1. A policy maker in the Occupational Safety and Health Administration is under pressure from industry to permit the use of certain chemicals in a newly developed industrial process. Two different versions of the process use two different chemicals, A and B. The risks associated with these chemicals are not known with certainty, but the available information indicates that they may affect two groups of people in the following ways:

• Chemical AThere is a 50% chance that Group 1 will be adversely affected, while Group 2 is unaffected; and a 50% chance that Group 2 will be adversely affected, while Group 1 is unaffected;
• Chemical BThere is a 50% chance that both groups will be adversely affected, and a 50% chance that neither group will be affected.
• Assume that "adversely affected" means the same in every case?an expected increase of one death in the affected group over the next two years. The decision maker's problem looks like the decision tree in Figure 1.

(a) Calculate the expected number of deaths for each chemical.

(b)A decision maker who values consequences using an overall utility might calculate the utility for each consequence as

U(Chemical)=k1U1(Group 1 Deaths)+ k2U2(Group 2 Deaths)

For both U1and U2, the best and worst possible outcomes are 0 deaths and 1 death, respectively. Thus

U1(1 Death)=0 U1(0 Death)=1

U2(1 Death)=0 U2(0 Death)=1

Explain why k1and 1-k1may not be equal.

(c)Assume that k1= 0.4. Show that the decision maker who evaluates the two chemicals in terms of their expected overall utilities (as defined above) would be indifferent between them. Does the value of k1matter?

(d)Why might the decision maker not be indifferent between the two programs? (Most people think about the decision maker's risk attitude toward the number of deaths or lives saved. Besides this, think about the following: Suppose you are a number of Group 1, and the decision maker has chosen Chemical A. It turned out that Group 1 was affected. How would you feel? What would you do? What does this imply for the decision maker? )

FIGURE 16.16 Deciding between Expected deaths in: alternative chemicals in Chemical (0.5) Group 1 Group 2 0 Problem 16.25. A (0.5) 0 (0.5) B 0 0 (0.5) Cengage Learning