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Suppose that a recent study shows that each week each of 300 families buys a gallon of apple juice from company A, B, or C. Let denote the probability that a gallon produced by company A is of unsatisfactory quality, and define
and
similarly for companies B and C. If the last gallon of juice purchased by a family is satisfactory, 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 one 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.
-After a year, what will the market share for each of the three companies be? Assume = 0.10,
= 0.15, and
= 0.20. (Hint: Use the RISKBINOMIAL function to model how many people switch from A, then how many switch from A to B and from A to C.)
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The Securities and Exchange Commission, a U.S. government agency that oversees the securities markets and protects investors.
Registration Statements
Documents filed with regulatory authorities, such as the SEC, detailing the obligations and financial conditions of entities offering securities for sale to the public.
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Mandatory reports filed by publicly traded companies at regular intervals as required by regulatory authorities.
Reconciliation Statements
Reconciliation Statements are financial documents that compare two sets of records to check that figures are correct and in agreement, commonly used to reconcile bank statements to accounting records.
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