Problem 2
a) The marketing department of a vitamin water company wishes to evaluate the maximum expected payoff from introducing a new strawberry drink. What decision, in terms of choosing the best investment level, could the marketing department make using the payoff table below? Consider that the probability that the market share is less than 1% is 0.2, that the probability that market share is between 1 and 4% is 0.5, and that the probability that market share is at least 4% is 0.3. Consider that the marketing department is risk neutral.
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Market Share
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Investment Level
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< 1%
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1%-4%
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³ 4%
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Low
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300,000
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400,000
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500,000
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High
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-400,000
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300,000
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3,000,000
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b) What is the maximum amount of money the company could spend to get more information about the market share?
c) The company can conduct some market research to get more information about the eventual market share. The research will result in a report with two possible results: “Predict High Market Share” and “Predict Low Market Share”. The conditional probabilities for these two types of reports depending on the three possible market shares in the past are given in the following table. How much should the company be willing to spend to conduct the market research that will result in one of the two possible reports? (10 Points)
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Market Share
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Report
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Below 1%
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Between 1% - 4%
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Above 4%
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“Predict Low Market Share”
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0.8
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0.6
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0.3
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“Predict High Market Share”
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0.2
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0.4
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0.7
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