Suppose research on three major cell phones companies revealed the following transition matrix for the probability that a person with one cell phone carrier switches to another.
Will Switch to
Company A Company B Company C
Company A .91 .07 .02
Now has Comp. B .03 .87 .10
Company C .14 .04 .82
The current share of the market is [.26, .36, .38] for Companies A, B, and C respectively. Find the share of the market held by each company after
a) 1 year
b) 2 years
c) 3 years
d) What is the long-range prediction?