Question

2. Market share of Brand A, B, C are 50%,30%,and 20%. Customers shift their brands. Brand
switching matrix every quarter is given below.
Find the market share at the end of each quarter.
To A B с
From
A
50% 30% 20%
B
20% 70% 10%
С
20% 20% 60%​

Answer 1

Answer:

We have the initial system state s1 given by s1 = [0.30, 0.70] and the transition matrix P is given by

P = | 0.85 0.15 |2 = | 0.7375 0.2625 |

| 0.10 0.90 | | 0.1750 0.8250 |

where the square term arises as Business Class customers make 2 flights a year on average.

Hence after one year has elapsed the state of the system s2 = s1P = [0.34375, 0.65625]

After two years have elapsed the state of the system = s3 = s2P = [0.368, 0.632]

and note here that the elements of s2 and s3 add to one (as required).

So after two years have elapsed BA's share of the Business Class market is 36.8%