Classroom Companion: Business

18.2 · Bass Diffusion Model

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who have already purchased the good. There are B such customers. Note that the 
total population (potential adopters plus adopters) is assumed to be constant and 
equal to N and that anyone having bought the good keeps it indefinitely. This 
implies that birth or death processes are not included in the model. To be able to 
solve the equations using analytic tools, it is also assumed that all flow parameters 
are constants.
When individuals buy a good, they become customers and move from the 
potential customers container to the customers container. This is the basic dynamics 
of the model.
There are two flows of new buyers of the good:
5
Flow of innovators consists of individuals who buy the good independently of 
who else has bought it. These are the spontaneous buyers—also referred to as 
early adopters. The strength of the flow is p(N − B) in which the intensity by 
which an arbitrary individual will buy the good is p. The parameter p is called 
the coefficient of innovation.
5
Flow of imitators consists of individuals who buy the good because others have 
bought it. These individuals are also called late followers (or just followers) or 
stimulated buyers. The strength of the flow is qB(N − B) in which qB is the 
intensity by which an individual is stimulated into buying the good, expressing 
that the intensity by which the imitator will buy the good is proportional to the 
current number of customers. The parameter q is called the coefficient of 
 imitation.
The model also contains a feedback loop representing the network effect. The strength 
of the feedback is proportional to the number of customers who have already bought 
the good. This is a network effect of the Metcalfe type; see 
7
Chap. 
9
. 
.
Table 
18.1
 
summarizes the parameters used in the Bass diffusion model.
The total flow of customers at any instant of time, dB/dt, is equal to the sum of 
innovators and imitators buying the service at that instant of time. The differential 
equation for the market dynamics follows then directly from 
.
Fig. 
18.1
:
. Table 18.1 Parameters in the Bass diffusion model. (Authors’ compilation)