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Symmetries, Scaling Laws and Phase Transitions in Consumer Advertising Response

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  • Javier Marin

Abstract

Understanding how consumers respond to business advertising efforts is essential for optimizing marketing investment. This research introduces a new modeling approach based on the concepts of symmetries and scaling laws in physics to describe consumer response to advertising dynamics. Drawing from mathematical frameworks used in physics and social sciences, we propose a model that accounts for a key aspect: the saturation effect. The model is validated against commonly used models, including the Michaelis-Menten and Hill equations, showing its ability to better capture nonlinearities in advertising effects. We introduce new key parameters like Marketing Sensitivity, Response Sensitivity, and Behavioral Sensitivit, that offer additional insights into the drivers of audience engagement and advertising performance. Our model provides a rigorous yet practical tool for understanding audience behavior, contributing to the improvement of budget allocation strategies.

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  • Javier Marin, 2024. "Symmetries, Scaling Laws and Phase Transitions in Consumer Advertising Response," Papers 2404.02175, arXiv.org, revised Mar 2025.
    • Handle: RePEc:arx:papers:2404.02175
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    1. John D. C. Little & Leonard M. Lodish, 1969. "A Media Planning Calculus," Operations Research, INFORMS, vol. 17(1), pages 1-35, February.
    2. Gary Charness & Yan Chen, 2020. "Social Identity, Group Behavior, and Teams," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 691-713, August.
    3. Fred M. Feinberg, 2001. "On Continuous-Time Optimal Advertising Under S-Shaped Response," Management Science, INFORMS, vol. 47(11), pages 1476-1487, November.
    4. Nelson, Phillip J, 1975. "The Economic Consequences of Advertising," The Journal of Business, University of Chicago Press, vol. 48(2), pages 213-241, April.
    5. John R. Hauser & Kenneth J. Wisniewski, 1982. "Dynamic Analysis of Consumer Response to Marketing Strategies," Management Science, INFORMS, vol. 28(5), pages 455-486, May.
    6. John D. C. Little, 1979. "Feature Article—Aggregate Advertising Models: The State of the Art," Operations Research, INFORMS, vol. 27(4), pages 629-667, August.
    7. Huang, Jian & Leng, Mingming & Liang, Liping, 2012. "Recent developments in dynamic advertising research," European Journal of Operational Research, Elsevier, vol. 220(3), pages 591-609.
    8. 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.
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