Question

Risk and Insurance A football team signs a player who has had a history of injuries and there is 20% chance that the player will be injured for the next season. If the player is not injured the team makes a profit of $ 60. However, if the player is injured the team can earn a profit of only $ 30. 1. Find the expected profit for the team.

Answer 1

let, bi probability of injury. Pni probability of no injury. T, → Profit in case of injury. Ani Profit in case of no injury. Given. bi = 20% = 0.2 Pri = 80% =0.8 Ti = $30 Ani = $60 (16) Expected profit (EA) = piti + pni Ini - 0.2 x 30 to 8 x 60 = 6 + 48 = $54 (2.) U (a) = ln (a) Expected utility (EU) - Pi U11;) + poi U (Tni)

Ell - bidn (ai) + Pridn (ani) - 0.2 ln (30) + 0.8 ln (60) - 0.68 + 3.28 - 3.96 13 let Then d be the certainity Equivalent. According to question, u(x) = EU In (a) = 3.96 x = 3.96 x = 52.46

Date: 14) Expected utility with insurance, - B; 4(55) + Pneulss) - 0.2 ln (55) toog ln (ss) - 0.80 +3.21 = 4:01 Since expected utility with insurance is greater than expected utility without insurance, the team should buy insurance