Question

Bob's farm harvests corns worth 90 dollars (and nothing else). In each year, there is a 30% chance that a storm will attack and leaves him with only 21 dollars worth of the corns. Bob's preferences over wealth are represented by U = vw. What is the maximum that Bob is willing to pay for full insurance (in unit of thousand dollars)? Please round your answer to the nearest integer.

Answer 1

Expected utility=0.3 U(21)+0.7 U(70)=0.3(21)^0.5+0.7(70)^0.5=1.374772+5.8566=7.231392

after insurance, this amount of utility must be required and wealth required to get same utility

U(W)=W^1/2=7.231392

W=52.29

Thus full insurance amount=90-52.29=37.7069