Health Economics
14th Edition
ISBN: 9781137029966
Author: Jay Bhattacharya
Publisher: SPRINGER NATURE CUSTOMER SERVICE
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Question
Chapter 7, Problem 1E
To determine
Determine whether the given statement is true or false.
Expert Solution & Answer
Explanation of Solution
According to the simple model, the income utility curve is determined by an individual’s taste for risk. If an individual exhibits the declining
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Students have asked these similar questions
Draw a utility function over income u(I) that describes a man who is a risk
lover when his income is low but risk averse when his income is high.
1.) Using the 3-point curved line drawing tool, draw the low income portion of
his utility function. Label it U₁.
2.) Using the 3-point curved line drawing tool, draw the high income portion of
his utility function. Label it UH.
Carefully follow the instructions above, and only draw the required objects.
C
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0
Utility
20,000
40,000 60,000 80,000 100,000
Income
Can you explain how Constant Relative Risk Aversion utility function should be understood and how it works mathematically
Economists define the 'certainty equivalent' of a risky stream of income as the amount of guaranteed money an
individual would accept instead of taking a risk. The certainty equivalent varies between individuals based on their risk
preference. Consider a risky bet that involves a 50-50 chance of losing $5,000 or winning $5,000 for an individual with
starting income of $50,000. Calculate the certainty equivalent income that provides the same utility as this bet for
individuals with these different utility functions: a. U(1) Vi b. U(1) = In(1) where In represents the natural logarithm
function C. U(I) = -1/1 d. What can you conclude about the relative level of risk aversion for these three individuals? e
What would be the certainty equivalent income for this bet for a risk neutral individual? f. What is the likelihood that a
profit maximizing risk neutral insurance company would be willing and able to purchase these bets from the individuals
in a, b and c? Explain.
Knowledge Booster
Similar questions
- The lecture mentions that diminishing marginal utility applies to the consumption of money as well as the consumption of certain food. Can you give another example where diminishing marginal utility applies? Can you think of any example where diminishing marginal utility does not apply? From utility theory, the demand for insurance depends on the level of risk aversion (i.e. how much you hate uncertainty), the cost of insurance (i.e. if it is within your willingness to pay), as well as wealth. Can you think of anything else that affects demand for insurance? One of the predictions of prospect theory is that we tend to be overly concerned with relatively small risk. Can you think of any example (besides those given in the lecture) that either speaks to this or is an exception?arrow_forwardSuppose that a person's utility function is the square root of wealth. Suppose the person earns $100,000 per year. He or she has an illness with a probability of 0.2, and the cost of the treatment is $30,000. Would the person pay $6,000 for insurance? Why or why not? What is the most this person would pay to be insured (hint: equate expected utility to utility with certainty)? Suppose their utility function changed to wealth squared (hint: are they now risk averse?). Would they pay $6,000 for insurance? Why or why not?arrow_forwardQuestion 5 Suppose that there is a 10% chance Ja'Marr is sick and earns $10,000, and a 90% chance he is healthy and will earn $70,000. Suppose further that his utility function is the following (utility = square root of income) U (I) = VIncome Ja'Marr's utility from expected income is , and his expected utility of his income is 264.58; 100 248.12; 252.98 100; 265.58 252.98; 248.12arrow_forward
- Economists define the ‘certainty equivalent’ of a risky stream of income as the amount of guaranteed money an individual would accept instead of taking a risk. The certainty equivalent varies between individuals based on their risk preference. Consider a risky bet that involves a 25% chance of losing $5,000 or a 75% winning $5,000 for an individual with starting income of $50,000. Calculate the certainty equivalent income that provides the same utility as this bet for individuals with these different utility functions: 1. U(I) = I 2. U(I) = I–√ 3. U(I) = ln(I)where ln represents the natural logarithm function Type the numerical answers in the corresponding numbered boxes below. Round your answers to two decimal places. Do not use $ or , in your answers. (for example, enter 45223.45 or 46500.00) What can you conclude about the relative level of risk aversion for these three individuals? Explain.arrow_forwardAnita bought a new scooter for $500. She is deciding whether she should insureher scooter against theft. She has recently read in the news that one out of 10 scooters arestolen in her town. She can buy scooter theft insurance at the price of 12 cents per $1 ofinsurance. How much insurance will Anita buy if her utility function is U(C) = 2C + 100?arrow_forwardIn the field of financial management, it has been observed that there is a trade-off between the rate of return that one earns on investments and the amount of risk that one must bear to earn that return. a) Draw a set of indifference curves between risk and return for a person that is risk-averse (a person that does not like risk).arrow_forward
- 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.arrow_forwardConsider 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.arrow_forward4. An individual's Bernoulli utility function is u(w) = Vw, and the individual has initial wealth 100. The individual might develop a health problem, which would reduce his or her wealth to 0. The individual might be "healthy" or "unhealthy." A healthy person develops the health problem with probability qL = 0.3, while an unhealthy person develops the health problem with probability qH = 0.7. The probability that the individual in question is healthy is 1/2. An individual knows whether he or she is healthy, but an insurer does not. Without insurance, a healthy person's wealth is 100 with probability 0.7 and 0 with probability 0.3. Without insurance, an unhealthy person's wealth is 100 with probability 0.3 and 0 with probability 0.7. Insurers only offer "full insurance." That is, if the adverse event occurs, they will pay back 100, restoring the individual's full wealth. Insurers set a price for this policy that is "actuarially fair." Insurance company makes no money on average.…arrow_forward
- 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.arrow_forwardWhich of the following shapes is the most likely plot of the utility-of-wealth function for a risk-averse person? Utility OA B D B D A Wealth Carrow_forwardThe marginal utility of income for a risk-averse individual will be: Select one: a. diminishing. b. constant. c. increasing. d. unknown; the answer depends on the value of income.arrow_forward
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