Management Science: Markov Processes 1 answer below »

1. In the market share analysis of Section 16.1, suppose that we are considering the Markov process associated with the shopping trips of one customer, but we do not know where the customer shopped during the last week. Thus, we might assume a 0.5 probability that the customer shopped at Murphy and a 0.5 probability that the customer shopped at Ashley at period 0; that is, (pi1(0)=0.5) and (pi2(0)=0.5) . Given these initial state probabilities, develop a table similar to Table 16.2 showing the probability of each state in future periods. What do you observe about the long-run probabilities of each state?

2. Management of the New Fangled Softdrink Company believes that the probability of a customer purchasing Red Pop or the company major competition, Super Cola, is based on the customers most recent purchase. Suppose that the following transition probabilities are appropriate:

To

From Red Pop Super Cola

Red Pop 0.9 0.1

Super Cola 0.1 0.9

a. Show the two-period tree diagram for a customer who last purchased Red Pop. What is the probability that this customer purchases Red Pop on the second purchase?

b. What is the long-run market share for each of these two products?