doi: 10.3934/jimo.2020036

Independent sales or bundling? Decisions under different market-dominant powers

School of Management and Economics, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, China

* Corresponding author: Feng Wei

Received  June 2019 Revised  September 2019 Published  February 2020

Fund Project: This research is supported by the National Natural Science Foundation of China(71472026)

Enterprises are aware that bundling strategies can improve profitability in the highly competitive marketplace. This study evaluates an online to offline (O2O) supply chain system made up of a supplier and an e-retailer who can sell two products independently or bundled through online and offline channels, and discuss the influence of pricing strategy and channel choice on profit under different market-dominant powers. Based on a game theory model, we derive an optimal wholesale price for the supplier, an optimal sale price for the e-retailer, and their respective profit. We demonstrate that a Stackelberg leader is more profitable, irrespective of whether independent sales or bundling are chosen. Regardless of who the leader is, the whole supply chain receive equal profit. For a market leader, independent sales or bundling decisions should be made according to market size. Sensitivity analysis show that as the self-price sensitivity coefficient increases, the profit monotonically decreases for both independent sales and bundling; this occur for both the market dominated by the supplier and that dominated by the e-retailer. For independent sales, as the cross-price sensitivity coefficient increases, the profit monotonically increases; for bundled sales, the profit of the game players is not affected.

Citation: Feng Wei, Hong Chen. Independent sales or bundling? Decisions under different market-dominant powers. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020036
References:
[1]

A. BalakrishnanS. Sundaresan and B. Zhang, Browse-and-Switch: Retail-online competition under value uncertainty, Prod. Oper. Management, 23 (2014), 1129-1145.  doi: 10.1111/poms.12165.  Google Scholar

[2]

M. Banciu and F. Degaard, Optimal product bundling with dependent valuations: The price of independence, European J. Oper. Res., 255 (2016), 481-495.  doi: 10.1016/j.ejor.2016.05.022.  Google Scholar

[3]

H. K. Bhargava, Retailer-driven product bundling in a distribution channel, Marketing Sci., 31 (2012), 1014-1021.  doi: 10.1287/mksc.1120.0725.  Google Scholar

[4]

Q. N. CaoX. J. Geng and J. Zhang, Strategic role of retailer bundling in a distribution channel, J. Retailing, 91 (2015), 50-67.  doi: 10.1016/j.jretai.2014.10.005.  Google Scholar

[5]

Q. N. CaoK. E. Stecke and J. Zhang, The impact of limited supply on a firm's bundling strategy, Prod. Oper. Management, 24 (2015), 1931-1944.  doi: 10.1111/poms.12388.  Google Scholar

[6]

W. CaoB. Jiang and D. M. Zhou, The effects of demand uncertainty on channel structure, European J. Oper. Res., 207 (2010), 1471-1488.  doi: 10.1016/j.ejor.2010.06.001.  Google Scholar

[7]

A. ChakravartyA. Mild and A. Taudes, Bundling decisions in supply chains, European J. Oper. Res., 231 (2013), 617-630.  doi: 10.1016/j.ejor.2013.06.026.  Google Scholar

[8]

J. ChenH. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583.  doi: 10.1016/j.omega.2011.11.005.  Google Scholar

[9]

Y. C. ChenS. C. Fang and U. P. Wen, Pricing policies for substitutable products in a supply chain with Internet and traditional channels, European J. Oper. Res., 224 (2013), 542-551.  doi: 10.1016/j.ejor.2012.09.003.  Google Scholar

[10]

W. Y. K. ChiangD. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Management Sci., 49 (2003), 1-20.  doi: 10.1287/mnsc.49.1.1.12749.  Google Scholar

[11]

P. K. ChintaguntaJ. H. Chu and J. Cebollada, Quantifying transaction costs in online/off-line grocery channel choice, Marketing Sci., 31 (2012), 96-114.  doi: 10.1287/mksc.1110.0678.  Google Scholar

[12]

S. C. Choi, Price competition in a channel structure with a common retailer, Marketing Sci., 10 (1991), 271-296.  doi: 10.1287/mksc.10.4.271.  Google Scholar

[13]

