A team of decision analysts is asked to asses a multiattribute utility function for the government that wishes to revise its healthcare policies. The team identified the cost and the quality of care provided to be the two main attributes in this context. They also agreed to assume that these attributes satisfy utility independence. They used reference lotteries to estimate utility functions uC (c) for cost and uQ(q) for quality of care. They also collected the following information:
(i) The government is indifferent between the certain outcome (c, q) with uC (c) = uQ(q) = 0.5, and getting best cost-worst quality with probability 70% and worst cost-best quality with probability 30%.
(ii) The government is also indifferent between the certain outcome of worst cost-best quality, and getting best cost-best quality with probability 35% and worst cost-worst quality with probability 65%.
(a) Suggest a utility function for this government and justify your suggestion.
(b) Discuss whether the cost and the quality substitutes or complements with respect to the utility function you suggested. Justify and interpret your claim.
(c) What would be the compromise from using an additive utility function in this case?