Consider a risk averse individual who faces uncertainty with two outcomes: good, bad. The individual has income $360 under good and $90 under bad outcome. The probability of good outcome is 5/9 (so the probability of bad outcome is 1 5/9 = 4/9). 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.

(a) [2 points] Suppose the unit price of insurance is p = 1/2. Determine if the insurance market is competitive or not. (b) [6 points] 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) [5 points] 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) [4 points] Suppose the individual is risk neutral instead of risk averse. Determine best choice of insurance for the individual.