A policy maker in OSHA 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 way:

Chemical A There is a 50% chance that Group 1 will be adversely affected, while Group 2 is unaffected; and a 50% chance that Group 2 is adversely affected, while Group 1 is unaffected.

Chemical B There 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. Also note that the best case possible is when there are no deaths and the worst case is when there is an increase of one death in a group.

(a) Calculate the expected number of deaths for each chemical. (10 points)

(b) Assuming the decision makers overall utility function is a simple additive function and k₁ = 0.4, where k₁ is the weight on Group 1 deaths, what can you say about the decision makers preferences for the two chemicals in terms of their expected overall utilities (i.e., is he indifferent between them, prefers A to B, or B to A)? Show mathematically. Also, does the value of k₁ matter? (15 points)