Adam has wealth of $40,000 as long as his business does not burn down. However, there is a 50% probability that his business will burn down and cause a $30,000 loss, leaving him with $10,000 of wealth. Adam's utility function is given by U = W^0.5, where W is wealth. What is the maximum price that Adam would pay for full insurance that covers the potential $30,000 loss? (Hint: The maximum price equals the actuarially fair premium plus the risk premium.)

Question

Quizplus · Accepted Answer

The actuarially fair premium is 0.5 * $30,000 = $15,000. The risk premium is the difference between the expected utility with insurance and the expected utility without insurance. The expected utility with insurance is U(40,000) = 40,000^0.5 = 200. The expected utility without insurance is 0.5 * U(10,000) + 0.5 * U(40,000) = 0.5 * 10,000^0.5 + 0.5 * 40,000^0.5 = 150. Therefore, the risk premium is 200 - 150 = $50. The maximum price that Adam would pay for full insurance is the actuarially fair premium plus the risk premium, which is $15,000 + $50 = $15,050.

Adam Has Wealth of $40,000 as Long as His Business