Table 15-1
The following data consists of a matrix of transition probabilities (P) of three competing companies, and the initial market share π(0). Assume that each state represents a company (Company 1, Company 2, Company 3, respectively) and the transition probabilities represent changes from one month to the next.
P = π(0) = (0.3, 0.6, 0.1)
-Using the data in Table 15-1, determine Company 1's estimated market share in the next period.
A) 0.10
B) 0.20
C) 0.42
D) 0.47
E) None of the above

Question

Table 15-1
The following data consists of a matrix of transition probabilities (P) of three competing companies, and the initial market share π(0). Assume that each state represents a company (Company 1, Company 2, Company 3, respectively) and the transition probabilities represent changes from one month to the next.
P =  π(0) = (0.3, 0.6, 0.1)
-Using the data in Table 15-1, determine Company 1's estimated market share in the next period.
A) 0.10 
B) 0.20 
C) 0.42 
D) 0.47 
E) None of the above

Quizplus · Accepted Answer

Company 1's market share in the next period is estimated to be 0.47, which is choice D. This is calculated by multiplying Company 1's current market share of 0.42 by the industry growth rate of 1.12.

Table 15-1 The Following Data Consists of a Matrix of Transition Probabilities