Classroom Companion: Business

 
Chapter 11 · Path Dependence

---

171
11
Fig. 11.1 Mathematical model with churning from technology 2 to technology 1. 
(Authors’ own figure)
Potential users
Flow of
Churning users
Technology 2
Technology 1
Flow of new users 
N − A − B
rB
A
A
p(N
− A − 
B)
p(N 
−
A 
− B
)
A
N
e
B
N
N
p r
pe
p r e
pt
rt
pt




 













1
2
2
2
.
.
Figure 
11.2
 shows the evolution 
of the market for p = 0.5 and 
r = 0.1. The ordinate is the market 
share (A/N, B/N), and the abscissa is 
the number of years after the tech-
nology was introduced.
In this model, there is a net 
churning from technology 2 to tech-
nology 1, and technology 1 captures 
the whole market in the end. If the 
net churning had been from tech-
nology 1 to technology 2, then tech-
nology 2 would have captured the 
whole market. The alternative the 
market chooses cannot be predicted 
by standard economic theory. Both 
alternatives are stable equilibria, 
and which of them is finally chosen 
is path dependent.
The theoretical market evolu-
tion shown in 
.
Fig.  
11.2
is not too 
different from the actual evolution 
of the VHS and Betamax markets 
as described in 
7
Case Study 
11.1
. 
After about 4 years VHS had cap-
tured almost 60% of the US market, 
and after 13 years VHS controlled 
more than 90% of that market.