The Bass Model
The Bass Model was first published in 1969 by Frank M. Bass1 in a scholarly paper that became the most widely cited paper in marketing science.
The Bass Model is the most widely applied
new-product diffusion model. It been tested in many
industries and with many new products (including
services) and technologies.
The Purdue working paper2 has additional empirical cases and
Frank's handwritten notes.
The Bass Model assumes that sales of a new
technology are primarily driven by word-of-mouth
from satisfied customers. At the launch of a new
technology, mostly innovators purchase the
technology. Early owners who like the new technology
influence others to adopt it. hose who purchase
primarily because of the influence of owners are
called imitators.
The preferred Bass Model equation is the solution
to the differential equation, mathematically
where A(t) is cumulative adoptions by time t. Adoptions are sales to
first-time buyers. Mxxxxxxxxxx is the potential market, the maximum number of
cumulative adopters. F(t) is the portion of the potential market M that has
adopted by time t.
The above formula is the solution to the Bass model differential equation
described on the Bass Math page.
The three Bass Model parameters (or coefficients)are:
- M -- the maximum number of cumulative adopters
- p -- coefficient of innovation
- q -- coefficient of imitation
The portion of adopters who adopt in time period
t is
The above formula for f(t) is the
Srinivasan-Mason3 form, which is
preferred for estimation of Bass model parameters M,
p and q as well as for forecasting. These formulae are implemented in
Bass Model Forecaster.
Adoptions at time t are
The Bass Math
page
has the complete mathematical derivation of the Bass
Model from basic principles.
1.
Bass, Frank M. 1969. A new product growth for model consumer durables.
Management Science 15 215-227.
2.
Bass, Frank M. 1967. A new product growth model for consumer durables.
Purdue Working Paper.
3. Srinivasan, V., and Charlotte Mason. 1986. Nonlinear least squares
estimation of new product diffusion models. Marketing Science, 5 (2),
169–178.
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