John has his wealth of €1000 invested in ripoff.com shares. There is a 50% chance that the share market crashes and his shares will be worth nothing. There is a 50% chance his shares will remain worth €1000. John has the opportunity to insure a fraction a of the €1000. The insurance premium is 600a. Suppose John has a utility function U(y)= y 0.5 where y is wealth. If John maximises expected utility, what value of a will he choose?

If there is no insurance market but John has the opportunity to sell a fraction ß of the ripoff shares and can invest the proceeds in shares in the oil company blackgold. If the technology share market crashes, he loses all his ripoff.com investment but only 25% of his investment in the company blackgold. If the technology share market does not crash, he keeps all his investment in ripoff but loses 75% of his investment in the other company blackgold. As in part A there is a 50% chance the share market crashes. If John maximises expected utility, what value of ß should he choose?