Market share models for consumer goods.
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(2) Ö MARKET SHARE MODELS FOR CONSUMER GOODS ABSTRACT ∗ Market share models • “classical“; • attraction; ∗ Relative marketing variables; ∗ Expressions for direct and cross elasticities; ∗ Are direct elasticities robust? ∗ Case study: • Compare alternative market share models; • Compare alternative relative marketing variables; • Compare elasticities obtained by alternative market share models and relative marketing variables.. 2.
(3) Ö MARKET SHARE ELASTICITIES. Direct:. ∂mi X ik eik = ⋅ ∂X ik mi Cross:. ∂mi X jk eijk = × ∂X jk mi. where:. eik = direct elasticity of brand i with respect to marketing variable Xik; eijk = cross elasticity of brand i with respect to marketing variable Xjk; mi = market share of brand i; Xik = marketing variable k for brand i;. 3.
(4) Ö MARKET SHARE: “CLASSICAL MODELS“ Linear Model:. mi = αi + ∑ βik ⋅ X ik k. Multiplicative Model:. mi = αi ⋅ ∏ X ikβik k. Exponential Model:. mi = exp (αi + ∑ βik ⋅ X ik ) k. ∑m = ? (≈1) i. 4.
(5) Ö MARKET SHARE: AT T R A C T I O N M O D E L S. Multiplicative Competitive Interaction Model (MCI):. mi =. αi ⋅ ∏ X ikβik k. β jk α j ⋅ ∏ X jk ∑ k j =1 n. MultiNomial Logit Model (MNL):. mi =. exp(αi + ∑ βik ⋅ X ik ) k. exp(α j + ∑ β jk ⋅ X jk ) ∑ j =1 k n. ∑m. i. 5. =1.
(6) Ö RELATIVE MARKETING VARIABLES. * ik. X =. * ik. X =. X ik 1 n X lk ∑ n l =1. (1) Non-weighted average. X ik n. (2) Weighted average. ∑ ml ⋅ X lk l =1. X ik. * ik. X = n. ∏X l. (3) Geometric mean. lk. 1 X = X ik − ∑ X lk n l * ik. (4) Difference to mean. 6.
(7) Ö DIRECT ELASTICITIES COMPLETE REFERENCE. Market Share Models Linear. Multiplica. Exponent.. MCI. MNL. Comom fraction ßik⋅Xik*/ /mi⋅c. ßik⋅Xik*⋅c. ßik⋅c. ßik⋅(1-mi)⋅c+ ßik⋅Xik*⋅(1-mi)⋅c+ +∑l≠iβlk⋅ml⋅d ∑l≠iβlk⋅ml⋅Xlk*⋅d. Non-relative variable c=1. d=0 (1) Non-weighted average. c=1-Xik*/n. d=Xik*/n (2) Weighted average d=Xlk*⋅Xik/Xlk⋅mi’/(1-ml’). c=1. (3) Geometric mean c=(n-1)/n. d=1/n (4) Difference to mean. c=(n-1)/n⋅Xik/Xik*. d=1/n⋅Xik/Xlk*. Note: for non-relative variables Xik substitutes Xik*.. 7.
(8) Ö DIRECT ELASTICITIES Non-relative variable. Relative variable (2). Linear Model: eik = βik ⋅ X ik / mi. eik = βik ⋅ X ik * ⋅ (1 − m'i ⋅ X ik * ) / mi. ∗ varies directly with marketing variables;. ∗ mixed variation with marketing variables;. Multiplicative Model:. (. ). eik = β ik. eik = β ik ⋅ 1 − m'i ⋅ X ik*. ∗ time invariable; ∗ market share invariable;. ∗ decreases with marketing variables;. MCI Model: eik = β ik ⋅ (1 − mi ). eik = β ik ⋅ (1 − mi ) ⋅ (1 − m'i ⋅ X ik* ) + ∑ β lk ⋅ ml ⋅ m'i ⋅ X ik* l ≠i. ∗ decreases with marketing variables of brand i;. Direct Elasticities. M u ltip lic a tiv e m o d e l w ith n o n -re la tiv e v a ria b le. M u ltip lic a tiv e & M C I m o d e ls w ith re la tiv e v a ria b le a n d M C I w ith n o n -re la tiv e v a ria b le L in e a r m o d e l w ith re la tiv e v a ria b le L in e a r m o d e l w ith n o n -re la tiv e v a ria b le. M a rk e tin g V a r iab le. 8.
