health economics

Spring 2021 Name___________________________ Economics 5860: Health Economics Prof. Tamar Oostrom Final Exam The exam is out of 75 points total. You may use your notes and textbook, but this exam must be your own work. You may not discuss any part of this exam with any other individuals. If you have an extended deadline for this exam due to a previously discussed exception, please write your new deadline below: Part A. True/False Explain: [3 points each, 18 points total] Indicate whether each of the following statements is true or false and then explain. Include in your explanation any pertinent institutional details and economic reasoning (including appropriate graphs and equations). A correct True or False statement is worth one point; a correct, concise, and clear explanation is worth two points. 1. Empirical evidence (in addition to in-class zoom polling) shows that people are roughly evenly split between risk-loving and risk-averse.

2. Gruber (2008) suggests that an individual mandate would be very costly and thus not an effective way to insure the uninsured in the United States.

3. A risk averse individual prefers a certain outcome to an uncertain outcome with the same expected income. 4. Suppose there is a separating equilibrium in the Rothschild-Stiglitz model. If everyone becomes more risk averse, this can cause the equilibrium to collapse.

5. There is empirical evidence that young people subsidize the cost of insurance for older people in the ACA health insurance exchanges.

6. A risk-loving individual prefers no insurance to actuarially fair, full insurance.

Part B. Analytical Questions [35 points total]: 7. Individual Health Insurance Mandates and Adverse Selection [20 points total] Consider a market for health insurance similar to the one depicted below that we discussed in class.

Suppose individuals have different health levels H, where H is distributed uniformly between 0 and 1. Individuals are risk averse, there is a single insurance plan available for purchase (as in the Akerlof model, NOT the R-S model).

The marginal cost of medical care depends on an individual’s health H, and is characterized by the function MC=2000-1000*H (notice that a higher value of H corresponds to a healthier person, with lower marginal costs, so the left edge of the graph corresponds to the sickest person with H=0, and the right edge of the graph corresponds to the healthiest person with H=1). Individuals have utility functions for this insurance plan that result in a risk premium equal to RP=750 – 500H.

a) [1 point] Write down the equation describing the demand function for this insurance plan. (Hint: the demand function is the sum of the marginal cost and risk premium and should express willingness to pay for insurance as a function of H).

b) [2 points] Write down the equation describing the average cost function of the insurer. (Hint: since the MC function is linear, the AC function is also linear. If you find any two points along the line you can figure out the equation for the line.)

c) [4 points] Draw a graph similar to the one above containing the demand function, MC function, and AC functions. For each function indicate the values of the vertical intercepts on the left (H=0) and right (H=1) sides of the graph. Clearly label the deadweight loss.

d) [2 points] What is the equilibrium price p* of the insurance plan in this market?

e) [2 points] Calculate the size of the deadweight loss from adverse selection in the insurance market.

Now suppose an individual insurance mandate is imposed that forces all consumers to purchase insurance or else pay a tax of $250.

f) [4 points] What will the insurance mandate do to the equilibrium price of insurance?

g) [3 points] What is the effect of the mandate on the deadweight loss from adverse selection in the market? What is the gain in consumer surplus from lowered prices? What is the loss in consumer surplus from the mandate?

h) [2 points] Considering only the DWL from adverse selection and the consumer surplus components mentioned above, is the mandate welfare improving on average? For whom is the mandate most costly?

8. The Rothschild-Stiglitz Model and Universal Insurance [15 points]

Consider a hypothetical country HealthEconomia that has decided to adopt a Bismark model of insurance. Before this decision, the insurance market in that country was depicted by the figure below. There are two types of citizens of HealthEconomia, robust types with a low probability of getting sick and frail types with a higher probability of getting sick. Point E represents their initial endowment, and the dashed lines that intersect at E represent zero-profit lines. The only insurance plans offered were a separating equilibrium at points F and H.

(a) Explain why no insurance company would enter at point G. [2pts]

(b) Draw your own version of the figure above that includes the indifference curve for the robust types. Be sure to draw it so that the separating equilibrium is valid. [2pts]

(c) Now suppose that HealthEconomia creates a new health insurance contract at point P and forbids any private insurance contract from offering any other contract. Assume both types of citizens join this contract. Draw another indifference curve for the robust type that also fits this assumption. [2pts]

(d) Is everyone better off with this universal insurance? Compare the welfare change of frail types to that of robust types. [4pts]

(e) Suppose the universal insurance monopoly were deemed unconstitutional. Namely, private companies are now allowed to enter a market that previously only contained point P. