A hospital administrator is making a decision regarding the hospital’s policy of treating individuals who have no insurance coverage. The policy involves examination of a prospective patient’s financial resources. The issue is what level of net worth should be required in order for the patient to be provided treatment. Clearly, there are two competing objectives in this decision. One is to maximize the hospital’s revenue, and the other is to provide as much care as possible to the uninsured poor. Attributes to measure achievement toward these two objectives are (1) prospective revenue (R), and (2) percentage of uninsured poor who are treated (P).
The two attributes were examined for independence, and the administrator concluded that they were mutually utility independent. Utility functions UR (r) and UP (p) for the two attributes were assessed. Then two more assessments were made. Lottery A and its certain alternative B were judged to be equivalent by the administrator:
A Best on revenue, worst on treating poor with probability 0.65
Worst on revenue, best on treating poor with probability 0.35
B Levels of revenue and treatment of poor that give UR (r) = 0.5 and UP (p) = 0.5
In the second assessment, Lottery C and its certain alternative D were judged to be equivalent:
C Best on both revenue and treating poor with probability 0.46
Worst on both revenue and treating poor with probability 0.54
D Worst on revenue and best on treating the poor
a. Find values for kR and kP. Should the administrator consider these two attributes to be substitutes or complements? Why or why not?
b. Comment on using an additive utility model in this situation. Would such a model seriously compromise the analysis of the decision?