The first quick-oil-change store in Problem 14-28 retains 73% of its market share. This represents a probability of 0.73 in the first row and first column of the matrix of transition probabilities. The other probability values in the first row are equally distributed across the other stores (namely, 3% each). What impact does this have on the steady-state market shares for the quick-oil-change stores?
In Problem 14-28, Sandy Sprunger is part owner in one of the largest quick-oil-change operations for a medium-sized city in the Midwest. Currently, the firm has 60% of the market. There are a total of 10 quick lubrication shops in the area. After performing some basic marketing research, Sandy has been able to capture the initial probabilities, or market shares, along with the matrix of transition, which represents probabilities that customers will switch from one quick lubrication shop to another. These values are shown in the table on the next page: Initial probabilities, or market share, for shops 1 through 10 are 0.6, 0.1, 0.1, 0.1, 0.05, 0.01, 0.01, 0.01, 0.01, and 0.01.