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 pB and pC 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 pA
0.10, pB
0.15, and pC

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 pA, pB, and pC as in part a.)

Skill-Extending Problems