Solve the following:
Markov Analysis
Q1. Three fast food hamburger restaurants are competing for the college lunch crowd. Burger Bills has 40% of the market while Hungary Heifer and Salty Sams each have 30% of the market. Burger Bills loses 10% of its customers to the Hungary Heifer and 10% to Salty Sams each month. The Hungary Heifer loses 5% of its customers to Burger Bills and 10% to Salty Sams each month. Salty Sams loses 10% of its customers to the Burger Bills while 20% go to the Hungary Heifer. What will the market shares be for the three businesses next month? What will the market shares be in the long run? (Equilibrium)
Q2. There is a 30% chance that any client of company A will switch to company B this year. There is a 20% chance that any client of company B will switch to company A this year. If these probabilities are stable over the years, and if company A has 1,000 clients and company B has 1,000 clients, in the long run (assuming probabilities do not change), what will the market shares be?