Assume Shoa, Samson and Africa are the only three competing Bakeries in town. A marketing Cresearch firm has found out that each bakery retains 75% of its customers every month. Every month 10% of Shoa bakery's cutomers switch to Samson bakery, while 20% of customers of Samson bakery switch to Shoa bakery. Moreover, Samson bakery gains 15% of customers of Africa every month. In addition, for the month of June, the market share of Shoa and Samson bakery is 30% and 20% respectively.

a) Present the transition matrix for the above case

b) Find the respective market shares of the three bakeries for the month of July and September.

c) What will each bakery's market share be at equilibrium?​