Question

Consider the world of Carolina. There are two types of people in Carolina. Type A people make up 5% of the population and Type B people make of 95% of the population. Everybody knows their own type. Each Type A person experiences health costs in this way: 10% of the time their costs are $10,000 and 90% of the time their costs are $2,000. Each Type B person experiences health costs in this way: 8% of the time their costs are 5,000 and 92% of the time their costs are $1500. i. For Part i, assume that any insurance company can reliably observe what type each person is. If the insurer is selling actuarially-fair, full insurance what premium would they charge Type A people? What premium would they charge Type B people? Show your work/explain. ii. Now assume that any insurance company DOES NOT observe what type each person is. They sell one plan to everyone. If everyone buys (actuarially fair full) health insurance, what is the premium charged? Show your work/explain. iii. Given your answer in part ii, will Type A people buy the health insurance at that price? Given your answer in part ii, will Type B people buy the health insurance at that price? iv. Given your answers in part iii, does the insurance company want to change their price?

Answer 1