Question

g Bob's farm harvests corns worth 83 thousand dollars (and nothing else). In each year, there is a 38% chance that a storm will attack and leaves him with only 20 thousand dollars worth of the corns. Bob's preferences over wealth are represented by U=\ln{w} . What is the maximum that Bob is willing to pay for full insurance (in unit of thousand dollars)?

Answer 1

Hence Bob will pay a maximum of 35 thousand dollars for the insurance.

Explanation:

The expected Utility for Bob is given by:

wealth w is measured in thousands of dollars

E(U) = Probability of storm * Utility if storm happens + (1- Probability of storm) * Utility if there is no storm)

E(U) = 0.38 * ln(20) + 0.62 * ln(83)

=0.38 * 2.9957 + 0.62 * 4.4188

=1.138378 + 2.73968

=3.878059

≅3.88

E(U) = 3.88

The wealth corresponding to this expected utility is given by w = exp(E(U)) = exp(3.88) = 48.33

≅48

= 48 dollars.

Hence the maximum Bob is willing to pay for the insurance can be given by = 83- 48

= 35 dollars.

Since it in unit of thousand dollars

Hence Bob will pay a maximum of 35 thousand dollars for the insurance.