not the most exensive: L6 is $7. G5 and G0 are on the same row and symmetric with resect to the center line, yet riced differently at $7 and $50 3. Non-monotone, non-convex, non-concave: C is $50; D is $30; Q is $7; R is $30; 4. D- are $30, a high rice island in the middle of low rices Page 4 Acoustics must be the best in the center For acoustics, watch The Myerson (Concert Hall) Dance htts:// Quality of acoustics Concave, maximized at the center Droing towards the sides, front & back Eye-contact: Cellist: Orchestra floor, 4. row, left of center Violinist: Orchestra floor, 4. row, right of center Pianist hands: Dress circle, left of center Conductor Van Zweden: Grand tier, highest seats Question: Lowest rice, best acoustics?

5 On Jun, 08 Center Line $9 Version Deendent Pricing Dallas Symhony Page 5 A B C D G H J K L $7 $50 Product: Scheherazade Concert Jun 9, 8 Versions: Locations on Orchestra Floor Over a week from May 5 to Jun, some seats are sold D, D are sold G0 is sold Prices and regions on Jun are the same as those last week on May 5: $9, 50, 7, 94, 30. Q R $94 $9 $30 $30 W X $9 Question: Reduce ticket rices?

6 On Jun 8, 08 AA BB CC DD A B C D G H J K L $8=9- $69=7-3 $48=50- Version Deendent Pricing Dallas Symhony Product: Scheherazade Concert Jun 9, 8 Versions: Locations on Orchestra Floor Over a week from Jun to Jun 8, more seats are sold Regions on Jun 8 are the same as those last week on Jun Question: Reduce ticket rices? Answer: Yes, by ${,,3,?,5} Page 6 Q R Orchestra Center $??=94-? Prices are now $8, 48, 69,??, 5. No seat left in reviously $94-region, so no rice information Estimate the rice of $94-region a) 94, b) 93, c) 9, d) 9, e) 90 W X $5=30-5

7 Price Differentiation: À la Carte Consider lunches at Nazar restaurant in Addison. Suose: the demand dd() = 00 8 and the cost cc = $5 er lunch. The total contribution (rofit) [ =(-5)(00-8)] maximizing rice solves [-6+40=0] & it is $8.75=$40/6. The demand at = 8.75 is [30=00-8*8.75], the rofit is $.5. Page 7 00 d() 30 $.5 30 eole are willing to ay $

8 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. Page 8 w() /.5 Lunch Buffet À la Carte For 7.5 dd = DD WW = For 0 7 dd = DD WW = = = 56 8 D(-W()) 00 WWWWPP uniform over [0,7] 7.5 WWWWPP uniform over [7,.5] d ( ) = D ( W ( )) ( 7) = = min{44,(00 8) } for 0.5 = 00-8 for 7 + = 44 (8 56).5; ignore + < d ( ) = D ( W ( )) = 56 = (56 8) for = 56-8 for 0 7; ignore > 7. xx + = max{0, xx} indicates the ositive art of number xx

9 Lunch Buffet and À la Carte Demands via Pictures Page 9 w() /.5 Lunch Buffet À la Carte For 7.5 dd = 44 7 = For 0 7 dd = 56 0 = D(-W()) Lunch Buffet 7.5 À la Carte 7.5

10 Lunch Buffet Lunch Buffet and À la Carte Demands Segment Demands via Pictures À la Carte For 7.5 dd 56 = 00 8 À la Carte For 0 7 dd = 56 8 Lunch Buffet Page Before segmentation w(x) 7 ww ll (xx) Lunch Buffet After segmentation 5.5 ww aa (xx) À la Carte 0 WTP=x WWWWPP ll = xx 7 Remark: If you know about conditioning in robability, segmentation is conditioning of random variable WTP: WWWWPP ll [WWWWWW WWWWWW 7] and WWWWPP aa [WWWWWW WWWWWW 7] 7 WWWWPPaa = xx.5

11 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 dd ( = 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 dd ( = 6) = 8 eole. This brings in an additional rofit of 8=8(6-5) er lunch time. The rofit $.5 $0.5 er lunch time. This difference can draw the fine line between success and bankrutcy in the restaurant business. Page 00 d()= Lunch buffet $8 À la Carte $

12 Price Differentiation: Lunch Buffet at $6.5 and À la Carte at $9 Page With $9 à la cart, demand is dd ( = 9) = 8 brining rofit of =8(9-5) er lunch time. With $6.5 buffet, demand is dd ( = 6.5) = 4 bringing 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. Lower rices on the revious age yielded higher total rofit. Some rices under differentiation are better than others. 00 d()= Lunch buffet $6 À la Carte $

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

14 Perfect Price Differentiation is an Utoia Page 4 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 dd ( = 6) = 44 the market size due to high aying customers and the lunch buffet demand dd ( = 6) = 8 due to low aying customers. Or 44+8=5=00-8*6.» This gives rofit of 5=5(6-5) with differentiation the original rofit of.5 without 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.