(9) Ö CROSS ELASTICITIES COMPLETE REFERENCE Market Share Models Linear. Multiplica. Exponent.. MCI. MNL. Comom fraction -ßik⋅Xik*/ /mi⋅c. -ßik⋅Xik*⋅ ⋅c. -ßik⋅c. -ßjk⋅mj⋅c+. -ßjk⋅Xjk*⋅mj⋅c+. +∑l≠jβlk⋅(ml-δil)⋅d ∑l≠jβlk⋅(ml-δil)⋅Xlk*⋅d. Non-relative variable c=1. c=1 d=0 (1) Non-weighted average. c=Xjk*/n. c=1-Xjk*/n d=Xjk*/n (2) Weighted average. c=Xjk*⋅mj’. c=1-mj’⋅Xjk* d= Xjk*⋅mj’ (3) Geometric mean. c=1/n. c=(n-1)/n d=1/n (4) Difference to mean. c=1/n⋅Xjk/Xik*. c=(n-1)/n⋅Xjk/Xjk* d=1/n⋅Xjk/Xlk*. Note: for non-relative variables Xik substitutes Xik*.. 9.
(10) Ö CROSS ELASTICITIES Non-relative variable Linear Model:. Relative variable (2). eijk = − βik ⋅ X ik / mi. eijk = − βik ⋅ X ik * ⋅ X jk * ⋅ m' j / mi. ∗ invariable with brand j; ∗ increases with share and brand i marketing variables;. ∗ decreases with brand j variables; ∗ increases with share and decreases with brand i marketing variables;. Multiplicative Model: eijk = − βik. eijk = − βik ⋅ X *jk ⋅ m' j. ∗ time invariable; ∗ invariable with brand j;. ∗ decreases with brand j variables;. MCI Model: eijk = − βik ⋅ m j. *. eijk = − β jk ⋅ m j ⋅ (1 − m' j ⋅ X jk ) + *. + βik ⋅ (mi − 1) ⋅ m' j ⋅ X ik* ⋅ X jk + + ∑ βlk ⋅ ml ⋅m' j ⋅ X lk* ⋅ X jk. *. l ≠i , j. ∗ decreases with brand j share;. ∗ varies directly with marketing variables of brand j and brand i; ∗ varies inversely with share of brand j and directly with share of brand i;. Cross Elasticities. L in e a r m o d e l w ith n o n re la tiv e v a ria b le. L in e a r & M C I m o d e ls w ith re la tiv e v a ria b le. M u ltip lic a tiv e m o d e l w ith re la tiv e v a ria b le & M C I m o d e l w ith n o n -re la tiv e v a r ia b le. M u ltip lic a tiv e m o d e l w ith n o n -re la tiv e v a ria b le. M a r k e tin g V a r ia b le fo r B r a n d i. 10.
(11) Ö ARE DIRECT ELASTICITIES ROBUST? lim eik a) m →1. Legend:. b). i. lim eik. X ik →±∞. Market Share Models Linear. Multiplica. Exponent.. MCI. MNL. Nonrelative. a)=ßik⋅Xik b)=1. a)= ßik b)= ßik. a)= ßik⋅Xik b)= ±∞. a)=0 b)=0. a)=0 b)=0. equation. a)=ßik⋅Xik*⋅ ⋅(1-Xik*/n) b)=0. a)=ßik⋅ (1-Xik*/n) b)=0. a)=ßik⋅Xik* ⋅(1-Xik*/n) b)=0. a)=0 b)=0. a)=0 b)=0. a)=0 b)=0. a)=0 b)=0. a)=0 b)=0. a)=0 b)=0. a)=0 b)=0. a)=ßik⋅Xik*⋅ ⋅(n-1)/n b)=(n-1)/n. a)=ßik (n-1)/ a)=ßik⋅Xik*⋅ /n ⋅(n-1)/n b)=ßik(n-1)/n b)=±∞. a)=0 b)=0. a)=0 b)=0. a)=ßik⋅ Xik⋅ ⋅(n-1)/n b)=1. a)=ßik⋅Xik/Xik* a)=ßik⋅Xik⋅ ⋅(n-1)/n ⋅(n-1)/n b)=ßik b)=±∞. a)=0 b)=0. a)=0 b)=0. (1) equation (2) equation (3) equation (4). Ö BEHAVIOUR OF ROBUST MODELS ___. M u lt ip lic a t iv e & M C I m o d e ls L in e a r , E x p o n e n t ia l & M N L m o d e ls. Direct Elasticity. ___. M a r k e tin g V a r ia b le. 11.
