BassModell

BassModell

The Bass-Modell, also known as the Bass diffusion model, is a mathematical framework for describing how new products and technologies are adopted within a bounded market over time. Developed by Frank M. Bass in 1969, it is widely used in marketing and diffusion research to forecast sales and understand the dynamics of adoption. The model emphasizes two sources of influence: external influence from mass media and advertising, and internal influence from interactions among existing adopters.

The core idea is that the market potential is finite and that adoption follows an S-shaped curve. The model uses two parameters: p, the coefficient of innovation (external influence), and q, the coefficient of imitation (internal influence). Let F(t) be the cumulative share of potential adopters who have adopted by time t. The differential equation is dF/dt = (p + q F)(1 - F). A common closed-form solution for F(t) is F(t) = [1 − exp(−(p+q)t)] / [1 + (q/p) exp(−(p+q)t)], assuming initial adoption is negligible. The absolute number of adopters at time t equals m dF/dt, where m is the market potential (the total number of potential adopters). As t grows, F(t) approaches 1 (or m adopters in absolute terms).

Applications and variants: The Bass-Modell is used to forecast the spread of consumer durables and other technologies, estimate market potential, and evaluate marketing strategies. It has numerous variants, including generalized or multi-segment versions, and discrete-time formulations that incorporate price effects, marketing interventions, or competition.

Limitations: The model assumes a homogeneous population, constant p and q over time, and a fixed market potential, while ignoring network structures, competitive dynamics, and external changes that can alter adoption patterns.