Health Economics
14th Edition
ISBN: 9781137029966
Author: Jay Bhattacharya
Publisher: SPRINGER NATURE CUSTOMER SERVICE
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Question
Chapter 7, Problem 10AP
(a)
To determine
Determine the Utility function (U-I).
(b)
To determine
Describe the relationship between risk aversion and
(c)
To determine
Determine whether the given statement is true or false.
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Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I (U'>0) and convex (U">0).a. Draw a utility function in U–I space that fits this description.b. Explain the connection between U'' and risk aversion.c. True or false: this individual prefers no insurance to (IS, IH) to an actuarially fair, full contract.
Consider an individual whose utility function over income I is U(I), where U is increasing smoothly in I (U’ > 0) and convex (U” > 0).
Draw a utility function in U - I space that fits this description.
Explain the connection between U” and risk aversion.
True or false: this individual prefers no insurance to an actuarially fair, full contract. Be sure to explain your answer.
Suppose that there is a 20% chance Malik is injured and earns $100,000, and an 80% chance he stays healthy and will earn $500,000. Suppose further that his utility function is the following (utility = square root of income)
Malik is risk ____. He will prefer ____ (given the same expected income).
a. lover; actuarially fair and full insurance to no insurance
b. averse; no insurance to actuarially fair and full insurance
c. neutral; he will be indifferent between actuarially fair and full insurance to no insurance
d. lover; no insurance to actuarially fair and full insurance
e. averse; actuarially fair and full insurance to no insurance
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- Suppose a company offers a standard insurance contract with a premium (r) of $2,000 and a payout (q) of $10,000. Suppose that Adelia earns a healthy state income of $70,000, a sick state income of $50,000, and has a 20% chance of becoming ill. For Adelia, this insurance contract would be: A. actuarially fair and partial B. actuarially fair and full C. actuarially unfair and full D. actuarially unfair and partialarrow_forwardConsider an economy with two agents where agents A and B where both have the same risk attitude given by u(x)=ln(x). Suppose in state 1, only agent A has a job that earns $3 and B does not earn anything. In state 2, only B works and earns $2. Solve for the equilibrium in this economy when mutual insurance is feasible. Assume both states are equally likely.arrow_forwardConsider 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?arrow_forward
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