Exam 2017, questions and answers PDF

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CARLETON UNIVERSITY, Department of Economics ECON 4460 A Health Economics Midterm Exam, October 30 2017 Time: 2.5 hours (6.10 pm till 8.40 pm)

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The exam has SIX questions, three Essay Questions (E 1 to E 3) and three Calculation Questions (C 1 to C 3). Answer ANY FIVE questions. All questions are equally weighted. Be careful to allocate your time so that you give at least a partial answer to each of the five questions you answer.

Part I: Essay Questions E 1. a) State approximately what proportions of GDP have been spent on healthcare in Canada, the U.S., and two other countries, in recent years, and roughly what percentages were paid for by government in these countries. See table in HEC 1 b) List the 5 largest expenditure items in the Canadian healthcare system, and roughly what proportions of total healthcare spending they account for. See table in HEC 1 c) Describe the way responsibility for financing and managing healthcare is divided between Canada’s federal and provincial governments. Also explain the role of the Canada Health Act, and what expenditure items it refers to. Financing and managing healthcare are provincial responsibilities, but the federal government transfers certain sums for healthcare to the provinces; the transfers are conditional on the provinces abiding by the rules of the CHA which specifies that all hospital and physician services must be universally available at no out-of-pocket charges

d) Describe the methods that are used in Canada to pay for most of the services of the following providers: hospitals; primary care doctors; specialist doctors in outpatient care; specialist doctors who treat patients in hospitals. Hospitals are funded through annually negotiated global budgets out of which they have to cover all their costs. The majority of doctors in all these categories, including those treating patients in hospitals, are paid via fee for service. E 2. a) Explain the difference between static and dynamic models in micro-economics, and why Michael Grossman believes that the demand for health care can best be analyzed with the help of a dynamic model. Write down and describe the objective function that is maximized, and the life-time budget constraint that must be satisfied, in the Grossman model of investing in health. Define what is meant by the investment and consumption motives for investing in health, and identify these motives in your description of the model. Dynamic economic models deal with decisions that have consequences over time and that will change as circumstances change. This applies to health, as it changes over individuals’ lifetime and because investments in health have consequences in future time periods. Consumption motive: more health capital directly raises utility (point to the utility function) Investment motive: more health capital increases time available for work, and hence enters the life-time budget constraint. A good answer should contain both the sum of life-time utilities (use the sum notation) and the life-time present value budget constraint (ditto). b) State and explain every part of the first-order condition that Grossman uses to characterize the factors that determine the optimal investment in health capital in each period. Illustrate the formula in a diagram similar to the one we have discussed in class. MB = sum of consumption and investment motives = MC(r+ d +n) = cost of using and additional unit of health capital in a given year. (MC is cost of creating a unit, d + r + n is cost attributable to the given year.) Picture see below c) State the relationship between age-specific death rates and survival rates, and use the survival rates to write down a formula for the life expectancy at birth of an individual who is subject to the death rates in a given population. Also explain how the formula must be modified if it is to be used in estimating the expected number of Quality-Adjusted Life Years in a population s i=si−1∗(1−d i) . For LE(0) and QALY formulae, see website material and slides

d) Briefly discuss the differences and similarities between the concepts of quality-adjusted life expectancy and the Grossman model The QALY formula is similar to the utility function that is maximized in the Grossman model, except that the expressions that multiply consecutive life-years in the QALY formulae are just the h quality of life factors; in the Grossman model, they are utilities that depend on consumption. The big difference, though, is that the QALY expression is just an index that doesn’t tell us anything about how individuals’ make choices so as to maximize it E 3. a) Explain the difference between a producer in a perfectly competitive market on one hand, and a producer who sells a differentiated product in a monopolistic competition market, such as that for dental care or physician services when fees are not regulated by government, on the other hand. How does each decide what quantity to produce? Both seek to maximize profits by producing at the point where MC=MR. However, producers under perfect competition are price takers, meaning that for them MR=P, while a producer in a market for differentiated products face a downward sloping demand curve, meaning that for them, MR < P. b) Using a diagram, explain why the equilibrium price in the market for a monopolistically competitive producer’s services is not equal to the marginal cost of production, and how this will lead to an efficiency loss that can be measured by an area in the diagram. In your answer, assume that the demand curve reflects the quantities chosen by well-informed consumers who pay for the services out of their own pockets, and explain why this assumption is needed in order to correctly measure the efficiency loss. See picture below. The picture only applies if demand is by well-informed consumers, since it is only if consumers know what they are buying that areas under demand curves are accurate measures of economic value. c) Explain how your answer to b) will change if consumers are insured, and if the quantities they demand are influenced by biased advice from the sellers so that there is Supplier-Induced Demand in these markets Both effects shift the demand curves facing producers to the right. If these effects are large enough, the inefficiency associated with underutilization from part b) may end up leading to inefficient overutilization (see picture below) d) Explain the difference between capitation and fee for service as methods of paying for physician services, and the different incentives that doctors are subject to under these two methods. State which of these methods is assumed in your answers to parts a), b), and c), and how the analysis in parts b) and c) would change if the other one was used.

