A new product has the following profit projections and associated probabilities:

Profit

Probability

$$150,000$

$0\mathrm{.}10$

$$100,000$

$0\mathrm{.}25$

$ $50,000$

$0\mathrm{.}20$

$$0$

$0\mathrm{.}15$

$$$ $50,000$

$0\mathrm{.}20$

$$$$100,000$

$0\mathrm{.}10$

Use the expected value approach to decide whether to market the new product.

Because of the high dollar values involved, especially the possibility of a $$100,000$ loss, the marketing vice president has expressed some concern about the use of the expected value approach. As a consequence, if a utility analysis is performed, what is the appropriate lottery?

Assume that the following indifference probabilities are assigned. Do the utilities reflect the behavior of a risk taker or a risk avoider?

Profit

Indifference Probability$($p$)$

$$100,000$

$0\mathrm{.}95$

$ $50,000$

$0\mathrm{.}70$

$$0$

$0\mathrm{.}50$

$$$ $50,000$

$0\mathrm{.}25$

Use expected utility to make a recommended decision.

Should the decision maker feel comfortable with the final decision recommended by the analysis?