A risk averse individual faces uncertainty with two outcomes: good, bad. The individual has income $840 at good and $480 at bad outcome. The probability of good outcome is 7/12 (so the probability of bad outcome is 1 7/12 = 5/12). The individual can buy any non negative x units of insurance. Every unit of insurance has price $p and it pays $1 in the event of bad outcome. In this insurance market, the unit price of insurance is known to be p = 2/3.

(a) Determine if the insurance market is competitive or not.

(b) Suppose the individual buys x units of insurance. Determine the individual's net income under good income, net income under bad income and the average net income. Draw these three in a diagram as functions of x.

(c)For the individual: (i) compare full insurance with over insurance and (ii) compare full insurance with partial insurance. Then determine best choice of insurance for the individual.

(d) Consider the same problem, but suppose the individual is risk neutral instead of risk averse. Determine best choice of insurance for the individual.