A firm is considering the marketing of a new product. For convenience, suppose that the events of interest are simply θ1="new product is a success" and θ2="new product is a failure." The prior probabilities are P(θ1)=0.3 and P(θ2)=0.7. If the product is marketed and is a failure, the firm suffers a loss of $300,000. If the product is not marketed and it would be a success, the firm suffers an opportunity loss of $500,000. The firm is considering two separate surveys, A and B, and the results from each survey can be classified as favorable, neutral, and unfavorable. The conditional probabilities for survey A are

   P(favorable | θ1) = 0.6,   P(neural | θ1) = 0.3,   P(unfavorable | θ1) = 0.1,

   P(favorable | θ2) = 0.1,   P(neural | θ2) = 0.2,   P(unfavorable | θ2) = 0.7.

The conditional probabilities for survey B are

   P(favorable | θ1) = 0.8,   P(neural | θ1) = 0.1,   P(unfavorable | θ1) = 0.1,

   P(favorable | θ2) = 0.1,   P(neural | θ2) = 0.4,   P(unfavorable | θ2) = 0.5.

Survey A costs $20,000 and survey B costs $30,000.

 

Suppose that the firm also has the option of using both surveys. Furthermore, since both surveys would be conducted by the same marketing research firm, the total cost of the two surveys is only $40,000, provided that a decision is made in advance to use both surveys (that is, the firm cannot use one survey and then decide whether or not to use the other). Given any one of the three events θ1, θ2, and θ3, the results of survey B are considered to be independent of the results of survey A. What should the firm do?

Answer rating: 100% (QA)

To determine what the firm should do we can use the concept of expected utility to compare the different options available The expected utility is calculated by multiplying the payoff of each outcome ... View the full answer