Bass model

The Bass diffusion model was developed by Frank Bass and describes the process of how new products get adopted as an interaction between users and potential users. An excel that can help calculate the adoption rate can be downloaded

here

(source: http://leeds-faculty.colorado.edu/lawrence/Tools/index.htm)

This model has been widely influential in marketing and management science. In 2004 it was selected as one of the ten most frequently cited papers in the 50-year history of Management Science e Bass diffusion model was developed by Frank Bass and describes the process of how new products get adopted as an interaction between users and potential users.

Model formulation

${\frac {f(t)}{1-F(t)}}=p+qF(t)$

Where:

• $f(t)$ is the rate of change of the installed base fraction
• $F(t)$ is the installed base fraction
• $p$ is the coefficient of innovation
• $q$ is the coefficient of imitation

Sales $S(t)$ is the rate of change of installed base (i.e. adoption) $f(t)$ multiplied by the ultimate market potential $m$ :

$S(t)=mf(t)$ $S(t)$=$m{\frac {(p+q)^{2}}{p}}$ ${\frac {e^{-(p+q)t}}{(1+{\frac {q}{p}}e^{-(p+q)t})^{2}}}$

The time of peak sales $t^{*}$

$t^{*}={\frac {\ln q-\ln p}{p+q}}$

Explanation

The coefficient p is called the coefficient of innovation, external influence or advertising effect. The coefficient q is called the coefficient of imitation, internal influence or word-of-mouth effect.Typical values of p and q when time t is measured in years

• The average value of p has been found to be 0.03, and is often less than 0.01
• The average value of q has been found to be 0.38, with a typical range between 0.3 and 0.5