B. DanG. Y. Xu and C. Liu, Pricing policies in a dual-channel supply chain with retail services, Internat. J. Prod. Econ., 139 (2012), 312-320.  doi: 10.1016/j.ijpe.2012.05.014.  Google Scholar

[14]

F. Gao and X. M. Su, Omnichannel retail operations with buy-online-and-pick-up-in-store, Management Sci., 63 (2016), 1-15.  doi: 10.1287/mnsc.2016.2473.  Google Scholar

[15]

M. GirjuA. Prasad and B. T. Ratchford, Pure components versus pure bundling in a marketing channel, J. Retailing, 89 (2013), 423-437.  doi: 10.1016/j.jretai.2013.06.001.  Google Scholar

[16]

U. GurlerS. Oztop and A. Sen, Optimal bundle formation and pricing of two products with limited stock, Internat. J. Prod. Econ., 118 (2009), 442-462.  doi: 10.1016/j.ijpe.2008.11.012.  Google Scholar

[17]

W. Hanson and R. K. Martin, Optimal bundle pricing, Management Sci., 36 (1990), 155-174.  doi: 10.1287/mnsc.36.2.155.  Google Scholar

[18]

Y. Y. HeJ. ZhangQ. L. Gou and G. B. Bi, Supply chain decisions with reference quality effect under the O2O environment, Ann. Oper. Res., 268 (2018), 273-292.  doi: 10.1007/s10479-016-2224-2.  Google Scholar

[19]

D. Honhon and X. J. A. Pan, Improving profits by bundling vertically differentiated products, Prod. Oper. Management, 26 (2017), 1481-1497.  doi: 10.1111/poms.12686.  Google Scholar

[20]

W. Hu and Y. J. Li, Retail service for mixed retail and e-tail channels, Ann. Oper. Res., 192 (2012), 151-171.  doi: 10.1007/s10479-010-0818-7.  Google Scholar

[21]

G. W. HuaS. Y. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European Internat. J. Prod. Econ., 205 (2010), 113-126.  doi: 10.1016/j.ejor.2009.12.012.  Google Scholar

[22]

J. N. JiZ. Y. Zhang and L. Yang, Comparisons of initial carbon allowance allocation rules in an O2O retail supply chain with the cap-and-trade regulation, Internat. J. Prod. Econ., 187 (2017), 68-84.  doi: 10.1016/j.ijpe.2017.02.011.  Google Scholar

[23]

Y. C. JiangY. Z. LiuH. WangJ. Shang and S. Ding, Online pricing with bundling and coupon discounts, Internat. J. Prod. Res., 56 (2018), 1773-1788.  doi: 10.1080/00207543.2015.1112443.  Google Scholar

[24]

Q. H. Lu and N. Liu, Pricing games of mixed conventional and e-commerce distribution channels, Comput. Industrial Engineering, 64 (2013), 122-132.  doi: 10.1016/j.cie.2012.09.018.  Google Scholar

[25]

Z. LuoX. ChenJ. Chen and X. J. Wang, Optimal pricing policies for differentiated brands under different supply chain power structures, European J. Oper. Res., 259 (2017), 437-451.  doi: 10.1016/j.ejor.2016.10.046.  Google Scholar

[26]

Z. LuoX. Chen and M. Kai, The effect of customer value and power structure on retail supply chain product choice and pricing decisions, Omega, 77 (2018), 115-126.  doi: 10.1016/j.omega.2017.06.003.  Google Scholar

[27]

S. MayerR. Klein and S. Seiermann, A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints, Internat. J. Prod. Econ., 145 (2013), 584-598.  doi: 10.1016/j.ijpe.2013.05.014.  Google Scholar

[28]

A. MehraS. Kumar and J. S. Raju, Competitive strategies for brick-and-mortar stores to counter "showrooming", Management Sci., 64 (2018), 3076-3090.  doi: 10.1287/mnsc.2017.2764.  Google Scholar

[29]

A. PrasadR. Venkatesh and V. Mahajan, Optimal bundling of technological products with network externality, Management Sci., 56 (2010), 2224-2236.  doi: 10.1287/mnsc.1100.1259.  Google Scholar

[30]

