5. [15] Michal is a proud owner of a ``shoebox'' condo worth $600,000. The location is very attractive (it's eye-level with the Gardener Expressway in downtown Toronto), however it has one drawback. Occasionally in the spring heavy rains result in flooding thanks to faulty weatherproofing of his 2 sq. ft. balcony. When this happens, the value of his condo drops to $60,000. The flooding occurs with probability 0.2. Michal finds the situation very stressful so he is going to sell the condo in the summer (after the potential flooding has taken place). Denote his wealth and when his condo floods and does not flood, respectively.

Fortunately, Michal can buy insurance that pays-out dollars when there is a flood by paying premium 0.2. Suppose Michal's expected utility is given by ( , ) = 0.2 + 0.8

a. [3] Is Michal risk loving, risk neutral, or risk averse (show your calculations)?

b. [5] What is his MRS at the endowment point (no insurance)?

c. [5] Find the optimal insurance and wealth levels under two contingencies. Does he insure fully?

d. [2] If there was market-power in the insurance industry, describe how this would this affect the price of insurance and Michal's optimal level of coverage