15 Tactics to Segment Customers Pricing by Grou, Channel and Region Page 5 Grou ricing: Student discounts Unambiguous indicator of membershi: UTD-ID card Exerience Dallas Program of Comet Center High correlation between grou membershi & willingness to ay Legal & ethical accetance of grouing for health insurance Higher remiums for re-existing (genetic) condition Higher remiums for smokers. I am a honor student! I want 0% extra credit Channel ricing Channel choice indicates willingness to ay: Outlet stores. Tablet users are imulse buyers who buy in large quantities. Conversion rate = # of urchases/# of visits Tablet users = 4 5% Traditional PC users = 3% ipad uses as but not Flash software when browsing. Tablet users lace 0-0% larger orders than PC users. Source: Tablets: Ultimate Buying Machines by D. Mattioli in WSJ, Se 8, 0. I handwrote hw solutions for 0% extra credit I did my hw in class for 0% extra credit Regional ricing Costs and willingness to ay in affluent areas, so rices. Chea video games in Estonia; Chea Sotify membershi in Turkey. 3 versions of a cartoon

16 Couoning & Self-Selection Tactics to Segment Customers Couons, Versions, Seed Those willing to make an effort for the discount are rice sensitive Manufacturer issued mail-in discount/rebate couons Not everybody mails the couon Sometimes no rebates even after couon is mailed in Make the effort, follow u A couon towards 0% extra credit Page 6 Versioning Minor differences among versions to exloit rice sensitivity Adding minor features: a suerior roduct an inferior one Proctor -Silex iron ready button Deleting minor features: an inferior roduct a suerior one Disabled math rocessor of Intel 486DX rocessor Creating roduct lines Software with basic-ro-remier-enterrise editions Seed (time-based) differentiation Faster delivery costs more -day Amazon delivery vs. 3-day Amazon delivery Submitting two solutions for the same hw question, Please, 0% extra credit Submitting my hw day in advance! Pls, 0% 3 more versions

17 Volume Discounts Page 7 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.

18 Two Discounting Schemes Page 8 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.

19 Decreasing Marginal Value of Number of CPA Certified Emloyees Page 9 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 college forecasts the demand to be DD() = 50( /500) = 50 /50. Revenue RR() = 50 /50 so the revenue maximizing rice is found from solving 50 /5 = 0 and it is $50.

20 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, otimize this rice? This discounting scheme rovides the bank with an additional revenue of $5000, reresented by the red box on the left.

21 Market Segmentation vs. Volume Discounting Page 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. Hint: Does the resence of the box above deend on the box below?

22 Calculating Differentiated Prices by Eliminating Arbitrage Page Arbitrage haens when a lower riced roduct i is transorted to be sold as a higher riced roduct j aa iiii j transortation cost a ij ugraded to be sold as a higher riced roduct j i aa jjjj 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 jj ii + aa iiii on the rice decision variables. and ii jj + aa jjjj Constraints are called arbitrage elimination constraint. The constraint makes the cost of using arbitrage i + a ij higher than the rice i.

23 Motivating Examle of Chis Page 3 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 a = + a = =.54 and = =.43 but =.54 >. 5 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. 0

24 Quadratic Program Formulation to Eliminate Arbitrage Page 4 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.

25 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 5 > + a and + a In the otimal solution, the violated constraint must be satisfied as an equality, so we can let = + a and = for some that we shall find next This rearameterization reduces the number of decision variables to one and hence simlifies the solution rocedure. 0

26 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 whose derivative is this can be shown to be nonnegative by using the violatedconstraint a This argument also leads to < = > Page 6 Plugging in the arameters of US-Brazil ricing roblem, we obtain = + a + b = 0000(0.08) = =.537 and =.457 a b a b = =.457

27 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 7 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 d ( ) = ( α) min{44,(00 8) ( ) = (56 8 ) α + }

28 Calculating Differentiated Prices by Incororating Cannibalization Page 8 The otimal rice for à la cart service is found by maximizing ( 5)( α) min{44,(00 8 } = ( The otimal rice satisfies ( α)(40 6 ) + 5)( α)(00 8 ) = 0, so ) = for 7.5 The otimal rice for lunch buffet is found by maximizing ( 5)((56 8 ) α ) = ( The otimal rice satisfies ( α 6 5)( α 8 ) ) = 0, so for 0 7 = min{7,6 +.75α }.

29 Effect of Cannibalization on Total Profit Page 9 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 -?

30 Best Segmentation Obtain Demands The restaurant divided its market into two: those aying below and above $7. Is this value of vv = 7 the best rice to segment the market? What is the best segmentation value vv?.5 00 ww() Lunch Buffet DD( WW()) À la Carte d ( ; v) = D ( W ( )) d.5 v ( v) = v = 8(. 5-) for v.5 ( ; v) = D ( W ( )) v 0 = 00.5 v = 8( v-) for 0 v Page For vv.5 dd ; vv = 00 8 For 0 vv dd ; vv = 8vv 8 vv.5 For 0 vv.5 dd ; vv = 00 8 dd ; vv = 8vv 8

31 Best Segmentation Obtain Otimal Segmentation Value & Prices Formulation of the segmentation roblem Outer maximization over the segmentation value vv: max { } vv Inner maximizations over rices and : max max vv and max For 0 vv.5 dd ; vv = 00 8 dd ; vv = 8vv 8 max max 5 8vv 8 for 0 vv.5 Page 3 Inner maximizations: For a fixed vv, the otimal rices are = max{vv, 8.75} max 8 + ( ) 500 yields = 0 = min vv, vv+5 If 0 vv.5, then 0 = min vv, vv+5 Since vv cc = 5, we obtain vv vv+5 The objective then for 0 vv.5 is max vv max{vv, 8.75} max{vv, 8.75} + vv vv 8 vv + 5 This objective can be evaluated in Excel for various vv; see best_segmentation.xlsx. Segment with vv = $0: max 8 + (40 + 8vv 40vv} yields 6 + (40 + 8vv) = 0 = 0% for à la cart & Price with = $0 for à la cart & = $7.5 for buffet Selling to 00% of à la cart & 5% of buffet customers and = vv+5 vv max vv, 8.75 =.5 = 80% for buffet

32 Consumer Surlus Page 3 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 ll 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.

33 Price Differentiation Page 33 Summary Price Differentiation: Limitations and Tactics Volume Discounts Otimal Pricing with Arbitrage Cannibalization Market segmentation Consumer Welfare

34 Legally Eliminate Arbitrage Page 34 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, DemReAn 0 Teaching Assistant.