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Understanding the optimal strategy of carbon labelled product advertising delivery: A dynamic differential equation analysis

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  • Peng, Yifeng
  • Tao, Xiangyang
  • Hong, Jingke
  • Sun, Lulu
  • Yuan, Xin

Abstract

In the rapidly evolving landscape of sustainable marketing, the advertising of carbon labelled products represents a critical intersection of environmental awareness and marketing strategy. Existing studies have mainly discussed optimization strategies for content and forms of advertising. Less attention has been paid to optimization strategies related to the quantity of advertising delivery. Setting an advertiser's optimal advertising intensity is a problem that has puzzled researchers for a long time. To this end, we investigate the optimal strategy for advertising delivery based on a differential equation analysis of advertising dynamics to maximize market size for advertisers with regard to carbon labelled products. We first show that the vitality index can reflect the carryover effect of advertisers, and that there exists an optimal advertising intensity to maximize market size if competition is not taken into account. We then find that current and global solutions of optimal strategies are consistent, from which we can determine the sustainability of an advertiser's carbon labelled product market by calculating the equilibrium vitality index. Moreover, we provide numerical experiments that illustrate the quantitative relationship that exists between greenness and the proportion of green consumers jointly determining the feasibility of the optimal strategy and the sustainability of advertisers in management practices. This research not only charts a course for optimal advertising strategy but also equips managers with data-driven tools to navigate the complexities of eco-conscious marketing.

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  • Peng, Yifeng & Tao, Xiangyang & Hong, Jingke & Sun, Lulu & Yuan, Xin, 2024. "Understanding the optimal strategy of carbon labelled product advertising delivery: A dynamic differential equation analysis," Journal of Retailing and Consumer Services, Elsevier, vol. 81(C).
    • Handle: RePEc:eee:joreco:v:81:y:2024:i:c:s0969698924002467
    DOI: 10.1016/j.jretconser.2024.103950
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    as
    1. Kar, Sumi & Basu, Kajla & Sarkar, Biswajit, 2023. "Advertisement policy for dual-channel within emissions-controlled flexible production system," Journal of Retailing and Consumer Services, Elsevier, vol. 71(C).
    2. Adrian R. Camilleri & Richard P. Larrick & Shajuti Hossain & Dalia Patino-Echeverri, 2019. "Consumers underestimate the emissions associated with food but are aided by labels," Nature Climate Change, Nature, vol. 9(1), pages 53-58, January.
    3. Prasad A. Naik & Murali K. Mantrala & Alan G. Sawyer, 1998. "Planning Media Schedules in the Presence of Dynamic Advertising Quality," Marketing Science, INFORMS, vol. 17(3), pages 214-235.
    4. Lee, Michael S.W. & Septianto, Felix & Frethey-Bentham, Catherine & Gao, Esther, 2020. "Condoms and bananas: Shock advertising explained through congruence theory," Journal of Retailing and Consumer Services, Elsevier, vol. 57(C).
    5. Kristen Giombi & Catherine Viator & Juliana Hoover & Janice Tzeng & Helen W Sullivan & Amie C O’Donoghue & Brian G Southwell & Leila C Kahwati, 2022. "The impact of interactive advertising on consumer engagement, recall, and understanding: A scoping systematic review for informing regulatory science," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-18, February.
    6. Brunner, Florentine & Kurz, Verena & Bryngelsson, David & Hedenus, Fredrik, 2018. "Carbon Label at a University Restaurant – Label Implementation and Evaluation," Ecological Economics, Elsevier, vol. 146(C), pages 658-667.
    7. Chen, Yenming J. & Sheu, Jiuh-Biing, 2009. "Environmental-regulation pricing strategies for green supply chain management," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(5), pages 667-677, September.
    8. S. A. Ozga, 1960. "Imperfect Markets Through Lack of Knowledge," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 74(1), pages 29-52.
    9. Yang, Chaolin & Xiong, Yi, 2020. "Nonparametric advertising budget allocation with inventory constraint," European Journal of Operational Research, Elsevier, vol. 285(2), pages 631-641.
    10. Schmid, David & Morschett, Dirk, 2023. "Retailers’ foreign market exits over time: A strategic management perspective," International Business Review, Elsevier, vol. 32(5).
    11. Jessica Jewell & David McCollum & Johannes Emmerling & Christoph Bertram & David E. H. J. Gernaat & Volker Krey & Leonidas Paroussos & Loïc Berger & Kostas Fragkiadakis & Ilkka Keppo & Nawfal Saadi & , 2018. "Limited emission reductions from fuel subsidy removal except in energy-exporting regions," Nature, Nature, vol. 554(7691), pages 229-233, February.
