Now consider another individual who is risk-loving instead of risk-averse.

a. Is U (I) concave or convex?

b. Suppose this person is offered an actuarially fair insurance product that guarantees her a certain income, E[I]. Graph the consumer surplus this person receives from buying this insurance as p, the probability of being sick, varies from 0 to 1. You should plot p on the horizontal axis and consumer surplus on the vertical axis.

c. Suppose, finally, that this person is offered a subsidy (perhaps from her parents) for buying insurance so that, if she buys insurance, she will be guaranteed an income γE[I], where γ > 1. With the subsidy, insurance is now actuarially unfair in her favor. Graph how her consumer surplus (M) changes as p, the probability of being sick, varies from 0 to 1.

Based on this graph, under what conditions is she least likely to buy the subsidized insurance?