Health Economics
14th Edition
ISBN: 9781137029966
Author: Jay Bhattacharya
Publisher: SPRINGER NATURE CUSTOMER SERVICE
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Question
Chapter 7, Problem 13AP
(a)
To determine
Describe the algebraic expression for both
(b)
To determine
Determine an individual utility curve.
(c)
To determine
Describe an algebraic expression for M.
(d)
To determine
Derive the coordinate plane with p on x axis and M on Y axis.
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and you have a 10% chance of getting sick. Your income when sick is $0 and your income when healthy is $100.
1. Assume your utility over income is U=T ¥
1. Graph your utility and income with income on the x-axis and utility on the y-axis. Show your income/utility when healthy and sick on the graph.
2. calculate your expected income. Show on graph.
3. calculate your expected utility. Show on graph.
1. Now you are offerred health insurance by Prof. Grossman's Totally Full and Fair Insurance Company. For a premium of $20, you will get a payout of $50 if you get sick.
1. Is the insurance company's name accurate (is this actuarially fair and full)?
2. What is the expected payout from this insurance?
3. What is the Income when sick and income when healthy under insurance? Show on your graph
4. What is the expected income and expected utility under this insurance? Show each on your graph
5. Propose a full and fair insurance given your 10% chance of getting sick and your healthy and sick…
4. 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.…
Suppose Diane's utility function is U=-
Vincome . Diane earns an income of
$102,400, but there is a 15% chance that she will get sick and have a $62,400 medical bill.
The health insurance company, DenialCare, will offer her a health insurance policy to pay
for her medical bills. What would an actuarially fair premium be and what is the
maximum she would be willing to pay for the insurance?
Knowledge Booster
Similar questions
- Suppose 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_forward1. Suppose a person's utility is equal to U = Y and the initial income is $80,000. Medical expenses for a sick person amount to $40,000 and the probability of getting sick is 25%. Assume that the individual is required to pay the actuarially fair premium (r = p * M). a. b. What is the expected income when you are healthy? When you are sick? What is the expected utility if you buy insurance? What is the expected utility without insurance? C. What is the actuarially fair premium for the individual? d. Graph the individual's utility function. Clearly indicate the expected disposable income, utility with insurance, and expected utility without insurance. What is the dollar value of the individual's risk premium? Show this on the graph. How much is the individual willing to pay for insurance? e. f.arrow_forwardSuppose that your utility function over health care (h) and other goods (c) is given by U(h, c) and that you have a fixed income of $100. (Assume that the indifference curves of your utility function bear the usual convex shape.) Each year, you choose h and c to maximize your utility subject to a budget constraint: phh+pcc=Ywhere ph is the price of health care, pc is the price of other goods, and Y is your income. In year 1, the price of health care is $1, while the price of other goods is $2. At these prices, you demand 30 units of health care and 35 units of other goods. In year 2, your utility function and your income do not change, but prices do. Health care becomes more expensive at $1.50, while other goods become cheaper at $1.50. At these prices, you demand 20 units of health care. a. Assuming you spend all your income in year 2, how many units of other goods do you buy?b. Draw a graph with your demand for health care on the horizontal axis and your demand for other goods on the…arrow_forward
- A person's utility function is U = C1/2 . C is the amount of consumption they have in a given period. Their income is $40,000/year and there is a 2% chance that they'll be involved in a catastrophic accident that will cost them $30,000 next year. a. Calculate the actuarially fair insurance premium. What would your expected utility be if you were to purchase the actuarially fair insurance premium? b. What is the most you would be willing to pay for insurance, given your utility function?arrow_forwardJeremiah faces probability of illness p=0.20, healthy-state income $310, and sick-state income is $110 Jerimiah's satisfaction depends on his earned income. His utility function () is summarized in the table below INCOME 50 100 110 150 200 250 300 310 350 400 UTILITY 171 200 205 218 230 240 248 249 255 260 Using the information above, calculate Jeremiah's expected utility of income E[U] without health insurance PLEASE INCLUDE ONE DIGIT AFTER THE DECIMAL POINTarrow_forwardThe doctor must decide which medication to prescribe to the patient. Possible states are s∈[0,1]. She has three medications available: A, B, and C. The effect of medication A is described by the blue function, the effect of medication B by the red function, and the effect of medication C by the black function. For which medication will the doctor decide if she decides based on the maximax criterion and Wald's maximin criterion? The blue function is defined as fA(s)=1/5(cos(4s)+2), the red function is fB(s)=2/5(sin(4s)+1), and the black function is fC(s)=1/2. For which medication will the doctor decide if she decides based on Laplace's criterion?arrow_forward
- Suppose the probability that Recall Scarlett is sued is .1 and her income is 1000. In the case, she is sued she will lose all of her income in the settlement. She may purchase malpractice insurance at a rate of $r per $1 of coverage. Finally assume that her utility of income is U($) = ($)^1/2. What is Scarlett’s demand curve for insurance (that is find her demand for insurance for all r ≥ .1)?arrow_forward. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index . There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. a) Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain.arrow_forwardAn individual has the utility function U(I) = I^(1/2), where I is their net income. (Note that I to the exponent/power of 1/2 is the same as the square root of I.) The individual starts with $1600 in income. The individual has a 20% probability of being very sick, 30% probability of being slightly sick, and 50% probability of being healthy. If the individual is sick, they lose net income because they need to pay healthcare costs. The healthcare costs are $1600 if they are very sick, $700 if they are slightly sick, and $0 if they are healthy. Please use this information for the following parts of this question unless otherwise specified. What is the individual's expected utility? Suppose a health insurance company offers the individual a full insurance contract. What is the actuarially fair, full insurance premium for this individual? What is the individual's expected utility if they purchase a full insurance contract at the actuarially fair, full insurance premium?arrow_forward
- When Shalini is sick, she values wealth according to the utility function US(w) = ln (w). When she is healthy, she values wealth according to UH(w) = 1.1 ln (w). Shalini allocates wealth of $1,000 for each week and has a 5% chance of getting sick. a) Would Shalini be willing to spend $30 of her of her $1,000 wealth in order to guarantee avoiding getting sick, if it were possible for her to do so? (b) Would Shalini be willing to spend $30 of her of her $1,000 wealth in order to buy an (actuarially fair) insurance policy under which she receives $600 in indemnity if she gets sick? (c) How do you explain your answers to parts a and b above? How do the answers compare and how you can intuitively explain them in this context?arrow_forwardDraw 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 500- 450- 400- 350- 300- 250- 200- 150- 100- 50- 0 Utility 20,000 40,000 60,000 80,000 100,000 Incomearrow_forwardSuppose 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_forward
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