Based on Babich XXXXXXXXXXSuppose that each week, each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of...

Based on Babich (1992). Suppose that each week, each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define p_B
and p_C
similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, then the next week they will purchase a gallon of juice from the same company. If the last gallon of juice purchased by a family is not satisfactory, then the family will purchase a gallon from a competitor. Consider a week in which A families have purchased juice A, B families have purchased juice B, and C families have purchased juice C. Assume that families that switch brands during a period are allocated to the remaining brands in a manner that is proportional to the current market shares of the other brands. Thus, if a customer switches from brand A, there is probability B/(B+  C) that he will switch to brand B and probability C/(B + C) that he will switch to brand C. Suppose that the market is currently divided equally: 100 families for each of the three brands.

a. After a year, what will the market share for each firm be? Assume
0.20. (Hint: You will need to use the RISKBINOMIAL function to see how many people switch from A and then use the RISKBINOMIAL function again to see how many switch from A to B and from A to C.)

b. Suppose a 1% increase in market share is worth $10,000 per week to company A. Company A believes that for a cost of $1 million per year, it can cut the percentage of unsatisfactory juice cartons in half. Is this worthwhile? (Use the same values of p_A, p_B, and p_C
as in part a.)