Symmetries, Scaling Laws and Phase Transitions in Consumer Advertising Response

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.