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EC9790
May Examinations 2020/21
Health Economics
Section A: Answer ONE question
1. This question has two parts, please answer both parts.
Part I
A profit-maximising hospital is able to perform only one type of surgery. For each surgery it performs, the hospital receives a payment of 1,000 and if the operation is successful it receives an additional 2,000. There is only one doctor capable of performing this type of surgery and they can only do one per day. The probability that the surgery will succeed depends on the level of effort that the doctor exerts. If the doctor exerts a high level of effort, the probability that the surgery will succeed is 0.5 and if they exert a low level then the surgery fails with certainty. The doctor’s cost of exerting the low level of effort is 0 while their cost of exerting the high level is 10. The doctor’s (daily) utility if the surgery succeeds is given by:
and if it fails by:
where w is the doctor’s (daily) income and ce is their cost of exerting effort. The doctor has the option of working for a different hospital where their (daily) utility is U = 6.
(a) Assume that the surgery outcome is verifiable but in order to induce the doctor to exert a high level of effort, the hospital’s policy is that doctors should not receive any payment if the surgery fails. How does the profit-maximising contract look in this case? What is the hospital’s profit in this case? (10 marks)
(b) Given that the hospital’s objective is to maximise profit, do you think that its policy of zero payment in case of failure is a god idea? Explain. (10 marks)
(c) Now assume that the hospital’s policy is not to condition the doctor’s payment on the surgery’s outcome. However, there is a probability of 0.5 that if the doctor exerts the high level of effort, that effort will be verifiable (that is, payment can depend on the doctor’s effort). How does the profit-maximising contract look in this case? What is the hospital’s profit in this case? (10 marks)
Part II
The term “remote medicine” refers to any encounter between a caregiver and a patient when they are located in different places. Essentially, they can be located almost anywhere during treatment. The contact between them can be accomplished by various means, such as by phone, email, text messages, or videoconferencing. Remote medicine is not a new phenomenon and began long before the outbreak of the Corona pandemic. Nonetheless, the pandemic provided a major impetus for its increased usage. The post-Corona medical world will be radically different, and the most notable change will be the use of remote medicine in almost every caregiver-patient encounter.
Answer the following questions:
(a) One major concern is that remote medicine will exacerbate inefficiency due to patients’ moral hazard. Can you explain why this might be the case? (10 marks)
(b) Another concern is that remote medicine may exacerbate inefficiency due to adverse selection, especially when premiums are exogenously fixed. Can you explain why this might be the case? (10 marks)
2. This question has two parts, please answer both parts.
Part I
Individuals can be one of two types: H (healthy) or C (chronically ill). The probability of an individual being of type H is 0.5. During the coming year, both types will experience some acute medical problem with a probability of 0.25, in which case they will require treatment. For the H type, the treatment is less intense and hence its cost is 64, whereas for the C type the treatment is more intense and hence its cost is 84. Further assume that all individuals are risk averse and their objective is to maximise their expected utility.
(a) Assume that profit-maximising insurers can freely enter the market and are able to identify whether an individual is of type H or type C. Characterise the contract(s) that will be offered in equilibrium in this case. Is there a moral hazard problem in this case? Is the market equilibrium efficient? (10 marks)
(b) Now answer part (a) under the assumption that insurers cannot identify whether an individual is of type H or C. (10 marks)
(c) Now assume that that insurers cannot identify an individual’s type but are obligated by law to offer a contract that pays at least 72 in the case of illness. Further assume that the initial wealth is 100 for all individuals and that their utility function (from wealth) is given by:
Characterise the contract(s) that will be offered in equilibrium in this case. Is the market equilibrium efficient? Is there a moral hazard problem in this case? (10 marks)
Part II
A risk-averse employee of a particular company needs to decide between two alternatives for the calculation of their salary: under the first, they will receive a fixed monthly salary of $10,000; under the second, they will receive 20% of the company's monthly revenue. The company's revenue depends on the degree of “effort” that the employee invests in their work (e.g., the “inputs” that the employee provides to the project they are working on). The employee can choose a “low” or “high” level of effort. If they choose to exert a low level of effort, then with a probability of 0.75 the project will fail and the company's revenues will be 0, and with a probability of 0.25 the project will succeed, and the company's revenues will be $100,000. If, on the other hand, the worker chooses a high level of effort, then the project will succeed with a probability of 0.9 and fail with a probability of 0.1. Correspondingly, if the employee chooses a high level of effort, then the “cost” to them is equivalent to a loss of income of $8000 and if they choose a low level of effort, then the cost to them is 0.
