help with question 2

2. [30 points total] Andy faces an income rislc his income will be 10 with probability 0.8 or 0 with probability 0.2. Assume that his utility function is 1n (3; + 1) with 3; being income. A risk-neutral rm sells \"income insurance,\" which gives benet B in case of the zero income but requires premium P. Answer the following questions. (You may have to use the following approximation: 10\" z 6.3, 1108 a: 6.8.} (a) [5 points] Calculate the expected utility for Andy without the insurance. (b) [5 points] Find the certainty equivalent and risk premium due to the income risk 1 (c) [15 points] The rm determines B and P to maximize expected prot subject to the constraint that Andy's expected utility with the insurance (P, B) is at least as high as his utility without the insurance. Find (P*,B*) that solves the rm's problem. Interpret. (d) [5 points] Is it a Pareto improvement if Andy buys the insurance with (13* , 3*)