(solution) A company is considering using Markov theory to analyse brand switching between three different…

(solution) A company is considering using Markov theory to analyse brand switching between three different…

A company is considering using Markov theory to analyse brand switching between three different brands of floppy disks. Survey data has been gathered and has been used to estimate the following transition matrix for the probability of moving between brands each month: To Brand 1 2 3 From Brand 1 | 0.80 0.10 0.10 2 | 0.03 0.95 0.02 3 | 0.20 0.05 0.75 The current (month 1) market shares are 45%, 25% and 30% for brands 1, 2 and 3 respectively. •What will be the expected market shares after two months have elapsed (i.e. in month 3)? •What is the long-run prediction for the expected market share for each of the three brands? •Would you expect the actual market share to approach the long-run prediction for the market or not (and why)?