Capitation does not pay doctors for the quantity of services produced, but instead for the number of patients to whom they have agreed to provide services as needed. Hence their incentive is to use their information advantage to reduce patients’ service demand, not increase it. [Exam continues on next page] Part II. Calculation Questions C 1. In a market for health services, providers are paid $50 per unit, which also equals the (constant) social opportunity cost of producing a unit. In a given population, 25% of the people will be ill once each year; the ex ante probability of illness is the same for everyone. If an ill person pays nothing out of pocket for health services, they will utilize 30 units. Every ill person’s compensated demand curve for health services is such that if they have to pay $50 per unit, they would utilize only 20 units. Those who are not ill do not use any health services. Answer the following. a) What is the actuarially fair premium for an insurance plan that pays for 100% of the consumer’s health services? Assuming the relevant demand curve is a straight line, what is the moral hazard welfare loss per person who is ill? What is the loss per insured person? AFP = Prob (ill) * P*Q = .25*50*30 = 375. For MH loss see picture below (it is 250 per sick consumer, and a quarter of that per insured consumer, since only 25% of insured consumers are sick) b) Answer the same questions as in a), but now assuming that everyone is covered by an insurance plan that pays only 50% of the healthcare costs of those who are ill (continue to assume the demand curve is a straight line) AFP now is only half of P*Q*Prob(ill), and Q falls from 30 to 25. So AFP = 0.5*0.25*25*50 =156.25. MH loss is only ¼ of what it was under a), or 62.5 per sick consumer, and ¼ of that per insured one c) Answer the same questions as in a), but now assuming that everyone is covered by an insurance plan with an annual deductible of $500, and a co-insurance rate of 50% for healthcare costs beyond the deductible Since the co-insurance rate is 50%, Q remains at 25, and the MH loss is the same as under b). The AFP is one-half*Prob(ill)*(P*Q – 500)=0.5*0.25*(50*25 – 500)=93.75 C 2.

In a population of ex ante identical individuals, every person has an annual income of 800 if there is no loss. However, each year 20% of the population suffers a loss which reduces their income to 200 per person. Each member of the population has a utility function given by 200 =2.25−200∗y −1 y where y is the person’s income during the year. Answer the following. u=2.25−

a) Find the actuarially fair premium for an insurance contract that covers the entire loss for those who have one. Also find expressions for the gains from full insurance on actuarially fair terms, both expressed in units of utility, and expressed in terms of money AFP is Prob(loss)*Loss = 0.2*600=120. With no insurance, u is either 2 or 1.25, so EU = . 8*2+.2*1.25=1.85. With full insurance, everyone’s utility always is 2 – 200/(800-120)=1.96, so the gain from full insurance is 1. 96 – 1.85, in utility terms. To find gain in money terms, we first find the minimum income that gives a fully insured person the same utility as the EU of a person without insurance. That is, we solve 1.85 = 2.25 – 200/x which gives x = 500. This means that the maximum premium that a person is willing to pay is 800 – 500 = 300, so the gains from full AF insurance is Max WTP – AFP = 300 – 120 = 180 b) Now assume that insurance is not available on actuarially fair terms, but that plans with different payouts B are offered at premiums given by π =0.3∗B . Drawing on your answer in part a), calculate the gains from full insurance, expressed in terms of money, at the higher premium. With full insurance, B is 600, so the premium is 180. The max WTP is the same as before (300), so the gains now is 300 – 180 =120 c) Discuss the general principle which suggests that in this case, each individual’s best choice would be a plan with a benefit B that was smaller than the size of the possible loss. Write down an expression in which an individual’s ex ante expected utility is expressed as a function of B and without actually solving for it, explain how you could find their best choice. The principle just is that when the premium, as a fraction of the loss, is larger than the AFP, it is better for the individual to be less than fully insured. To show this, one may write the individual’s expected utility in this case as 200 EU =0.8∗ 2− 200 +0.2∗(2− ) 800−.3 B 200+ B−.3 B The optimal B can then be found by taking the derivative of this expression with respect to B, setting the result equal to zero, and solving for B*. The general principle then tells us that the result will be B* < 600.

