Initially, three firms A, B, and C share the market for a certain commodity. Firm A has 30% of the market, Firm B has 45%, and C
has 25%. Each year, the following changes occur:
• A keeps 75% of its customers, while losing 15% to B and 10% to C.
• B keeps 60% of its customers, while losing 5% to A and 35% to C.
• C keeps 65% of its customers, while losing 15% to A and 20% to B.
(a) What is the current market share vector (ordered for A, B, and C)?
(b) Find the transition matrix for this scenario.
(c) Find the share of the market that each company has after two years.
• A keeps 75% of its customers, while losing 15% to B and 10% to C.
• B keeps 60% of its customers, while losing 5% to A and 35% to C.
• C keeps 65% of its customers, while losing 15% to A and 20% to B.
(a) What is the current market share vector (ordered for A, B, and C)?
(b) Find the transition matrix for this scenario.
(c) Find the share of the market that each company has after two years.
1 answer:
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