A. PrasadR. Venkatesh and V. Mahajan, Product bundling or reserved product pricing? Price discrimination with myopic and strategic consumers, Internat. J. Res. Marketing, 32 (2015), 1-8.  doi: 10.1016/j.ijresmar.2014.06.004.  Google Scholar

[31]

A. PrasadR. Venkatesh and V. Mahajan, Temporal product bundling with myopic and strategic consumers: Manifestations and relative effectiveness, Quantitative Marketing Economics, 15 (2017), 341-368.  doi: 10.1007/s11129-017-9189-6.  Google Scholar

[32]

J. K. RyanD. Sun and X. Y. Zhao, Coordinating a supply chain with a manufacturer-owned online channel: A dual channel model under price competition, IEEE Transac. Engineering Manag., 60 (2013), 247-259.  doi: 10.1109/TEM.2012.2207903.  Google Scholar

[33]

M. Sarkar and Y. H. Lee, Optimum pricing strategy for complementary products with reservation price in a supply chain model, J. Ind. Manag. Optim., 13 (2017), 1579-1612.  doi: 10.3934/jimo.2017007.  Google Scholar

[34]

M. Sheikhzadeh and E. Elahi, Product bundling: Impacts of product heterogeneity and risk considerations, Internat. J. Prod. Econ., 144 (2013), 209-222.  doi: 10.1016/j.ijpe.2013.02.006.  Google Scholar

[35]

W. WangG. Li and T. C. E. Cheng, Channel selection in a supply chain with a multi-channel retailer: The role of channel operating costs, Internat. J. Prod. Econ., 173 (2016), 54-65.  doi: 10.1016/j.ijpe.2015.12.004.  Google Scholar

[36]

J. P. XieL. LiangL. H. Liu and P. Ieromonachou, Coordination contracts of dual-channel with cooperation advertising in closed-loop supply chains, Internat. J. Prod. Econ., 183 (2017), 528-538.  doi: 10.1016/j.ijpe.2016.07.026.  Google Scholar

[37]

R. L. Yan and S. Bandyopadhyay, The profit benefits of bundle pricing of complementary products, J. Retailing Consumer Services, 18 (2011), 355-361.  doi: 10.1016/j.jretconser.2011.04.001.  Google Scholar

[38]

R. L. YanC. MyersJ. Wang and S. Ghose, Bundling products to success: The influence of complementarity and advertising, J. Retailing Consumer Services, 21 (2014), 48-53.  doi: 10.1016/j.jretconser.2013.07.007.  Google Scholar

[39]

R. L. Yan and Z. Pei, Retail services and firm profit in a dual-channel market, J. Retailing Consumer Services, 16 (2009), 306-314.  doi: 10.1016/j.jretconser.2009.02.006.  Google Scholar

[40]

D. Q. Yao and J. J. Liu, Competitive pricing of mixed retail and e-tail distribution channels, Omega, 33 (2005), 235-247.  doi: 10.1016/j.omega.2004.04.007.  Google Scholar

[41]

R. ZhangB. Liu and W. L. Wang, Pricing decisions in a dual channels system with different power structures, Economic Modelling, 29 (2012), 523-533.  doi: 10.1016/j.econmod.2011.08.024.  Google Scholar

show all references

References:
[1]

A. BalakrishnanS. Sundaresan and B. Zhang, Browse-and-Switch: Retail-online competition under value uncertainty, Prod. Oper. Management, 23 (2014), 1129-1145.  doi: 10.1111/poms.12165.  Google Scholar

[2]

M. Banciu and F. Degaard, Optimal product bundling with dependent valuations: The price of independence, European J. Oper. Res., 255 (2016), 481-495.  doi: 10.1016/j.ejor.2016.05.022.  Google Scholar

[3]

H. K. Bhargava, Retailer-driven product bundling in a distribution channel, Marketing Sci., 31 (2012), 1014-1021.  doi: 10.1287/mksc.1120.0725.  Google Scholar

[4]

Q. N. CaoX. J. Geng and J. Zhang, Strategic role of retailer bundling in a distribution channel, J. Retailing, 91 (2015), 50-67.  doi: 10.1016/j.jretai.2014.10.005.  Google Scholar

[5]

