(Table: Amy's Utility Function) Look at the table Choosing Insurance.Amy is an entrepreneur with current income equal to $40,000.Amy is considering development of a new product.The probability that her new product earns Amy $10,000 in additional income is 0.5, and the probability that Amy incurs a reduction of $10,000 from her current income is also 0.5.Suppose Amy can buy a fair insurance policy that will compensate her for any losses.Amy's premium will be ________, her guaranteed income will be , and her expected utility
Will be utils.
A)$5,000; $10,000; 200
B)$10,000; $30,000; 500
C)$10,000; $40,000; 620
D)$30,000; $50,000; 720

Question

Quizplus · Accepted Answer

To determine the premium, we must find the expected value of the insurance payout. Since there is a 0.5 probability of both gaining and losing $10,000, the expected payout is $0. Therefore, Amy's premium should equal the expected payout, which is $10,000.

With insurance, Amy's guaranteed income will be her current income of $40,000 plus the insurance payout of $10,000, for a total of $50,000.

To find expected utility, we can use the formula: EU = U(W_guaranteed) + p(U(W_high) + (1-p)(U(W_low))), where W_high is the wealth with the high outcome, W_low is the wealth with the low outcome, and p is the probability of the high outcome.

Plugging in the numbers, we get: 
EU = U($50,000) + 0.5(U($50,000)) + 0.5(U($30,000))
Using the values from the table, we can calculate:
EU = 620

Therefore, option C is the best choice as it gives the highest expected utility.

(Table: Amy's Utility Function) Look at the Table Choosing Insurance