Question

Bob's farm harvests corns worth 109 dollars (and nothing else). In each year, there is a 24% chance that a storm will attack and leaves him with only 28 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

Bob will pay a maximum of 39 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) = 0.33 * ln(28) + 0.67 * ln(109)

=0.33 * 3.3322 + 0.67 * 4.6913

=1.0996 + 3.1432

=4.24

E(U) = 4.24

The wealth corresponding to this expected utility is given by w = exp(E(U)) = exp(4.24) = 69.602

= 70 dollars.

Hence the maximum Bob is willing to pay for the insurance can be given by = 109 - 70

= 39 dollars.

Since it in unit of thousand dollars

Hence Bob will pay a maximum of 39 thousand dollars for the insurance.