A decision-maker must choose between two lotteries, L₁ and L2. The lottery L₁ gives 0 dollars with probability 1/4 and 20 dollars with probability 3/4, whereas L2 gives 12 dollars for sure. The decision-maker is an expected utility maximizer with utility u(w), where w is the change in the consumers wealth. Assume that u(-) is continuous and strictly increasing. (a) Suppose that the decision-maker is risk averse. Can you determine which lottery she will choose? (b) Suppose that someone who knows the outcome of the lottery L₁ is willing to sell the information to the decision-maker. If the decision-maker is risk neutral, how much would she be willing to pay to know the outcome of lottery L₁ before making her choice between L₁ and L₂? (c) Suppose that the decision-maker is risk loving and, as in (b), she can buy information about the outcome of lottery L₁ prior to making her choice between L₁ and L₂. Is she willing to pay a positive amount to know the outcome of the lottery?
A decision-maker must choose between two lotteries, L₁ and L2. The lottery L₁ gives 0 dollars with probability 1/4 and 20 dollars with probability 3/4, whereas L2 gives 12 dollars for sure. The decision-maker is an expected utility maximizer with utility u(w), where w is the change in the consumers wealth. Assume that u(-) is continuous and strictly increasing. (a) Suppose that the decision-maker is risk averse. Can you determine which lottery she will choose? (b) Suppose that someone who knows the outcome of the lottery L₁ is willing to sell the information to the decision-maker. If the decision-maker is risk neutral, how much would she be willing to pay to know the outcome of lottery L₁ before making her choice between L₁ and L₂? (c) Suppose that the decision-maker is risk loving and, as in (b), she can buy information about the outcome of lottery L₁ prior to making her choice between L₁ and L₂. Is she willing to pay a positive amount to know the outcome of the lottery?
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.7P
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![4. A decision-maker must choose between two lotteries, L₁ and L2. The lottery L₁ gives 0 dollars
with probability 1/4 and 20 dollars with probability 3/4, whereas L2 gives 12 dollars for sure.
The decision-maker is an expected utility maximizer with utility u(w), where w is the change
in the consumers wealth. Assume that u(-) is continuous and strictly increasing.
(a) Suppose that the decision-maker is risk averse. Can you determine which lottery she
will choose?
(b) Suppose that someone who knows the outcome of the lottery L₁ is willing to sell the
information to the decision-maker. If the decision-maker is risk neutral, how much would
she be willing to pay to know the outcome of lottery L₁ before making her choice between
L₁ and L2?
(c) Suppose that the decision-maker is risk loving and, as in (b), she can buy information
about the outcome of lottery L₁ prior to making her choice between L₁ and L₂. Is she
willing to pay a positive amount to know the outcome of the lottery?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1ab2968-d288-4fd8-b87c-74963c459231%2F6d3bc717-a230-4ab3-9d08-994bf775ef25%2Figh3bm_processed.png&w=3840&q=75)
Transcribed Image Text:4. A decision-maker must choose between two lotteries, L₁ and L2. The lottery L₁ gives 0 dollars
with probability 1/4 and 20 dollars with probability 3/4, whereas L2 gives 12 dollars for sure.
The decision-maker is an expected utility maximizer with utility u(w), where w is the change
in the consumers wealth. Assume that u(-) is continuous and strictly increasing.
(a) Suppose that the decision-maker is risk averse. Can you determine which lottery she
will choose?
(b) Suppose that someone who knows the outcome of the lottery L₁ is willing to sell the
information to the decision-maker. If the decision-maker is risk neutral, how much would
she be willing to pay to know the outcome of lottery L₁ before making her choice between
L₁ and L2?
(c) Suppose that the decision-maker is risk loving and, as in (b), she can buy information
about the outcome of lottery L₁ prior to making her choice between L₁ and L₂. Is she
willing to pay a positive amount to know the outcome of the lottery?
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