Frank is considering, whether or not, to invest in space aviation. He has wealth, W= 10. Suppose Frank can avail of insider knowledge which says that if he invests, he is assured of a 50% return on any investment he makes. However, if he is caught, he will have to forfeit any return on the investment plus face a fine equal to 20% of any investment made. The probability of being caught is equal to 40%.

(a) Assume Frank's preferences are captured by the utility function u (Cs) = Inc, where s denotes the state of nature.

(b) Solve for Frank's optimal investment.