Question

Problem 16-09 (Algorithmic)

The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities:

	To
From	Special B	MDA
Special B	0.90	0.10
MDA	0.15	0.85

1. Which brand appears to have the most loyal customers?
   
   Special B
   
   Explain.
   
   The input in the box below will not be graded, but may be reviewed and considered by your instructor.
   
   
   
2. What are the projected market shares for the two brands? If required, round your answer to three decimal places.
   
   pie1 =
   
   pie 2 =

Answer 1

A) We can see here that P(special B --> Special B) = 0.9 while
P( MDA --> MDA) = 0.85

As P(special B --> Special B) > P( MDA --> MDA)

Therefore Special B customers are more loyal customers here.

b) Let the long term market shares for the two brands Special B and MDA here be X and Y respectively. Then, we have here:
X + Y = 1

From first column, we have here:
X = 0.9X + 0.15Y
0.1X = 0.15Y
X = 1.5Y

Therefore, 2.5Y = 1
Y = 0.4

X = 0.6

Therefore the projected market shares here are given as: