er to market a new А compan product. Assume, for simplicity, that if this product is marketed, there are only two possible outcomes: succese or failure. The company assesses that the probabilities of these two outcomes arep and 1 - p, respectively. If the product is marketed and it proves to be a failure, the company will have a net loss of $450,000. If the produc is marketed and it proves to be a success, the com- pany will have a net gain of $750,000. If the company decides not to market the product, there is no gain or loss. The company can first survey prospective buyers of this new product. The results of the consumer survey can be classified as favorable, neutral, or unfavorable. Based on similar surveys for previous products, the company assesses the probabilities of favorable, neutra and unfavorable survey results to be 0.6, 0.3, and 0.1 for a product that will eventually be a success, and it assesses these probabilities to be 0.1, 0.2, and 0.7 for a product that will eventually be a failure. The total cost administering this survey is C dollars.

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of these two outcomes are p and 1
marketed, there are only two possible outcomes: success
product. Assume, for simplicity, that if this product is
company will have a net loss of $450,000. If the product
or failure. The company assesses that the probabilities
pany will have a net gain of $750,000. If the company
42. A company is considering whether to market a new
the product is marketed and it proves to be a failure, the
is marketed and it proves to be a success, the com-
of these two outcomes are p and 1
p, respectively. If
-
it
a
is marketed and it proves to be a success, the com-
will have a net gain of $750,000. If the company
decides not to market the product, there is no gain or
loss. The company can first survey prospective buyers
of this new product. The results of the consumer survey
divan be classified as favorable, neutral, or unfavorable.
Based on similar surveys for previous products, the
company assesses the probabilities of favorable, neutral,
and unfavorable survey results to be 0.6, 0.3, and 0.1
for a product that will eventually be a success, and it
assesses these probabilities to be 0.1, 0.2, and 0.7 for a
product that will eventually be a failure. The total cost of
administering this survey is C dollars.
a. Let p = 0.4. For which values of C, if any, would this
company choose to conduct the survey?
b. Let p = 0.4. What is the largest amount this com-
pany would be willing to pay for perfect informa-
tion about the potential success or failure of the
new product?
C. Let p = 0.5 and C = $15.000. Find the strategy
that maximizes the company's expected net earn-
%3D
Ings. Does the optimal strategy involve conducting
the
survey? Explain why or why not.
Transcribed Image Text:of these two outcomes are p and 1 marketed, there are only two possible outcomes: success product. Assume, for simplicity, that if this product is company will have a net loss of $450,000. If the product or failure. The company assesses that the probabilities pany will have a net gain of $750,000. If the company 42. A company is considering whether to market a new the product is marketed and it proves to be a failure, the is marketed and it proves to be a success, the com- of these two outcomes are p and 1 p, respectively. If - it a is marketed and it proves to be a success, the com- will have a net gain of $750,000. If the company decides not to market the product, there is no gain or loss. The company can first survey prospective buyers of this new product. The results of the consumer survey divan be classified as favorable, neutral, or unfavorable. Based on similar surveys for previous products, the company assesses the probabilities of favorable, neutral, and unfavorable survey results to be 0.6, 0.3, and 0.1 for a product that will eventually be a success, and it assesses these probabilities to be 0.1, 0.2, and 0.7 for a product that will eventually be a failure. The total cost of administering this survey is C dollars. a. Let p = 0.4. For which values of C, if any, would this company choose to conduct the survey? b. Let p = 0.4. What is the largest amount this com- pany would be willing to pay for perfect informa- tion about the potential success or failure of the new product? C. Let p = 0.5 and C = $15.000. Find the strategy that maximizes the company's expected net earn- %3D Ings. Does the optimal strategy involve conducting the survey? Explain why or why not.
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