Suppose you are facing an investment decision in which you must think about cash flows in two different years. Regard these two cash flows as two different attributes, and let X represent the cash flow in Year 1, and Y as the cash flow in Year 2. The maximum cash flow you could receive in any year is $20,000, and the minimum is $5,000. You have assessed your individual utility functions for X and Y, and have fitted exponential utility functions to them:

Ux(x) = 1.05 – 2.86 exp{-x/5000);

Uy(y) = 1.29 – 2.12 exp{-y/1000};

Furthermore, you have decided that utility independence holds, and so there individual utility functions for each cash flow are appropriate regardless of the amount of the other cash flow. You also have made the following assessments:

You would be indifferent between a sure outcome of $7,500 each year for 2 years, and a risky investment with a 50% chance at $20,000 each year, and a 50% chance at $5,000 each year.

You would be indifferent between (1) getting $18,000 the first year and $5,000 the second, and (2) getting $5,000 the first year and $20,000 the second. (a). Use these assessments to find the scaling constants kx and ky. (b). Draw indifference curves for U(X, Y) = 0.25, 0.50, and 0.75.