Three companies A,B and C share a market of approximately 10,000. Suppose that their customers move back and forth between them in such a way that the number of customers of each in week t +1 is described by

1. What do the numbers 0.3, 0.5, 0.6 in the matrix above represent?

2. Suppose that the starting values A(0), B(0) and C(0) arc 1000, 4000 and 5000. In the long term, what will the values of A(t), B(1) and C(t) approximately be?

Hint: Theorem 7.4.1 of the book may be useful.

Transcribed Image Text:

[A(t+1)] B(t+1) [C(t+1)] [0.4 0.1 0.5] [A(t)] 0.4 0.3 0.1 B(t) [0.2 0.6 0.4] [C(t)] [A(t+1)] B(t+1) [C(t+1)] [0.4 0.1 0.5] [A(t)] 0.4 0.3 0.1 B(t) [0.2 0.6 0.4] [C(t)]

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1 The numbers 03 represents the probability that the market shar... View the full answer