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:

Credit Terms

Conditions under which credit is extended by a lender to a borrower, detailing the repayment time frame, interest rate, and other conditions of the credit agreement.

Merchandise

Goods bought for resale in the course of business, typically in a retail or wholesale establishment.

Payments

The act of transferring money in exchange for goods or services, or to settle debts.

Inventory System

A mechanism for tracking and managing items that a company holds in stock, covering aspects like ordering, storing, using, and selling these goods.