Joachim’s utility function is U(W) = ln (W), where ln (W) is the natural logarithm of W. Cindy’s utility function is U(W) = W0.5 (the square root function). Which of the projects described in Q&A 14.3 would be chosen by Joachim? Show that Cindy would favor a different project.

Q&A 14.3

The manager of a property development company must choose to pursue one of four possible development projects. Each project will be worth more if its rezoning application is approved. The following Excel spreadsheet shows the probability of approval for each project and the associated payoff conditional on whether approval is granted:

Augment this spreadsheet to determine the expected value, variance, and standard deviation for each project. Which project would a risk-neutral manager choose? If possible, determine which project a risk-preferring or risk averse manager would choose if the manager cares only about expected value and variance. If you cannot determine which project would be chosen, can any projects be ruled out?

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A B D E 1 Project Rezoned Not Rezoned 2 Probability Payoff Probability Payoff 3 A 0.4 0.6 5 4 B 0.7 5 0.3 4 C 0.5 12 0.5 3 D 0.2 11 0.8 4