Problem:
Transition matrix and market share
A city is served by three cable TV companies: Xcellent Cable, Your Cable, and Zephyr Cable. A survey of 1000 cable subscribers shows this breakdown of customers from the beginning to the end of August.
Company on Company on August 31
August 1 Xcellent Your Zephyr
Xcellent 300 50 50
Your 10 200 40
Zephyr 40 80 230
a. Construct the transition matrix.
b. What was each company's share of the market at the beginning and the end of the month?
c. If the current trend continues what will the market shares be?