A Local Business a Has Two Competitors, B and C

question 18

Multiple Choice

A local business A has two competitors, B and C. No customer patronizes more than one of these businesses at the same time. Initially, the probabilities that a customer patronizes A, B, or C are 0.2, 0.6, and 0.2, respectively. Suppose A initiates an advertising campaign to improve its business and finds the following transition matrix to describe the effect. ​ ​
Find the steady-state vector for this market-that is, the long-range share of the market that each business can expect if the transition matrix holds.
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Definitions:

Opportunity Cost

The expense incurred by not choosing the second-best option during a decision-making process.

Sweaters

A knitted garment typically made of wool, cotton, or synthetic yarn, worn over the upper body for warmth.

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Specialization

The process in economics and production where individuals or entities focus on a narrow area of expertise to increase efficiency and output.