    12. Bert de Reyck & Zeger Degraeve, 2003. "Broadcast Scheduling for Mobile Advertising," Operations Research, INFORMS, vol. 51(4), pages 509-517, August.
    13. Somayeh Moazeni & Boris Defourny & Monika J. Wilczak, 2020. "Sequential Learning in Designing Marketing Campaigns for Market Entry," Management Science, INFORMS, vol. 66(9), pages 4226-4245, September.
    14. Sharp, Anne & Wheeler, Meagan, 2013. "Reducing householders’ grocery carbon emissions: Carbon literacy and carbon label preferences," Australasian marketing journal, Elsevier, vol. 21(4), pages 240-249.
    15. Daniel Zantedeschi & Eleanor McDonnell Feit & Eric T. Bradlow, 2017. "Measuring Multichannel Advertising Response," Management Science, INFORMS, vol. 63(8), pages 2706-2728, August.
    16. Shekhar Jayanthi & Aleda V. Roth & Mehmet M. Kristal & Lauren Carter-Roth Venu, 2009. "Strategic Resource Dynamics of Manufacturing Firms," Management Science, INFORMS, vol. 55(6), pages 1060-1076, June.
    17. Henri Servaes & Ane Tamayo, 2013. "The Impact of Corporate Social Responsibility on Firm Value: The Role of Customer Awareness," Management Science, INFORMS, vol. 59(5), pages 1045-1061, May.
    18. S. P. Sethi & A. Prasad & X. He, 2008. "Optimal Advertising and Pricing in a New-Product Adoption Model," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 351-360, November.
    19. Nelson, Philip, 1974. "Advertising as Information," Journal of Political Economy, University of Chicago Press, vol. 82(4), pages 729-754, July/Aug..
    20. Doug J. Chung & Byungyeon Kim & Byoung G. Park, 2019. "How Do Sales Efforts Pay Off? Dynamic Panel Data Analysis in the Nerlove–Arrow Framework," Management Science, INFORMS, vol. 65(11), pages 5197-5218, November.
    21. Nan Zhou & Seung H. Park, 2020. "Growth or profit? Strategic orientations and long‐term performance in China," Strategic Management Journal, Wiley Blackwell, vol. 41(11), pages 2050-2071, November.
    22. Khan M. R. Taufique & Kristian S. Nielsen & Thomas Dietz & Rachael Shwom & Paul C. Stern & Michael P. Vandenbergh, 2022. "Revisiting the promise of carbon labelling," Nature Climate Change, Nature, vol. 12(2), pages 132-140, February.
    23. Yuan Huang & Steven Wei, 2012. "Advertising intensity, investor recognition, and implied cost of capital," Review of Quantitative Finance and Accounting, Springer, vol. 38(3), pages 275-298, April.
    24. Beth L. Fossen & David A. Schweidel, 2017. "Television Advertising and Online Word-of-Mouth: An Empirical Investigation of Social TV Activity," Marketing Science, INFORMS, vol. 36(1), pages 105-123, January.
    25. Pavel Castka & Charles J. Corbett, 2016. "Governance of Eco-Labels: Expert Opinion and Media Coverage," Journal of Business Ethics, Springer, vol. 135(2), pages 309-326, May.
    26. de Boer, Joop & Aiking, Harry, 2021. "Climate change and species decline: Distinct sources of European consumer concern supporting more sustainable diets," Ecological Economics, Elsevier, vol. 188(C).
    27. Luzon, Yossi & Pinchover, Rotem & Khmelnitsky, Eugene, 2022. "Dynamic budget allocation for social media advertising campaigns: optimization and learning," European Journal of Operational Research, Elsevier, vol. 299(1), pages 223-234.
    28. Demetrios Vakratsas & Fred M. Feinberg & Frank M. Bass & Gurumurthy Kalyanaram, 2004. "The Shape of Advertising Response Functions Revisited: A Model of Dynamic Probabilistic Thresholds," Marketing Science, INFORMS, vol. 23(1), pages 109-119, April.
    29. Reddy, Puduru V. & Wrzaczek, Stefan & Zaccour, Georges, 2016. "Quality effects in different advertising models - An impulse control approach," European Journal of Operational Research, Elsevier, vol. 255(3), pages 984-995.
    30. Michael Arnold & Eric Schmidbauer & Lan Zhang, 2022. "Uniform and targeted informative advertising with asymmetric customer loyalty," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 31(1), pages 90-114, February.
