Bass diffusion model

The classic bass model of diffusion describes the effect of the market launch of innovative products taking into account innovation and imitation effects with the aim of assessing the market situation with regard to the security of investments in new technologies without having to resort to complex modeling tools.

The basic model was presented by Frank M. Bass , professor at the University of Texas at Dallas, in 1961 and, in some modified form, is used very broadly in marketing and capital goods marketing, especially in innovation management, especially for products that are innovative because of their novelty have no analogies with existing market solutions.

The modeling of the function for the estimation of the sales takes place with the help of innovation and / or imitation coefficients, which indicate the proportion of first purchases due to the novelty of the product (innovators) or due to its dissemination (imitators), the former through advertising and the latter being initiated by "word of mouth".

If the innovation coefficient is smaller than the imitation coefficient (normal case), then the course of the sales curve corresponds to the life cycle hypothesis with initially increasing and then decreasing sales. In the other case the curve shows a descending course from the beginning:

${\displaystyle {}^{{\text{Absatz}}=\left({\text{Innovationskoeffizient}}+{\text{Imitationskoeffizient}}\cdot {\frac {\text{Bestand}}{\text{Marktpotential}}}\right)\cdot \left({\text{Marktpotential}}-{\text{Bestand}}\right)}}$

As a formula

${\displaystyle x_{t}=(p+q\cdot {\frac {Q_{t-1}}{M}})\cdot (M-Q_{t-1})}$

After reshaping you get:

${\displaystyle x_{t}=pM+(q-p)Q_{t-1}-{\frac {q}{M}}Q_{t-1}^{2}}$

Legend

variable	Description of the variables
${\displaystyle M}$	Market potential
${\displaystyle Q}$	Duration
${\displaystyle p}$	Innovation coefficient
${\displaystyle q}$	Imitation coefficient
${\displaystyle t}$	Period index

Since the parameters are mostly unknown due to the novelty of the product, they are estimated with the help of regression analysis , with the parameters appearing as regressors : ${\displaystyle \textstyle A_{i}}$

${\displaystyle x_{t}=A_{1}+A_{2}Q_{t-1}+A_{3}Q_{t-1}^{2}}$

With:

${\displaystyle \textstyle A_{1}=pM}$

${\displaystyle \textstyle A_{2}=q-p}$

${\displaystyle \textstyle A_{3}=-{\frac {q}{M}}}$

The missing data is determined by solving the equation:

${\displaystyle \textstyle M=\left(({\frac {A_{2}}{2A_{3}}})^{2}-{\frac {A_{1}}{A_{3}}}\right)^{\frac {1}{2}}-{\frac {A_{2}}{2A_{3}}}}$

${\displaystyle \textstyle p={\frac {A_{1}}{M}}}$

${\displaystyle \textstyle q=-A_{3}M}$

See also

Assessor (product policy)

Web links

• Bass Curve Diffusion