Let's now examine the decision to purchase insurance. Specifically, we want to examine how insurance that "costs" more than it ultimately pays out (via profit margins of the insurance company or simply administrative costs) distorts an individual's decision to insure against loss. Assume an individual's VNM utility over final wealth is u(x) = ln(x). She originally has $50,000. With a 10% probability, she will face a health crisis that costs $10,000. She can get health insurance that will pay her $H if she gets sick. The cost of $H of insurance is OH, where 0