Arthritis Case Essay Project
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Arthritis Case Essay Project
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Write My Essay For Me2.1 A patient with arthritis of the knee is planning to have a knee replacement. He has applied for a loan for this surgery; the loan has an annual interest rate of 6 percent. The artificial knee can function for 10 years before it needs to be replaced. Fees for knee replacement surgery are expected to grow at 5 percent annually.
Why is an artificial knee a form of health capital?
Assume the artificial knee depreciates at a constant rate every year until the time of replacement, which is 10 years hence. What is the cost of this capital?
Suppose that instead of a loan, the patient plans to pay the surgery from his or her own savings. Assume that the bank’ s interest rate on savings deposits equals its rate on loans. Does this change your answer to (b)? Why or why not?
Draw the COC (cost of capital) line on a graph, with health capital on the x -axis and the COC rate on the y -axis. What is the slope of the COC schedule? Explain why it looks the way it does.
2.2. Suppose a hospital has 500 beds. It faces a demand curve x = 1,200 – 2 p, where p is the price of a bed day and x is the number of patient days of care demanded. The fixed cost of adding a new bed is $150 and the total housekeeping cost is given by C = (B /3.5), 2 where B is the total number of beds.
2.3 Assume the health production function is h = 365 – 1/ H, where h is the number of healthy days a person has in each year and H is the person’ s health capital. Assume this person earns a wage of $100/day, and the marginal cost of health investment π = 25 and is constant over time. The annual interest rate is 5 percent, and health capital depreciates at a rate of 15 percent per annum. a. What does the MEC for this person’ s health capital look like? Draw the MEC curve on a graph, with health capital on the x -axis and the rate of return on the y -axis.
Explain the shape of this MEC curve. b. What is the cost of health capital in this problem? c. Find the optimal level of health this person demands under the above conditions. d. Suppose the person acquires a chronic disease and his health depreciation rate rises to 35 percent annually. How does this change your answer to part (c)? e. Suppose instead of having a chronic disease the person experiences a recession and his wage falls to $50/day. Assume the change in the price of time inputs accounts for 20 percent of the total change in cost of a unit of health investment. Show graphically how this change affects the MEC curve. What is the person’ s optimal health demand now? f. Now focus on the role of human capital in this model. Suppose a person’ s educational attainment increases.
How does the MEC curve shift in this case? How does this shift affect the person’ s investment in health capital? 2.4 A person with osteoarthritis of the knee (a common condition in middle-aged and elderly individuals) plans to have a knee replacement. Assume he has a quasi-linear utility function (U (·)) over wage w and his health H. That is, U (w, H) = w + 10 4 ln H. Suppose with an artificial knee, the person can enjoy 20 additional healthy days annually during the next 10 years, during which he can earn a wage of $150/day. The annual interest rate is 2 percent. a.
What is the increase in the person’ s wage income if the person decides to get his knee replaced? b. What is the net present value of the monetary return on knee replacement surgery? Now suppose that in addition to the above conditions, the person also has a current health capital of 500 units. In the next decade, the additional health capital attributable to the artificial knee is given in the following table: Year 1 2 3 4 5 6 7 8 9 10 Health Capital 50 49 48 46 43 39 34 28 21 12 The patient discounts his utility from health capital at a 10 percent annual rate. That is, he is indifferent between receiving 100 units of health capital this year and receiving 110 units next year.
- What is the present value of his utility gain from having knee replacement surgery? d. If the total cost (including both the monetary loss from paying the surgical fee and the disutility from undergoing the surgery and recovering) is 30,000, should the person undergo the surgical procedure? 2.5 Suppose a person is asked a standard gamble question about three kinds of diseases. For each disease, the person decides to undergo surgery if the expected utility from the operation exceeds or is equal to the patient’s utility if he or she does not undergo surgery and continues having the disease. The person’s expected utility is therefore (1 – Θ)Ua + ΘU d, where U a is the utility if the operation is successful, Ud is the utility if it fails, and Θ is the probability of failure. The patient assigns the following probabilities of surgical failure to the diseases:
Disease A B C Θ 0.25 0.4 0.01
- Assume U a = 1 and Ud = 0. Then what is the utility of having each of the diseases if the person is indifferent between having and not having the operation? b. If the diseases are liver cancer, glaucoma, and dental caries, which one is most likely to be denoted as A above? Viscusi and Evans (1990) took a similar approach to analyzing the loss in utility from being healthy to becoming sick. In the experiment they discussed in their paper, workers were randomly assigned to label four different chemicals: asbestos, TNT, sodium bicarbonate, and chloroacetophenone. The first two chemicals are quite dangerous and could cause death if they exploded. The third is rather harm-less, and the fourth will only cause some tearing if proper treatment is not received.
The authors asked the workers how much money they would have to receive in compensation if they were reassigned to label another chemical. We will now apply the standard gamble concept to this problem. Assume the workers’ utility function is U(w) = lnw, where w is the hourly wage received from the labeling work and U(death) = 0. c. The probability of TNT exploding is ΘTNT, and if it explodes, the worker cannot survive. Also suppose the wage of labeling sodium bicarbonate is wS per hour. What is the minimum wage a worker must receive if he were reassigned to label TNT as a function of ΘTNT and wS? d. Which labeling work must have a higher wage, asbestos or chloroacetophenone? e. What is the wage function for chloroacetophenone? Use wS as the benchmark again.
Which value(s) do you need to be able to solve this problem? f. One major implication of Viscusi and Evans’s research is that people may have different utility functions when healthy than when sick. Suppose the utility function is V(w) = 0.5ln w if the worker is sick but alive. How does this change your answer to part (e)? 2.6 Consider the following scenario, which is slightly different from the throat culture example in the chapter. A parent decides about her child’s care when the child is suspected to be infected by streptococci.
The parent has three choices: ask the physician to give her child an antibiotic without performing the culture, perform the culture and give the child antibiotics only if the result is positive, or do nothing. If the child receives an antibiotic without being infected, she will develop a resistance to antibiotics (i.e., antibiotics will not kill infections that the child may get in the future) with probability Θar and cost C ar for further treatment. If she is infected and receives the antibiotic, she will be cured immediately without any side effects. If she is infected but not treated, the infection will develop into a rheumatic heart disease, which will cost Crf as a result. The probability of being infected before the treatment, which is known by the parent, is Θs. The cost of antibiotics is Ca and the cost of a culture is Cc. The values for these probabilities and costs are given below:
Θs Θ ar Ca Cc Car Crf 0.5 0.2 10 8.5 30 1,000
- Draw the decision tree for the parent. Be sure to calculate the utility and cost of each possible outcome at the end of each branch. b. What is the expected cost to the parent if she decides to give her child antibiotics without having the test performed? c. If the parent’s object is to minimize expected cost, what is her optimal decision? d. What if the probability of infection fell from 0.5 to 0.2? Would this change your answer to part (c)?
Arthritis Case Essay Project Essay
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