A new product has the following profit projections and assoc

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

0.10

a. Use the expected value approach to decide whether to market the new product.
b. Because the high dollar values involved, especially that 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?
c. Assume that the following indifference probabilities are assigned. Do the utilities reflect the behavior of a rish taker or a risk avoider?

d. Use the expected utility to make a recommended decision.
e. Should the decision maker feel comfortable with the final decision recommended by the analysis?

Please label and answer all parts to the question.

Solution

Expected value of a variable, say x takes the values x1, x2, x3 .....xn with probabilities p1, p2, p3..... pn is calculated as x1p1 + x2p2 + x3p3 +........+xnpn Therefore expected value of profit is $30,000 (150,000*.10+100,000*.25+50,000*.20+0*.15+(-50,000)*.20+(-100,000)*.10)

a. New product yields expected profit of $30,000 hence marketable.

b. As the probability of gains is much more than the probability of loss therefore higher values of dollors of profits may be focused as gains and not losses. A lottery is as follows: if thereare two options X and Y with probability p and 1-p then lottery has linear contribution as L = pX + (1-p)y