1. A particular product is both manufactured and marketed by two different firms. The total demand for the product is virtually fixed, so neither firm has advertised in the past. However, the owner of firm A is considering an advertising campaign to woo customers away from Firm B. Many aspects of the problem are uncertain. The ad campaign will cost either $150k, $200k, or $250k with probabilities .2, .4, and .4 respectively. She is uncertain about the number of customers that will switch to her firm as a result of the advertising, but she assumes that she will either gain 10 percent, 20 percent, or 30 percent of the market. She believes that the events “gain 20 percent” and “gain 30 percent” are equally likely, and that each of these events is three times as likely as “gain 10 percent”. She believes that the increase in profits for each 10 percent of market gain will be $100k, $140k, or $180k with probabilities 0.3, 0.5, and 0.2 respectively. Assume the owner of Firm A is risk neutral.
a. What should she do?
b. Find the expected value of perfect information on the cost of the ad campaign
c. Find the expected value of perfect information on the increase in profits for each 10 percent gain in market share
d. Find the EVPI for both the cost of the campaign and the increase in profits.
e. Does the answer to part (d) equal the sum of (b) and (c)? Explain.