Q. N. CaoK. E. Stecke and J. Zhang, The impact of limited supply on a firm's bundling strategy, Prod. Oper. Management, 24 (2015), 1931-1944.  doi: 10.1111/poms.12388.  Google Scholar

[6]

W. CaoB. Jiang and D. M. Zhou, The effects of demand uncertainty on channel structure, European J. Oper. Res., 207 (2010), 1471-1488.  doi: 10.1016/j.ejor.2010.06.001.  Google Scholar

[7]

A. ChakravartyA. Mild and A. Taudes, Bundling decisions in supply chains, European J. Oper. Res., 231 (2013), 617-630.  doi: 10.1016/j.ejor.2013.06.026.  Google Scholar

[8]

J. ChenH. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583.  doi: 10.1016/j.omega.2011.11.005.  Google Scholar

[9]

Y. C. ChenS. C. Fang and U. P. Wen, Pricing policies for substitutable products in a supply chain with Internet and traditional channels, European J. Oper. Res., 224 (2013), 542-551.  doi: 10.1016/j.ejor.2012.09.003.  Google Scholar

[10]

W. Y. K. ChiangD. Chhajed and J. D. Hess, Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design, Management Sci., 49 (2003), 1-20.  doi: 10.1287/mnsc.49.1.1.12749.  Google Scholar

[11]

P. K. ChintaguntaJ. H. Chu and J. Cebollada, Quantifying transaction costs in online/off-line grocery channel choice, Marketing Sci., 31 (2012), 96-114.  doi: 10.1287/mksc.1110.0678.  Google Scholar

[12]

S. C. Choi, Price competition in a channel structure with a common retailer, Marketing Sci., 10 (1991), 271-296.  doi: 10.1287/mksc.10.4.271.  Google Scholar

[13]

B. DanG. Y. Xu and C. Liu, Pricing policies in a dual-channel supply chain with retail services, Internat. J. Prod. Econ., 139 (2012), 312-320.  doi: 10.1016/j.ijpe.2012.05.014.  Google Scholar

[14]

F. Gao and X. M. Su, Omnichannel retail operations with buy-online-and-pick-up-in-store, Management Sci., 63 (2016), 1-15.  doi: 10.1287/mnsc.2016.2473.  Google Scholar

[15]

M. GirjuA. Prasad and B. T. Ratchford, Pure components versus pure bundling in a marketing channel, J. Retailing, 89 (2013), 423-437.  doi: 10.1016/j.jretai.2013.06.001.  Google Scholar

[16]

U. GurlerS. Oztop and A. Sen, Optimal bundle formation and pricing of two products with limited stock, Internat. J. Prod. Econ., 118 (2009), 442-462.  doi: 10.1016/j.ijpe.2008.11.012.  Google Scholar

[17]

W. Hanson and R. K. Martin, Optimal bundle pricing, Management Sci., 36 (1990), 155-174.  doi: 10.1287/mnsc.36.2.155.  Google Scholar

[18]

Y. Y. HeJ. ZhangQ. L. Gou and G. B. Bi, Supply chain decisions with reference quality effect under the O2O environment, Ann. Oper. Res., 268 (2018), 273-292.  doi: 10.1007/s10479-016-2224-2.  Google Scholar

[19]

D. Honhon and X. J. A. Pan, Improving profits by bundling vertically differentiated products, Prod. Oper. Management, 26 (2017), 1481-1497.  doi: 10.1111/poms.12686.  Google Scholar

[20]

W. Hu and Y. J. Li, Retail service for mixed retail and e-tail channels, Ann. Oper. Res., 192 (2012), 151-171.  doi: 10.1007/s10479-010-0818-7.  Google Scholar

[21]

G. W. HuaS. Y. Wang and T. C. E. Cheng, Price and lead time decisions in dual-channel supply chains, European Internat. J. Prod. Econ., 205 (2010), 113-126.  doi: 10.1016/j.ejor.2009.12.012.  Google Scholar

[22]

J. N. JiZ. Y. Zhang and L. Yang, Comparisons of initial carbon allowance allocation rules in an O2O retail supply chain with the cap-and-trade regulation, Internat. J. Prod. Econ., 187 (2017), 68-84.  doi: 10.1016/j.ijpe.2017.02.011.  Google Scholar

[23]

