Classroom Companion: Business

Customers (B)
Year (t)
Only imitators (p=0)
Only innovators (q=0)
Latency time only innovators 2 years
Latency time only imitators 6 years
Market growth 50% 
60%
only imitators 1 year
Market growth 50% 
60%
only innovators 4 years
0
1 00 000
2 00 000
3 00 000
4 00 000
5 00 000
6 00 000
7 00 000
8 00 000
9 00 000
1 000 000
. Fig. 18.4 Latency period in the Bass diffusion model. (Authors’ own figure)
 
Chapter 18 · Digital Market Modeling

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5
The flow of new customers from potential customers to Supplier 1.
5
The flow of new customers from potential customers to Supplier 2.
5
The flow of customers from Supplier 1 to Supplier 2.
5
The flow of customers from Supplier 2 to Supplier 1.
The latter two flows are called churning. The model also includes four feedback 
loops as shown in the figure.
The rate of new customers choosing Supplier 1 is (p
1
+ q
1
B
1
)(N − B
1
− B
2
), and 
the rate of new customers choosing Supplier 2 is (p
2
+ q
2
B
2
)(N − B
1
− B
2
). Here, the 
Bass equation is used to express the dynamics of the flows.
The net number of customers churning from Supplier 2 to Supplier 1 is C
21
= B
2
(c
2
+ d
2
B
1
) − B
1
(c
1
+ d
1
B
2
). The first term is the rate at which Supplier 1 gains cus-
tomers from Supplier 2, and the second term is the rate at which Supplier 1 loses 
customers to Supplier 2. The net number of customers churning to Supplier 2 is C
12
= − C
21
= B
1
(c
1
+ d
1
B
2
) − B
2
(c
2
+ d
2
B
1
) since the churning process does not create 
new customers (the net result of the two churning flows must be zero). The param-
eters c
1
and c
2
are denoted coefficients of spontaneous churning, and the parameters 
d
1
and d
2
are denoted coefficients of stimulated churning (or imitated churning). 
Again, the Bass equation is applied to the churning flows. Imitated churning 
constitutes churners that switch suppliers because of the size of the competing 
s upplier.
The dotted lines in the figure are the feedback loops representing the network 
effect that stimulates imitators into choosing a supplier or stimulates customers 
into churning to the other supplier.
Putting all this together results in the following coupled set of dynamic market 
equations:
Customers
Supplier 1
Potential
customers
Customers
Supplier 2
. Fig. 18.5 Model of two competing suppliers with churning. (Authors’ own figure)