A Local Business a Has Two Competitors, B and C

question 134

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:

Customs Tariff

A schedule of duties imposed by a government on imported or exported goods.

Traded Commodities

Goods or raw materials that are bought and sold on commodity exchanges or the open market.

Extraterritorial Application

Laws or legal mandates that are applied beyond the territorial boundaries of the jurisdiction that created them.

Licensing Arrangement

A legal agreement allowing one party to use another's property, such as intellectual property, under certain conditions.