Consider an individual with a hypothesized utility function of

1u=w2

Where w = income.

Moreover, their stock of wealth is $100,000. In a given year, the individual faces a 10 percent chance of incurring a significant medical shock which will cost them $5,000. As a result, this individual is considering buying health insurance that will pay for the costs associated with the shock. Calculate both the annual actuarially fair premium and the maximum annual price this individual will pay. Use a graph to explain your result.