Billy has a von Neumann-Morgenstern utility function U(c)= c^1/2.If Billy is not injured this season, he will receive an income of 4 million dollars.If he is injured, his income will be only 10,000 dollars.The probability that he will be injured is .1 and the probability that he will not be injured is .9.His expected utility is A)3,620 dollars. B)1,810 dollars. C)between 3 and 4 million dollars. D)100,000 dollars. E)7,240 dollars.

Question

Quizplus · Accepted Answer

Billy's expected utility is calculated as the weighted average of his utility in each state, using the probabilities as weights: 0.9 * (4,000,000)^0.5 + 0.1 * (10,000)^0.5 = 1,810.

Billy Has a Von Neumann-Morgenstern Utility Function U(c)= C1/2

Billy Has a Von Neumann-Morgenstern Utility Function U(c)= C^1/2