A analytic model is presented based on the idea that the diffusion of a new product is governed by an evolutionary process, characterized by a reinforcing relation between demand and supply. If the market is heterogeneous, i.e. consumers are very price sensitive, the model suggests that the diffusion process is determined by Gompertz equation. The cumulativeadoption curve is S-shaped, but unlike logistic models, the Gompertz curve is not symmetric.
The theory require the presence of an economic potential that governs the dynamics of the evolutionary adjustment process. Four free parameters are necessary to model the time evolution of the market price, the market penetration and first purchase sales. The application of Gompertz diffusion model to three empirical investigations on consumer goods in the USA
confirms the intimate relationship between price decline and market penetration.
Universal Dynamics of Complex Systems