You decide to do a simple market survey irrespective of your first decision. One question is posed to the first 20 customers who search a keyword related to your business on the internet. Participants were asked about the likelihood of supporting:
1 = your business;
2 = competitor A; or
3 = competitor B from one month to the next.
The survey results are shown below.
Business supported Customer number Month 1 Month 2 1 3 3 3 2 2 N 3 1 3 3 4 5 3 6 3 7 2. 8 N 9 WN NNW WNNW NNW 2 10 1 3 11 12 13 N 2 2 2 2 14 N Nm 15 3 16 3 3 17 1 1 18 1 2 w N N E 19 3 2 20 2 a) Use the survey results to compile a matrix of transition probabilities and complete this table: Your business Competitor A Competitor B P = . Tip: You need to count the number of occurrences (frequency) for each of the following categories: support for your business in the first and second months; support for your business in the first month and competitor A in the second; support for your business in the first month and competitor B in the second; support for competitor A in the first month and your business in the second; support for competitor A in the first and second months; support for competitor A in the first month and competitor B in the second; support for competitor B in the first month and your business in the second; support for competitor B in the first month and competitor A in the second; and support for competitor B in the first and second months. b) What is the steady state for the three businesses? n = n P at: 11 TT 2 . . . TT 3 c) How long will it take for the market to reach stability? Business supported Customer number Month 1 Month 2 1 3 3 3 2 2 N 3 1 3 3 4 5 3 6 3 7 2. 8 N 9 WN NNW WNNW NNW 2 10 1 3 11 12 13 N 2 2 2 2 14 N Nm 15 3 16 3 3 17 1 1 18 1 2 w N N E 19 3 2 20 2 a) Use the survey results to compile a matrix of transition probabilities and complete this table: Your business Competitor A Competitor B P = . Tip: You need to count the number of occurrences (frequency) for each of the following categories: support for your business in the first and second months; support for your business in the first month and competitor A in the second; support for your business in the first month and competitor B in the second; support for competitor A in the first month and your business in the second; support for competitor A in the first and second months; support for competitor A in the first month and competitor B in the second; support for competitor B in the first month and your business in the second; support for competitor B in the first month and competitor A in the second; and support for competitor B in the first and second months. b) What is the steady state for the three businesses? n = n P at: 11 TT 2 . . . TT 3 c) How long will it take for the market to reach stability
