# Orange Juice Market Share1 Suppose that each week every

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```					                     Orange Juice Market Share1
Suppose that each week every family in the United States 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
1,000,000 gallons of orange juice are purchased each week.
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 binomial
distribution to see how many people switch from A and then use the
binomial distribution 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.)

1Based on 12-38 (p. 686) in Practical Management Science (2 nd ed., Winston and Albright, 2001
Duxbury Press). Based on Babich (1992).

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