Question 15 (7 pts). The market for a cosmetic product is divided between two competitors, Alpha and Beta. Suppose that Alpha and Beta start by sharing the market equally, i.e. they each initially hold 50% of the market share. Analysts predict that, each year, 30% of Alpha customers will switch to Beta, and 20% of Beta customers will switch to Alpha.

(a) (1 pt) What is the migration (or stochastic or transition) matrix P for this problem?

(b) (1 pt) Determine the market shares of Alpha and Beta after one year, according to the forecasts of the Analysts.

(c) (5 pts) Let's assume that Alpha and Beta do not change their marketing strategies and that the migration between the two competitors remains the same. What will be the long-term market shares?