Explore BrainMass

Explore BrainMass

    Uncertainty, insurance

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    A farmer can grow wheat, or potatoes, or both. If the weather is good, an acre of land yields a profit of $2000 if devoted to wheat, and $1000 if devoted to potatoes. Should the weather be bad, an acre of wheat yields $1000 and potatoes $1750. Good and bad weather are equally likely.

    a. Assuming that the farmer's utility of income, Y, is u(Y)= ln Y, what proportion of his land should he turn over to wheat?

    b. Suppose the farmer can buy an insurance policy which pays $2 if the weather is bad and nothing if the weather is good, for each $1 of premium. How much insurance will he take out, and what proportion of his land will he devote to wheat? What would the answer be if the policy only paid $1.50 to compensate for the bad weather?

    © BrainMass Inc. brainmass.com March 4, 2021, 9:06 pm ad1c9bdddf
    https://brainmass.com/economics/personal-finance-savings/uncertainty-insurance-218128

    Solution Preview

    Please refer to the attachment.

    Uncertainty, insurance

    A farmer can grow wheat, or potatoes, or both. If the weather is good, an acre of land yields a profit of $2000 if devoted to wheat, and $1000 if devoted to potatoes. Should the weather be bad, an acre of wheat yields $1000 and potatoes $1750. Good and bad weather are equally likely.

    a. Assuming that the farmer's utility of income, Y, is u(Y)= ln Y, what proportion of his land should he turn over to wheat?

    Let x be the proportion of his land should he turn over to wheat, then the proportion of potatoes is (1-x).
    When the weather is good, he can earn 2000x per acre from wheat, and 1000(1-x) per acre from potatoes. His total profit is then good Y=2000x +1000(1-x) = 1000+1000x.
    However, when the weather is bad, he can earn 1000x per acre from wheat, and 1750(1-x) per acre from potatoes. His total profit is then bad Y=1000x +1750(1-x) = 1750 -750x.
    The von Neumann-Morgenstern Utility function with uncertainty is
    U = pr(good)*u(good Y) + pr(bad)*u(bad Y)
    where pr(good) = pr(bad) = 0.5, and u = lnY.
    Thus, U ...

    Solution Summary

    Uncertainty, insurance, and other issues are noted.

    $2.49

    ADVERTISEMENT