A. The contractor's expected wealth if he purchases the land is $1,000,000 * 0.1 + $640,000 * 0.9 = $676,000.
B. To calculate the expected utility, we multiply the utility of each outcome by its respective probability and sum them up:
Expected utility = U($1,000,000) * 0.1 + U($640,000) * 0.9
Expected utility = 10(1,000,000)^0.5 * 0.1 + 10(640,000)^0.5 * 0.9
C. The utility if he does not purchase the land is U($810,000) = 10(810,000)^0.5.
To determine whether the contractor will purchase the land, we compare the expected utility of purchasing ($676,000) with the utility of not purchasing ($810,000). If the expected utility is greater than the utility of not purchasing, the contractor will choose to purchase the land.
D. Please refer to the graph below.
E. To find the probability that would make the contractor indifferent about purchasing the land, we set the expected utility of purchasing equal to the utility of not purchasing and solve for the probability.
Expected utility of purchasing = Utility of not purchasing
10(1,000,000)^0.5 * p + 10(640,000)^0.5 * (1-p) = 10(810,000)^0.5
Solving for p, the probability that would make the contractor indifferent, will yield the answer in percent.