The University of South Taiwan has had steady enrollments over the past 5 years. The school has its own bookstore, called University Book Store, but there are also three private bookstores in town: Loupot’s Book Store, College Book Store, and Battle’s Book Store. The university is concerned about the large number of students who are switching to one of the private stores. As a result, South Taiwan’s president, Akio Lang, has decided to give a student 3 hours of university credit to look into the problem. The following matrix of transition probabilities was obtained:

At the present time, each of the four bookstores has an equal share of the market. What will the market shares be for the next period?  

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UNIVERSITY BILL'S COLLEGE BATTLE'S UNIVERSITY 0.6 0 0.1 0.05 BILL'S COLLEGE BATTLE'S 0.2 0.1 0.1 0.7 0.2 0.1 0.1 0.8 0 0.05 0.1 0.8