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 nonnegative 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.