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)
E)π(1)= (0.33,0.33,0.33)

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) 
E)π(1)= (0.33,0.33,0.33)

Quizplus · Accepted Answer

We can use the formula for calculating the market share of each retailer in month 1, which is given by π(1) = π(0)P. 
Using the given transition probability matrix P and initial market share vector π(0), we get:

π(1) = (0.3, 0.6, 0.1) * 11eabb83_5a40_3a8a_b8db_1b08ea459678_TB2950_11_TB2950_11_TB2950_11
      = (0.55, 0.33, 0.12)

Therefore, the answer is B, and the market shares for the three retailers in month 1 are 0.55, 0.33, and 0.12 for Retailer 1, Retailer 2, and Retailer 3 respectively.

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