申論題

Please show all your work because (i) partial credit will sometimes be awarded and (ii) full credit will NOT be awarded for answers that appear without accompanying work. Please write your answers according to the order of the questions.

 3. (Total 30 points) Bryan Beaver is about to build his dam and lodge. There are two rivers that he can choose from: Rainbow River and Rose River. At Rainbow River, there is a 50% chance of flash flood, but the view along the river is rather plain. Whereas, at Rose River, there is a magnificent view of the rose valley, but the probability of flash flood is 75%. His value of having his dam and lodge located at both rivers are given in the following table:

(a) (5 points) Suppose that Bryan's utility function is . In this case, where should he build his dam and lodge? Please explain. Now the River God is offering insurance to Bryan. Despite the location, the insurance that pays back $1 costs $0.8.