Question

Bob's farm harvests corns worth 91 thousand dollars (and nothing else). In each year, there is a 33% chance that a storm will attack and leaves him with only 27 thousand dollars worth of the corns. Bob's preferences over wealth are represented by . What is the maximum that Bob is willing to pay for full insurance (in unit of thousand dollars)

Answer 1

$1.493 thousand

Step-by-step explanation:

Bob's utility function U = ln (w)

the highest price Bob is willing to pay for insurance = point where Bob is indifferent between purchasing insurance or not

expected utility with insurance = expected utility without insurance

ln(91 - P) = 0.67 ln(91) + 0.33 ln(27)

4.5109 - lnP = 3.0223 + 1.0876

4.5109 - lnP = 4.1099

lnP = 0.401

P = e⁰°⁴⁰¹ = 2.71828⁰°⁴⁰¹ = $1.493 thousand