Michaelis-Menten equations in marketing mix modeling

Marketing Mix Modeling relies on saturation curves to capture how marketing effectiveness changes with spend. While Hill functions offer flexibility through their shape parameter, the Michaelis-Menten equation provides a simpler, more interpretable model for channels that exhibit immediate diminishing returns.

Originally developed to describe enzyme kinetics in biochemistry, the Michaelis-Menten equation has become a fundamental tool in marketing analytics for modeling saturation effects without threshold behavior.

Where: - R is the response (e.g., conversions, sales) - X is the marketing spend - K is the half-saturation constant (spend level where response reaches 50% of maximum)

The Michaelis-Menten equation is actually a special case of the Hill function where n = 1. This makes it the simplest saturation model that still captures diminishing returns.