Table 14-2
The following data consists of a matrix of transition probabilities (P)of three competing retailers, the initial market share π(0).Assume that each state represents a retailer (Retailer 1, Retailer 2, Retailer 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 given in Table 14-2, find the market shares for the three retailers in month 1.
A)π(1)= (0.09, 0.42, 0.49)
B)π(1)= (0.55, 0.33, 0.12)
C)π(1)= (0.18, 0.12, 0.70)
D)π(1)= (0.55, 0.12, 0.33)

Question

Table 14-2
The following data consists of a matrix of transition probabilities (P)of three competing retailers, the initial market share π(0).Assume that each state represents a retailer (Retailer 1, Retailer 2, Retailer 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 given in Table 14-2, find the market shares for the three retailers in month 1.
A)π(1)= (0.09, 0.42, 0.49) 
B)π(1)= (0.55, 0.33, 0.12) 
C)π(1)= (0.18, 0.12, 0.70) 
D)π(1)= (0.55, 0.12, 0.33)

Quizplus · Accepted Answer

To find the market shares for the three retailers in month 1, we need to multiply the initial market share (π(0)) by the transition probability matrix (P) once. 
π(1) = π(0) x P
= (0.3, 0.6, 0.1) x 11eab9ea_e5cc_0442_b53a_fd4459cde4e5_TB5481_11_TB5481_11_TB5481_11 
= (0.55, 0.33, 0.12)
Therefore, the market shares for the three retailers in month 1 are 0.55 for Retailer 1, 0.33 for Retailer 2, and 0.12 for Retailer 3. The best choice is B.

Table 14-2 The Following Data Consists of a Matrix of Transition Probabilities