Markov Analysis
Markov Analysis
1. 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)
2. 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?
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Markov theory can be applied to analyze brand switching . The following is the transition matrix for the probability of moving between brands each month:
To
Burger Hungary Salty
Bills Heifer Sams
From
Burger Bill 0.80 0.10 0.10
Hungary Heifer 0.05 0.85 0.10
Salty Sams 0.10 0.20 0.70
The current (month 1) market shares are 40%, 30% and 30%
We have the initial system state S1 given by S1 = [0.40, 0.30, 0.30] and the transition matrix P given by
Let Si be the state of the system (market share) in the ith month
Si =Si-1P
S2 = S1.P = ...
Solution Summary
This solution describes Markov Analysis, Market Share and Brand switching calculations.