Asked by Sheryl Kambuni on Jul 03, 2024
Verified
(Table: Amy's Utility Function) Use Table: Amy's Utility Function.Amy is an entrepreneur with current income equal to $40,000.Amy is considering development of a new product.The probability that her new product earns Amy $10,000 in additional income is 0.5,and the probability that Amy incurs a reduction of $10,000 from her current income is also 0.5.Suppose Amy can buy a fair insurance policy that will compensate her for any losses.Amy's premium will be _____,her guaranteed income will be _____,and her expected utility will be _____ utils.
A) $5,000;$10,000;200
B) $10,000;$30,000;500
C) $10,000;$40,000;620
D) $30,000;$50,000;720
Fair Insurance Policy
An insurance policy characterized by equitable premiums, coverage, and terms that are just and reasonable for both the insurer and the insured.
Expected Utility
A theory in economics that predicts how individuals make choices under conditions of uncertainty to maximize their satisfaction.
Probability
A measure of the likelihood that a certain event will occur, often expressed as a number between 0 and 1.
- Engage probabilistic theories to ascertain expected earnings and utility during uncertain times.
- Evaluate the benefits of purchasing insurance based on expected utility theory.
Verified Answer
If Amy buys the insurance policy, her guaranteed income will be $40,000 - $5,000 = $35,000 if her new product does not sell, and $40,000 + $10,000 - $5,000 = $45,000 if her new product does sell.
Using the numbers in the table, we can calculate Amy's expected utility in each scenario:
- If Amy does not buy the insurance policy, her expected utility is: 0.5*150 + 0.5*80 = 115 utils
- If Amy buys the insurance policy, her expected utility is: 0.5*135 + 0.5*165 = 150 utils
Therefore, Amy should buy the insurance policy, and her expected utility will be 150 utils.
Learning Objectives
- Engage probabilistic theories to ascertain expected earnings and utility during uncertain times.
- Evaluate the benefits of purchasing insurance based on expected utility theory.
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