Y. C. JiangY. Z. LiuH. WangJ. Shang and S. Ding, Online pricing with bundling and coupon discounts, Internat. J. Prod. Res., 56 (2018), 1773-1788.  doi: 10.1080/00207543.2015.1112443.  Google Scholar

[24]

Q. H. Lu and N. Liu, Pricing games of mixed conventional and e-commerce distribution channels, Comput. Industrial Engineering, 64 (2013), 122-132.  doi: 10.1016/j.cie.2012.09.018.  Google Scholar

[25]

Z. LuoX. ChenJ. Chen and X. J. Wang, Optimal pricing policies for differentiated brands under different supply chain power structures, European J. Oper. Res., 259 (2017), 437-451.  doi: 10.1016/j.ejor.2016.10.046.  Google Scholar

[26]

Z. LuoX. Chen and M. Kai, The effect of customer value and power structure on retail supply chain product choice and pricing decisions, Omega, 77 (2018), 115-126.  doi: 10.1016/j.omega.2017.06.003.  Google Scholar

[27]

S. MayerR. Klein and S. Seiermann, A simulation-based approach to price optimisation of the mixed bundling problem with capacity constraints, Internat. J. Prod. Econ., 145 (2013), 584-598.  doi: 10.1016/j.ijpe.2013.05.014.  Google Scholar

[28]

A. MehraS. Kumar and J. S. Raju, Competitive strategies for brick-and-mortar stores to counter "showrooming", Management Sci., 64 (2018), 3076-3090.  doi: 10.1287/mnsc.2017.2764.  Google Scholar

[29]

A. PrasadR. Venkatesh and V. Mahajan, Optimal bundling of technological products with network externality, Management Sci., 56 (2010), 2224-2236.  doi: 10.1287/mnsc.1100.1259.  Google Scholar

[30]

A. PrasadR. Venkatesh and V. Mahajan, Product bundling or reserved product pricing? Price discrimination with myopic and strategic consumers, Internat. J. Res. Marketing, 32 (2015), 1-8.  doi: 10.1016/j.ijresmar.2014.06.004.  Google Scholar

[31]

A. PrasadR. Venkatesh and V. Mahajan, Temporal product bundling with myopic and strategic consumers: Manifestations and relative effectiveness, Quantitative Marketing Economics, 15 (2017), 341-368.  doi: 10.1007/s11129-017-9189-6.  Google Scholar

[32]

J. K. RyanD. Sun and X. Y. Zhao, Coordinating a supply chain with a manufacturer-owned online channel: A dual channel model under price competition, IEEE Transac. Engineering Manag., 60 (2013), 247-259.  doi: 10.1109/TEM.2012.2207903.  Google Scholar

[33]

M. Sarkar and Y. H. Lee, Optimum pricing strategy for complementary products with reservation price in a supply chain model, J. Ind. Manag. Optim., 13 (2017), 1579-1612.  doi: 10.3934/jimo.2017007.  Google Scholar

[34]

M. Sheikhzadeh and E. Elahi, Product bundling: Impacts of product heterogeneity and risk considerations, Internat. J. Prod. Econ., 144 (2013), 209-222.  doi: 10.1016/j.ijpe.2013.02.006.  Google Scholar

[35]

W. WangG. Li and T. C. E. Cheng, Channel selection in a supply chain with a multi-channel retailer: The role of channel operating costs, Internat. J. Prod. Econ., 173 (2016), 54-65.  doi: 10.1016/j.ijpe.2015.12.004.  Google Scholar

[36]

J. P. XieL. LiangL. H. Liu and P. Ieromonachou, Coordination contracts of dual-channel with cooperation advertising in closed-loop supply chains, Internat. J. Prod. Econ., 183 (2017), 528-538.  doi: 10.1016/j.ijpe.2016.07.026.  Google Scholar

[37]

R. L. Yan and S. Bandyopadhyay, The profit benefits of bundle pricing of complementary products, J. Retailing Consumer Services, 18 (2011), 355-361.  doi: 10.1016/j.jretconser.2011.04.001.  Google Scholar

[38]

R. L. YanC. MyersJ. Wang and S. Ghose, Bundling products to success: The influence of complementarity and advertising, J. Retailing Consumer Services, 21 (2014), 48-53.  doi: 10.1016/j.jretconser.2013.07.007.  Google Scholar

