[1][2] The model assumes that the rate of change in sales depend on three effects: response to advertising that acts positively on the unsold portion of the market, the loss due to forgetting or possibly due to competitive factors that act negatively on the sold portion of the market, and a random effect that can go either way.
Suresh Sethi published his paper "Deterministic and Stochastic Optimization of a Dynamic Advertising Model" in 1983.
[6][7][10][13] The Sethi advertising model or simply the Sethi model provides a sales-advertising dynamics in the form of the following stochastic differential equation: Where: The rate of change in sales depend on three effects: response to advertising that acts positively on the unsold portion of the market via
, and a random effect using a diffusion or White noise term that can go either way.
Subject to the Sethi model above with the initial market share
denotes the sales revenue corresponding to the total market, i.e., when