(a) Which of the two salary alternatives should the employee choose? Is there a moral hazard problem if they make that choice? (5 marks)
(b) How would your answer change if the company raises the employee’s salary under the second alternative to 25% of the company's revenue? (5 marks)
(c) It is now assumed that the company continues to offer the fixed salary alternative to the employee, but instead of the revenue-contingent alternative it now offers a salary contract that depends on the level of effort the employee invests in the project. Assuming that the company's goal is to maximise expected profit what salary calculation will it offer to the employee? What will be the company's profit in this case? Is there a moral hazard problem in this case? (10 marks)
Section B: Answer ONE question
3. Blake is contemplating starting a new 3-day fitness program which includes going for a run for the first time ever today. Running is hard, so running today involves a disutility of 10 relative to not running. But running becomes more enjoyable the more one engages in it. So, a person who has run s days in the past would get utility of running UR(s) relative to not running of:
UR(1) = 0 UR(2) = 19 (1)
(a) Assume that tomorrow there is a 50% chance that Blake's friends will show up and want to play videogames, which would give Blake a utility of 20 compared to running on that day. If the friends show up, does Blake want to run tomorrow? Having run on days 1 and 2, would Blake want to go running on day 3? If Blake runs today and the friends do not show up tomorrow, would Blake want to go running tomorrow? Assuming Blake is naïve, i.e., does not anticipate the possibility of the friends coming over, does Blake want to run today? What is Blake’s ex-post utility if the friends do or do not show up? (7 marks)
(b) If Blake runs on day 1 but not on day 2, does Blake want to go running on day 3? Now assume Blake is sophisticated, i.e., anticipates the friends might show up and plans might change. Given Blake’s expected utility for the next 3 days (today, tomorrow, the day after), does Blake want to start running today? What is Blake’s ex-post utility if the friends do or do not show up? How does this compare to your answer in point (a)? (7 marks)
(c) Assume that Blake can buy a commitment contract with the gym such that Blake pays 1 into the gym on day 1 and gets 3 on day 3 if Blake runs three days, else the gym gives the money to charity. What is the continuation utility of running on each day assuming Blake has signed the contract (i.e., the future utility from running on each day)? Is Blake willing to sign the contract if Blake is sophisticated? Interpret your findings. Is this contract sustainable for the gym if all people behave like Blake? (7 marks)
(d) Now suppose that this 3-day running program decreases the risk of heart failure in the population by 10%. One heart failure cost the NHS 100. If all individuals are like Blake and sophisticated, should the NHS subsidise this program? (7 marks)
(e) In certain colleges, first-year students are randomly assigned roommates. The table below shows the effect of these randomly assigned peers' fitness (measured in high school) on own fitness during college, estimated on a large sample of students. Columns 3 and 4 interact peers’ fitness with indicators of whether own fitness in high school was below or above average. Discuss the table. How do the coefficients in Columns 3 and 4 relate to the assumption we made above that running becomes easier and gives more utility the more one has run in the past? (7 marks)
(f) The following table shows the correlation of the education of biological and adoptive parents with their offspring's health (when they are adults) using Swedish data. Describe the table and interpret the results: what can explain these correlations? (5 marks)
(g) The following figure shows county-level 17-year long-term average of PM2.5 concentrations (2000–2016) in the United States in μg/m3 and (B) county-level number of COVID-19 deaths per 1 million population in the United States up to and including 18 June 2020. Describe the figure. Can you conclude that pollution causes COVID-19 deaths? What would you want to include in a regression to be able to interpret this relationship causally? Is it problematic that the authors use county-level data? (5 marks)
