Medical Costs Problem

Problem III. Medical Costs (25 points) Suppose that Cristina has a utility function that is given by U(e) = ve. Cristina has a yearly income of $80,000. However, there is 10% chance that she incurs a cost of $16,000 due to medical bills. An insurance company approaches Cristina and offers her the following contract: Cristina pays insurance premium $p 2 0 in order to receive $9p in case the bad state happens. 1. What does it mean to say that an insurance contract is actuarially fair? Is the contract offered by the insurance firm actuarially fair? If not, what is the actuarially fair contract? (5 pts) 2. What are Cristina's consumption in the good, co, and bad state, co, for an arbitrary choice of p? (5 pts) 3. How much insurance, p*, will Cristina purchase at the current rate i.e. paying $p* to get back $9p*? (5 pts) 4. How much of the actuarially fair contract, p, will Cristina purchase? (5 pts) 5. What will her state-contingent consumption be after she purchases the optimal p units of the contract? Explain the intuition. (5 pts)