Bass Diffusion

271. Bass Diffusion

A simple SD model of new-product adoption. Frank Bass (1969). Predicts the characteristic S-shaped adoption curve from two parameters.

Let = cumulative adopters, = total market size. Adoption rate:

Two parameters:

: coefficient of innovation — adoption driven by external influence (advertising, news, intrinsic appeal)
: coefficient of imitation — adoption driven by word-of-mouth (existing adopters influencing potential adopters)

Two interpreting terms:

: innovation — fraction of remaining non-adopters who’d adopt based on external info
: imitation — non-adopters influenced by the proportion of current adopters; total imitation pressure proportional to remaining market

Together: a limits-to-growth archetype with reinforcing word-of-mouth and balancing market exhaustion.

Early on (): adoption is mostly — small, driven by innovation only.

Middle: approaches ; imitation term peaks, growing very fast.

Late: shrinks; growth slows.

Peak adoption rate at:

Time of peak adoption:

For typical , : peak around 5-10 years after launch.

Bass fit the model to historical sales of color TVs, washing machines, and dozens of other durables. Excellent S-curve fits with just as parameters.

Common parameter values:

Generalized Bass: include effect of price, advertising → time-varying
Repeat purchase: cumulative installed base cumulative purchases
Substitute / next-generation products: previous-generation forms downstream pool

The Bass model is the default for:

Most consumer-electronics product launches use Bass as the baseline forecast.