(h) In an isolated village live 10 people, indexed by i ∈ {1,2, 3, 4, 5, 6, 7, 8, 9. 10}. There is an infectious disease in the village. Each person can get vaccinated at cost ci = i (so one has cost 1, one 2, etc up to 10). Assume the benefit from vaccination is b = 8, and each individual utility is Ui (vaccine) = b − ci if they get vaccinated and 0 otherwise. How many people get vaccinated (assume somebody gets vaccinated if their utility from the vaccine is 0) and what is the total utility from the vaccine in the village? Does total utility increase if the vaccine becomes mandatory and everyone gets the vaccine? Discuss. Now assume an infant is born who cannot get vaccinated. If the infant gets the disease, the village as a whole loses 8 utiles (so subtract 8 from total utility). Each non-vaccinated person might infect the child with probability 0.25. What is the probability that the child gets sick? (Hint: to avoid double counting the probability that the infant is infected, consider that the child is sick if one person alone infects it and others don't, and what is the probability of these events, or if multiple people infect it.) What is total expected utility if the same people vaccinate? Does total utility increase if the vaccine becomes mandatory? Discuss. (5 marks)
4. (a) Jordan's utility depends on consumption of food (f ) and spending time cycling (h). However, when they cycle, they are not working, so the opportunity cost of cycling is their wage (w). In other words, their budget constraint is f + wh = y. Their utility function is U(f, ℎ) = f ∗ ℎ. Suppose y = 10 and w = 2. They can choose the level of cycling to be either ℎ = 2/5 or ℎ = 5. What do they pick? What is their total utility? Would they pick a consumption bundle such that either h or f is 0? Discuss what this implies for whether cycling and food are complementary or substitute and why this could be. (7 marks)
(b) What would Jordan pick among these two choices if their wage was 1 instead? Discuss how the change in wage (aka opportunity cost of cycling) affects your result in relation to your answer under (a). (7 marks)
(c) Now assume that cycling makes Jordan healthier, meaning they can work more time and earn more, raising their income to y = 10 + 0.5 ∗ ℎ. If their wage is 1, what level of cycling would they pick between ℎ = 10 or ℎ = 5? How does the increased income change your answer? Discuss what happens here (hint: cycling here is an input for what?). (7 marks)
(d) Now assume that Jordan’s income does not depend on cycling anymore, and their wage equals to 1 as under point (c). But suppose they win the lottery, so now their income is 20 instead of 10. Would they pick a cycling level of 10 over ℎ = 5? Knowing that cycling makes one healthier, but knowing that Jordan only eats donuts and that consuming more than 5 donuts is bad for one’s health, do you think Jordan is healthier after having won the lottery than they were without the extra winnings? Discuss. (7 marks)
(e) To test the effect of increased income on health, researchers have compared individuals who won the lottery to the rest of the population. Why is this a better idea than comparing rich to poor individuals? Why could this comparison be affected by selection bias? The figures below show these comparisons for general health and social drinking. Discuss these findings in light of your answer to the previous point. (7 marks)
(f) The following table shows the correlation between the education of biological and adoptive parents with their offspring’s health (when they are adults) using Swedish data. Describe the table and interpret the results: what can explain these correlations? (5 marks)
(g) The following figure shows county-level 17-year long-term average of PM2.5 concentrations (2000–2016) in the United States in μg/m3 and (B) county-level number of COVID-19 deaths per 1 million population in the United States up to and including 18 June 2020. Describe the figure. Can you conclude that pollution causes COVID-19 deaths? What would you want to include in a regression to be able to interpret this relationship causally? Is it problematic that the authors use county-level data? (5 marks)
(h) In an isolated village live 10 people, indexed by i ∈ {1,2, 3, 4, 5, 6, 7, 8, 9. 10}. There is an infectious disease in the village. Each person can get vaccinated at cost ci = i (so one has cost 1, one 2, etc up to 10). Assume the benefit from vaccination is b = 8, and each individual utility is ui (vaccine) = b − ci if they get vaccinated and 0 otherwise. How many people get vaccinated (assume somebody gets vaccinated if their utility from the vaccine is 0) and what is the total utility from the vaccine in the village? Does total utility increase if the vaccine becomes mandatory and everyone gets the vaccine? Discuss. Now assume an infant is born, and they cannot get vaccinated. If they get the disease, the village as a whole loses 8 utiles (so subtract 8 from total utility). Each non-vaccinated person might infect the child with probability 0.25. What is the probability that the child gets sick? (Hint: to avoid double counting the probability that the infant is infected, consider that the child is sick if one person alone infects it and others don't, and what is the probability of these events, or if multiple people infect it.) What is total expected utility if the same people vaccinate? Does total utility increase if the vaccine becomes mandatory? Discuss. (5 marks)