5. Consider a risk neutral individual who faces a potential loss of size 1 with probability p. The individual can invest in safety to affect p, so that p depends on safety expenditure as p=1- In(1+S) (for S 01.718). . Please find the optimal level of safety investment for the individual, with no insurance. Now imagine that the individual has purchased I units of coverage at a premium P(I), and then has to choose the level of safety investment. What is the optimal level of safety investment as a function of I? Now imagine the insurer is smart and knows the person will choose safety as in (b). They set actuarially fair prices taking optimal safety behavior into account. What premiums will they set as a function of I, P(I)? Given the premium structure in (c), what amount of insurance I will the individual choose? Please show your work