Suppose that a company would like to purchase a fairly complicated machine to use in its manufacturing operation. Several different machines are available, and their prices are more or less equivalent. But the machines vary considerably in their available technical support (Attribute X) and reliability (Attribute Y). Some machines have a high degree of reliability and relatively low support, while others are less reliable but have excellent field support. The decision maker determined what the best and worst scenarios were for both attributes, and an assessment then was made regarding the independence of the decision maker’s preferences for these attributes. It was determined that utility independence held. Individual utility functions UX (x) and Uγ (y) were assessed. Finally, the decision maker was found to be indifferent in comparing Lottery A with its alternative B:
A Best on both reliability and support with probability 0.67 Worst on both reliability and support with probability 0.33 B Best on reliability and worst on support The decision maker also was indifferent between C Best on both reliability and support with probability 0.48 Worst on both reliability and support with probability 0.52 D Worst on reliability and best on support a. What are the values for kX and kγ? Write out the decision maker’s full two-attribute utility function for reliability and support.
b. Are the two attributes substitutes or complements? Explain, both intuitively and on the basis of kX and kγ.