(12) Ö THE RICE FAMILY: Code. Type. Brand. Quantity. Mean share. 5622 3662 3349 3347 5626. Rice Extra Long Rice Extra Long Rice Carolino Rice Carolino Rice Extra Long. Saludães Malandrinho Grão de Ouro D. Ana Oriente. 1 Kg 1 Kg 1 Kg 1 Kg 1 Kg. 63% 28% 5% 3% 1%. Ö SALES FOR THE TWO MAJOR BRANDS 9.000. September. 8.000. 5622 Qt. October. November. December. 3662 Qt. 7.000. Sales (Kg). 6.000. 5.000. 4.000. 3.000. 2.000. 1.000. 0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 2 4 6 8 10. Month Day. 12.
(13) Ö MARKET SHARE & PRICE SERIES MAJOR BRANDS 5622 5622 Preço. 100%. 180. 3662 3662 Preço. 160 140. 80%. 60%. 100. 28/9 1/10. 9/9. 80. 29/11. 40%. 3/12. 25/10. 60. 31/10. 3/11 40. 20%. 3662's promotion 1-2/9 0%. 6/10. 7-8/9. 1-2/11. 20. 30/11. 6/12 9/12. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 2 4 6 8 10. Month Day. MINOR BRANDS 18%. 3349. 3347. 5626. 3349 Preço. 3347 Preço. 5626 Preço/5. 22,5% 200. 16%. 180 14%. 160 140 10%. 120 8%. 100 3349 Promotion. 6%. 80. 4%. 60. 2%. 40. 3-4/9 20. 0% 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 2 4 6 8 10. Month Day. 13. Unit Price. Market Share. 12%. 0. Unit Price. Market Share. 120.
(14) Ö QUALITY OF FIT FOR CLASSICAL MODELS ADJUSTED R2 FOR MAJOR BRANDS Market Share Models. Explanatory Variable. Linear. Multiplicative. Brand 5622 - Rice Extra-Long Saludães Non-relative. 92,90%. 91,70%. Equation (2). 95,12%. 93,80%. Brand 3662 - Rice Extra-Long Malandrinho. 100%. Non-relative. 86,64%. 79,78%. Equation (2). 93,65% √. 87,03% √. m(5622) =3,77-3,16*PR(2)ag30 -0,113*Prom3662 -1,014*RtR5622 +0,805*RtR3662 m(3662)= 1,61-1,48*PR(2)ag17 +0,121*Prom3662 -0,025*Prom3349 +0,643*RtR5622 -1,000*RtR3662 Prev5622. Prev3662. 5622. 3662. Market Share. 80%. 60%. 40%. 20%. 0% 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 2 4 6 8 10. Month Day. 14.
(15) Ö QUALITY OF FIT FOR CLASSICAL MODELS ADJUSTED R2 FOR MINOR BRANDS Explanatory Variable. Market Share Models Linear. Multiplicative. Brand 3349 - Rice Carolino Grão de Ouro Non-relative. 71,38%. 59,76%. Equation (2). 74,51%. 63,02%. Brand 3347 - Rice Carolino D. Ana Non-relative. 53,48%. 59,66%. Equation (2). 53,98%. 60,13%. 18% m(3349)=- 1,00-1,42*PR(3) +0,0320*Prom3349 +0,258*RtR5622 +0,128*RtR3662 +1,35*RtR3347. 22,5%. m(3347) =exp(-12-0,54*PR(4) -0,154*Prom3662+ 0,86*RtB5622+ 1,49*RtR3662 -2,09*RtB334) 16%. 14%. 3349 Prev3349 3347. Market Share. 12%. Prev3347. 10%. 8%. 6%. 4%. 2%. 0% 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 2 4 6 8 10. Month Day. 15.