    31. Joep P. Cornelissen & Rodolphe Durand, 2014. "Moving Forward: Developing Theoretical Contributions in Management Studies," Journal of Management Studies, Wiley Blackwell, vol. 51(6), pages 995-1022, September.
    32. M. L. Vidale & H. B. Wolfe, 1957. "An Operations-Research Study of Sales Response to Advertising," Operations Research, INFORMS, vol. 5(3), pages 370-381, June.
    33. Hwang, Jiyoung, 2016. "Organic food as self-presentation: The role of psychological motivation in older consumers' purchase intention of organic food," Journal of Retailing and Consumer Services, Elsevier, vol. 28(C), pages 281-287.
    34. Erickson, Gary M., 2009. "An oligopoly model of dynamic advertising competition," European Journal of Operational Research, Elsevier, vol. 197(1), pages 374-388, August.
    35. Tunuguntla, Vaishnavi & Rakshit, Krishanu & Basu, Preetam, 2023. "Bidding for an optimal portfolio of keywords in sponsored search advertising: From generic to branded keywords," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1424-1440.
    36. Sue Hornibrook & Claire May & Andrew Fearne, 2015. "Sustainable Development and the Consumer: Exploring the Role of Carbon Labelling in Retail Supply Chains," Business Strategy and the Environment, Wiley Blackwell, vol. 24(4), pages 266-276, May.
    37. Dmitri Kuksov & Ashutosh Prasad & Mohammad Zia, 2017. "In-Store Advertising by Competitors," Marketing Science, INFORMS, vol. 36(3), pages 402-425, May.
    38. Ramla Jarrar & Guiomar Martín-Herrán & Georges Zaccour, 2004. "Markov Perfect Equilibrium Advertising Strategies of Lanchester Duopoly Model: A Technical Note," Management Science, INFORMS, vol. 50(7), pages 995-1000, July.
    39. Micael-Lee Johnstone & Lay Tan, 2015. "Exploring the Gap Between Consumers’ Green Rhetoric and Purchasing Behaviour," Journal of Business Ethics, Springer, vol. 132(2), pages 311-328, December.
    40. Liu, Longzhu & Chen, Rong & He, Feng, 2015. "How to promote purchase of carbon offset products: Labeling vs. calculation?," Journal of Business Research, Elsevier, vol. 68(5), pages 942-948.
    41. A. Tsoularis, 2014. "Deterministic and stochastic optimal inventory control with logistic stock-dependent demand rate," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 6(1), pages 41-69.
    42. Zizhuo Wang & Shiming Deng & Yinyu Ye, 2014. "Close the Gaps: A Learning-While-Doing Algorithm for Single-Product Revenue Management Problems," Operations Research, INFORMS, vol. 62(2), pages 318-331, April.
    43. Justin J. P. Jansen & Ciaran Heavey & Tom J. M. Mom & Zeki Simsek & Shaker A. Zahra, 2023. "Scaling‐up: Building, Leading and Sustaining Rapid Growth Over Time," Journal of Management Studies, Wiley Blackwell, vol. 60(3), pages 581-604, May.
    44. Zhen Lian & Garrett van Ryzin, 2021. "Optimal Growth in Two-Sided Markets," Management Science, INFORMS, vol. 67(11), pages 6862-6879, November.
    45. Soregaroli, Claudio & Ricci, Elena Claire & Stranieri, Stefanella & Nayga, Rodolfo M. & Capri, Ettore & Castellari, Elena, 2021. "Carbon footprint information, prices, and restaurant wine choices by customers: A natural field experiment," Ecological Economics, Elsevier, vol. 186(C).
    46. Peter J. Danaher, 2007. "Modeling Page Views Across Multiple Websites with an Application to Internet Reach and Frequency Prediction," Marketing Science, INFORMS, vol. 26(3), pages 422-437, 05-06.
    47. Grosset, Luca & Viscolani, Bruno, 2016. "Age-structured linear-state differential games," European Journal of Operational Research, Elsevier, vol. 254(1), pages 269-278.
    48. Chowdhury, Rafi M.M.I. & Olsen, G. Douglas & Pracejus, John W., 2011. "How many pictures should your print ad have?," Journal of Business Research, Elsevier, vol. 64(1), pages 3-6, January.
    49. Schöller, Vanessa & Ulmer, Clara, 2023. "Can monetized carbon information increase pro-environmental behavior? Experimental evidence," Ecological Economics, Elsevier, vol. 206(C).
    50. George E. Kimball, 1957. "Some Industrial Applications of Military Operations Research Methods," Operations Research, INFORMS, vol. 5(2), pages 201-204, April.
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