Two products A and B currently share the market with shares of 55% and 45% each respectively. Each week some brand switching takes place of those who bought A the previous week, 60%buy it again while 40% switch to B of those who bought B the previous week , 80% buy it again while 20% switch to A
i. Construct the initial probability transition matrix (T) of the switching probabilities(1 mark)
ii. Construct the initial market share matrix (ms) (1 mark)
iii. Find week two market share (3 marks)
iv. Find week three market share (3 marks)
v. Predict the market share at equilibrium (12 marks)