EBK INTERMEDIATE MICROECONOMICS AND ITS
12th Edition
ISBN: 9781305176386
Author: Snyder
Publisher: YUZU
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Question
Chapter 4A.3, Problem 1MQ
To determine
The reason which shows that the choices along the certainty line suggest that there is no risk is to be ascertained.
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Consider two individuals whose utility function over wealth I is ?(?) = √?. Both people face a 10 percent chance of getting sick, and foreach the total cost of illness equals $50,000. Suppose person A has a total net worth of $100,000, and person B has a total net worth of $1,000,000. Both people have the option to buy an actuarially fair insurance contract that would fully insure them against the cost of the illness.
a. Using expected utility calculations, show that person A would certainly buy full, actuarially fair insurance.
b. Suppose an insurance company wants to maximize profits and wants to charge each customer the maximum price they are willing to pay. How much should the insurance company charge each client so that both buy the contract? c. What is surprising about your result in part b? What does this tell you about how insurance companies may be pricing health insurance contracts in the real world?
Scenario 2
Tess and Lex earn $40,000 per year and all earnings are spent on consumption (c). Tess and Lex both have the utility function ( sqrt c) . Both could experience an adverse event that results in earnings of $0 per year. Tess has a 1% chance of experiencing an adverse event and Lex has a 12% chance of experiencing an adverse event. Tess and Lex are both aware of their risk of an adverse event.
Refer to Scenario 2
Calculate Lex’s and Tess' expected utilities without insurance. (each one separated) Round to two decimal places for both
We learned that we can use choice between a gamble over someone's best and worst outcomes and getting an outcome of interest (like getting pizza) for certain as a way to assign numeric values to utility (on a scale of 0 to 1).
Using this method, if you are indifferent between the following:
A gamble that has a 0.3 chance of your best possible outcome (and no lower chance), and a 0.7 chance of your worst possible outcome.
Getting pizza for certain.
it means that your utility for getting pizza is:
Chapter 4A Solutions
EBK INTERMEDIATE MICROECONOMICS AND ITS
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