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12 September, 22:53

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) ?

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  1. 12 September, 23:56
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    Hence Bob will pay a maximum of 35 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) = 0.38 * 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.
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