Subject: Decision and Risk Analysis

Refer to the discussion of the three automobiles in the section "Trading Off Conflicting Objectives: The Basics." Suppose we had the following individual utility functions for price and life span:

Life Span Price

U_L(6 Years)= 0.00 U_P($17,000)= 0.00

U_L(9 Years)=0.75 U_P($10,000)= 0.50

U_L(12 Years)= 1.00 U_P($8,000)= 1.00

The additive utility model discussed in this chapter would give us the

following:

U(Life Span, Price)= k_LU_L(Life Span) +(1 - k)_L U_P(Price)

a. With k_L =0.45, calculate the utility for the three cars. Which would be chosen?

b. Suppose that you are not completely comfortable with the assessment of k_L =0.45. How large could k_L be before the decision changes, and what would be the new choice? How small could kL be before the decision changes, and what would be the

new choice? Would you say that the choice among these three cars is very sensitive to the assessment of k_L?