Question

The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands.  

From/To	A	B	C	D	Number of Customers
A	0.2	0.3	0.1	0.4	2300
B	0	0.2	0.5	0.3	2800
C	0.3	0.5	0	0.2	2500
D	0.3	0.4	0.3	0	2400

a) What is the market share of Brand D in the long run? Answer in 2 decimal places.    

b) How many customers will shift preference in using  Brand C soap in the long run?  

c) What is the mean return time of Brand 1? Answer in 2 decimal places.   

d) What is the percentage change of Brand B? Answer in 2 decimal places.   

Answer 1