Thank you for visiting An agent is considering a risky option that will pay 484 with a probability of 0 6 and 1 681 with a probability of 0. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To determine the expected utility of the given option, we'll make use of the provided utility function [tex]u(x) = x^{0.5}[/tex] and the probabilities for each outcome.
The concept of expected utility involves calculating the sum of the utilities of each possible outcome, each weighted by its probability.
Given:
- Option 1 pays $484 with probability 0.6
- Option 2 pays $1,681 with probability 0.4
First, we calculate the utility for each outcome:
Utility for $484:
[tex]u(484) = 484^{0.5}[/tex]
[tex]u(484) = 22[/tex]
Utility for $1,681:
[tex]u(1,681) = 1,681^{0.5}[/tex]
[tex]u(1,681) = 41[/tex]
Next, we calculate the expected utility using the formula:
[tex]\text{Expected Utility} = (\text{Probability of Outcome 1} \times \text{Utility of Outcome 1}) + (\text{Probability of Outcome 2} \times \text{Utility of Outcome 2})[/tex]
[tex]= (0.6 \times 22) + (0.4 \times 41)[/tex]
[tex]= 13.2 + 16.4[/tex]
[tex]= 29.6[/tex]
The expected utility of the option is 29.6.
Therefore, the correct multiple-choice answer is 29.6.
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