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)

Question

Mathematics

Kiwi

5 May, 20:01

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)

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Jazlynn Bryant · Answer 1

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

Step-by-step 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.