Morley Properties is planning to build a condominium development on St Simons Island, Georgia. The company is trying to decide between building a small, medium, or large development. The payoffs received for each size of development will depend on the market demad for condominiums in the area, which could be low, medium, or high. The payoff matrix for this decision problem is:
Market Demand
Size of Development Low Med High
Small 400 400 400
Medium 200 500 500
Large -400 300 800
(Payoffs in 1,000s)
The owner of the company estimates a 21.75% chance that market demand will be low, a 35.5% chance that it will be medium, and a 42.75% chance that it will be high.
Suppose that the utility function for the owner of Morely Properties can be approximated by the exponential utility function U(X) = 1 - e^(-x/R) where the risk tolerance value R=100 (in $1,000s)
A. Convert the payoff matrix to utility values.
B. What decision provides the owner of the company with the largest expected utility?