*5. Customers tend to exhibit loyalty to product brands but may be persuaded through clever marketing and advertising to switch brands. Consider the case of three brands: A, B, and C. Customer "unyielding" loyalty to a given brand is estimated at 75%, giving the competitors only a 25% margin to realize a switch. Competitors launch their advertising campaigns once a year. For brand A customers, the probabilities of switching to brands B and Care .1 and .15, respectively. Customers of brand B are likely to switch to A and C with probabilities .2 and .05, respectively. Brand C customers can switch to brands A and B with equal probabilities.

(a) Express the situation as a Markov chain.

(b) In the long run, how much market share will each brand command?

(c) How long on the average will it take for a brand A customer to switch to brand B?

To brand C?