  Comprehending how consumers react to advertising inputs is essential for
marketers aiming to optimize advertising strategies and improve campaign
effectiveness. This study examines the complex nature of consumer behaviour by
applying theoretical frameworks derived from physics and social psychology. We
present an innovative equation that captures the relation between spending on
advertising and consumer response, using concepts such as symmetries, scaling
laws, and phase transitions. By validating our equation against well-known
models such as the Michaelis-Menten and Hill equations, we prove its
effectiveness in accurately representing the complexity of consumer response
dynamics. The analysis emphasizes the importance of key model parameters, such
as marketing effectiveness, response sensitivity, and behavioural sensitivity,
in influencing consumer behaviour. The work explores the practical implications
for advertisers and marketers, as well as discussing the limitations and future
research directions. In summary, this study provides a thorough framework for
comprehending and forecasting consumer reactions to advertising, which has
implications for optimizing advertising strategies and allocating resources.