(16) Ö QUALITYOFFITFORATTRACTIONMODELS A(5622) = 10,6*PR(1)^ -23,7 A(3662) = 13,2*PR(1)^ -60 + 0,69*Prom3662 90%. Qtm 5622. Prev. 5622. Qtm 3662. Prev. 3662. 80%. 70%. Market Share. 60%. 50%. 40%. 30%. 20%. 10%. 0% 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 2 4 6 8 10. 16%. 14%. Qtm 3349. A(3349) = 26,6*PR(1)^ -199 + 0,40*Prom3349 A(3347) = 17,3*PR(1)^ -77. Prev. 3349 Qtm 3347. 12%. Prev. 3347. Market Share. 10%. 8%. 6%. 4%. 2%. 0% 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 2 4 6 8 10. Month Day. 16.
(17) Ö TIME VARIATION OF DIRECT ELASTICITIES -12,00. -11,00. -10,00. Direct Elasticities. -9,00. MNL model for brand 3347. Linear model for brand 3662 time varying elasticities mean value. time varying elasticities mean value. -9,11 (0,19). -8,00. -7,00. -7,11 (0,16). -6,00. -5,5 (2,3). -5,00. -5,19 (0,84). -4,00. mean value time varying elasticities MNL model for brand 3662. mean value time varying elasticities -3,00 Multiplicative model for brand 3347 -2,00. 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 2 4 6 8 10. Month Day. 17.
(18) Ö COEFFICIENT OF VARIATION FOR DIRECT ELASTICITIES êik | σik/êik. Linear. Multiplicative. MNL. MCI. elasti. c. v. elasti. c. v. elasti. c. v. elasti. c. v. brand 5622 - Rice Extra-Long Saludães Non-relative. -1,8. 0,12. -1,8. 0,12. -1,4. 0,26. equation (2). -1,8. 0,10. -1,9. 0,10. -2,7. 0,25. ----2,70. 0,25. brand 3662 - Rice Extra-Long Malandrinho Non-relative. -4,7. 0,19. -7,3. 0,18. -5,7. 0,26. equation (2). -4, 7. 0,12. -5,3. 0,17. -5,9. 0,23. -5,9. 0,23. equation (3). -4,6. 0,12. -5,6. 0,15. -4,7. 0,27. -4,7. 0,27. ----. brand 3349 - Rice Carolino Grão de Ouro Non-relative. -6,4. 0,36. -9,3. 0,26. -14. 0,15. equation (2). -10. 0,23. -12. 0,21. -14. 0,17. -14. 0,17. equation (3). -14. 0,20. -16. 0,16. -20. 0,16. -20. 0,16. ----. brand 3347 - Rice Carolino D. Ana Non-relative. -2,3. 0.77. -3,2. 0,52. -6,9. 0,26. equation (2). -1,1. 1,89. -2,3. 0,77. -6,3. 0,32. equation (4). -5,3. 0,36. -7,7. 0,23. -9,9. 0,25. 18. ----6,3. 0,32 ----.
(19) Ö DIRECT & CROSS ELASTICITIES eij ∆mi. ∆Pj 5622. 3662 3349 3347 Classical Models 5622 -1,8 1,32 0,28 0,16 3662 3,92 -4,7 0,35 0,20 3349 6,39 2,61 -14 0,33 3347 1,92 1,70 1,67 -7,7 Attraction Models : MNL with relative price 5622 -1,3 1,72 0,76 -0,20 3662 1,91 -5,6 1,24 0,24 3349 4,08 3,99 -20 2,16 3347 2,21 2,40 1,54 -8,8 MNL with non-relative price any brand 2,86 2,27 0,70 0,17. Ö COMPETITIVE MAP: Direct (× ½) and Cross Elasticities 8,0 6,0 4,0 2,0 0,0 -2,0 -4,0 -6,0 -8,0. 5622 3662 3349 3347 brand j price variation. 3349 3662 5622. 19. 3347. resulting brand i market share variation.
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