Mark works hard to make money for his wedding with Kate. He has already accumulated 500,000 RUB over the years, yet he is trying to make as much money as possible during the last 20 days before the wedding. Alas, COVID is putting his plans at risk! If he works from his office, he can make 100,000 RUB (during the 20 days) but he risks that with a 10% probability he would get COVID and have to reschedule his wedding, which would cost him 50,000 RUB. Alternatively, he can work from home, in which case he would make only 80,000 RUB, and would stay healthy with certainty. He could also work every second day, in which case he would make 90,000 RUB and get infected with 5% probability. Besides that, his Uncle Gatsby offers him insurance for rescheduling his wedding. In order to get compensation of x 50, 000 towards the rescheduling expenses, he has to pay 0.12x

(a)How much would be the expected value of the money he will have for the wedding (excluding the cost of rescheduling the wedding), with full insurance and with no insurance, in either of the situations (i.e. working from home, working from the office, or alternating both)?

(b)Mark judges his situating by von Neumann-Morgenstein utility function u(w) = w^0.3 of the money he has for the wedding. What will be his utility in either of the cases mentioned above?

(c)How much would he choose to be insured (x) depending on how much he works from home and the office? What is the ideal thing he should do?

(d) If he could choose exactly the number of days d to work from the office (so that he would earn 80, 000 + 1, 000d RUB and get infected with the probability d/2 %), how many days would he work from the office and how much would he get insured?