Ryanair is Europes airline with competitive fares. Its main competitors are EasyJet and Norwegian. Ryanair wishes to see that passengers who chose Ryanair would continue to select its services next time. Market research shows that this currently happens with a probability of 0.4. More generally, the probabilities that passengers switch from one companys services to anothers are given as follows. Probability of switch Next purchase with Ryanair EasyJet Norwegian Last purchase with Ryanair 0.4 0.3 0.3 EasyJet 0.2 0.5 0.3 Norwegian 0.3 0.2 0.5 i.

The current market share for Ryanair is 30%, and those with EasyJet and Norwegian are 40% and 30% respectively. Statistics show that a typical customer makes two purchases per quarter. Calculate the market share a quarter later using the above transition probability matrix. [20% of marks for this question] ii. Given the transition probability matrix of purchases and the current market share in (i), construct a system of linear equations, and estimate the steady market share of Ryanair, EasyJet and Norwegian a year later using the matrix method.