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C 3. In a given population of 500 ex ante identical individuals, 70% are well in a given year, with each one having a utility function given by uW =ln(c W ) , where c W is consumption per person. However, 30% will be ill. 20% will have a minor illness, with each one in this category having utility function uS =ln ( c S ) +ln ( mS −10 ) −20 where c S is the amount of consumption per person with minor illness, and m S is their utilization of medical services. Further, everyone in the remaining 10% in the population will have a major illness, giving rise to the utility function uB =ln ( c B ) +ln ( m B −30 )−50 The ex ante risk of illness is the same for everyone in the population. Assume that in a given year, the amount of consumption goods that have been produced in this economy is 12,500 units, while the amount of medical services that have been produced is 5,500 units. Answer the following. a) First, assume that everyone in the economy gets the same amount of the consumption good (that is, c W =c S= c B=c ). Find the common value of c, and use the technique of constrained maximization to find the allocation of the available medical services that is efficient in the sense of maximizing expected utility in this population. [Hint: Remember that in general,

d ln ( x ) 1 = x dx

.]

The common value of c is simply 12,500/500=25. What is to be maximized is EU =350∗uW +100∗uS +50∗u B If you write this out just the definitions of utility and take into account that the c values are constant, you will find that this can be simplified to EU =Const +100 ln ( m S−10) + 50 ln(m B−30) The constraint now is that the total amount of medical care consumed by the 150 sick people cannot exceed 5,500: BC=100 mS +50 m B −5,500 ≤0 . The Lagrangean becomes EU −λ BC . Taking the derivatives w/r/t m S , m B , λ and setting equal to zero will enable you to see that at the optimum, m B =mS +20 , which means that the constraint is satisfied when m B =50, m S =30 .

b) Discuss why, in this example, allocating the same amount of consumption goods to everyone, regardless of whether they are ill or not, is efficient. (In the example in Assignment 1, an equal allocation of consumption goods was not efficient.)

The reason is that in this example, the function that measures an individual’s utility from consumption only depends on their consumption itself, not on their health status. Therefore, to distribute available consumption goods in such a way that marginal utility is equalized requires giving everyone, sick or well, the same amount of consumer goods in this case, but not in Assignment 1 c) Explain why resources in this economy will not be efficiently allocated if everyone, well or ill, receives the same income and has to buy the goods and service they need in the market. Also discuss how income would have to be redistributed so as to improve efficiency. If everyone had the same income, those who were sick and had to buy medical services would not have enough money to buy as large a quantity of consumer goods as those who were well. As a result, utility would not be maximized. To overcome this problem, one would have to redistribute money toward those who were sick. (That, of course, is what health insurance does.) d) If production conditions were such that the marginal opportunity cost of one unit of medical services was one unit of the consumption good, would it be efficient to produce more medical services in this economy? Explain your reasoning. The answer is yes, because the marginal utility of medical services is 1/20 (this is true for both those with the minor and major illness: 1/(30-10)=1/(50-30)). The marginal utility of consumption is lower; it is 1/25 for every person in the economy. So MU for an additional unit of medical services is higher than the MU for a unit of consumption, meaning that if we can reallocate resources in such a way that we increase medical services by one unit in exchange for a one unit decrease in consumption, we could raise total utility.

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