please help me with a and b

Your roommate asks to borrow some money. The roommate promises to pay back the money at some interest rate i. However, you know that there is some chance that the roommate will not pay you back and you will lose all the money you lend. a. (15 points) Assume there is a probability p that the roommate does not pay you back. You have preferences over wealth given by the utility function, u(w)=w. In terms of p and the interest rate, i, write an expression that solves for the optimal amount of money you would choose to lend your roommate if you choose to lend at all. Denote this amount L. b. (5 points) In terms of the probability that your roommate does not pay you back, p, how high does the interest rate, i, have to be in order for your to lend some amount greater than $0 ? Your roommate asks to borrow some money. The roommate promises to pay back the money at some interest rate i. However, you know that there is some chance that the roommate will not pay you back and you will lose all the money you lend. a. (15 points) Assume there is a probability p that the roommate does not pay you back. You have preferences over wealth given by the utility function, u(w)=w. In terms of p and the interest rate, i, write an expression that solves for the optimal amount of money you would choose to lend your roommate if you choose to lend at all. Denote this amount L. b. (5 points) In terms of the probability that your roommate does not pay you back, p, how high does the interest rate, i, have to be in order for your to lend some amount greater than $0