[39]

R. L. Yan and Z. Pei, Retail services and firm profit in a dual-channel market, J. Retailing Consumer Services, 16 (2009), 306-314.  doi: 10.1016/j.jretconser.2009.02.006.  Google Scholar

[40]

D. Q. Yao and J. J. Liu, Competitive pricing of mixed retail and e-tail distribution channels, Omega, 33 (2005), 235-247.  doi: 10.1016/j.omega.2004.04.007.  Google Scholar

[41]

R. ZhangB. Liu and W. L. Wang, Pricing decisions in a dual channels system with different power structures, Economic Modelling, 29 (2012), 523-533.  doi: 10.1016/j.econmod.2011.08.024.  Google Scholar

Figure 1.  Different sales strategies
Figure 2.  Game order dominated by supplier in independent sales
Figure 3.  Game order dominated by the e-retailer in independent sales
Figure 4.  Effect of $ \beta $ in a supplier-dominated market
Figure 5.  Effect of $ \beta $ in an e-retailer-dominated market
Figure 6.  Effect of $ \gamma $ in a supplier-dominated market
Figure 7.  Effect of $ \gamma $ in an e-retailer-dominated market
Table 1.  Recently published works on bundling
Literature Selling price Strategy Situation
Gurler et al. [7] Independent and bundled sales price Bundle pricing and inventory levels Inventory constraints and stochastic model
Prasad et al. [9] Mixed bundling Different bundling and network externality Technological products and network externality
Sheikhzadeh et al. [17] Bundled sales price Pure bundling and independent policy Product heterogeneity and risk considerations
Jiang et al. [19] Online pricing with bundling Online pricing strategy Coupon discounts Customer’s purchase preference and coupon
Prasad et al. [29] Inter-temporal pricing Pure components, pure bundling, and mixed bundling Myopic and strategic consumers
This study Independent and bundled sales price Channel selection, Online and offline sales E-commerce and differentmarket-dominant powers
Literature Selling price Strategy Situation
Gurler et al. [7] Independent and bundled sales price Bundle pricing and inventory levels Inventory constraints and stochastic model
Prasad et al. [9] Mixed bundling Different bundling and network externality Technological products and network externality
Sheikhzadeh et al. [17] Bundled sales price Pure bundling and independent policy Product heterogeneity and risk considerations
Jiang et al. [19] Online pricing with bundling Online pricing strategy Coupon discounts Customer’s purchase preference and coupon
Prasad et al. [29] Inter-temporal pricing Pure components, pure bundling, and mixed bundling Myopic and strategic consumers
This study Independent and bundled sales price Channel selection, Online and offline sales E-commerce and differentmarket-dominant powers
Table 2.  Notation and explanation
Notation Explanation
$ w_i $ The supplier's unit wholesale price, where $ i=1,2 $
$ p_1 $ Unit sale price through e-retailer's offline channel
$ p_2 $ Unit sale price through e-retailer's online channel
$ c_1 $ Unit sale cost through e-retailer's offline channel
$ c_2 $ Unit sale cost through e-retailer's online channel
$ a $ Maximum market size
$ \mu $ The proportion of offline demand
$ \beta $ The self-price sensitivity coefficient
$ \gamma $ The cross-price sensitivity coefficient
$ w_{12} $ The wholesale price of two bundled products
$ p_{12} $ The sale price of two bundled products
$ c_{12} $ The sale cost of two bundled products
Notation Explanation
$ w_i $ The supplier's unit wholesale price, where $ i=1,2 $
$ p_1 $ Unit sale price through e-retailer's offline channel
$ p_2 $ Unit sale price through e-retailer's online channel
$ c_1 $ Unit sale cost through e-retailer's offline channel
$ c_2 $ Unit sale cost through e-retailer's online channel
$ a $ Maximum market size
$ \mu $ The proportion of offline demand
$ \beta $ The self-price sensitivity coefficient
$ \gamma $ The cross-price sensitivity coefficient
$ w_{12} $ The wholesale price of two bundled products
$ p_{12} $ The sale price of two bundled products
$ c_{12} $ The sale cost of two bundled products
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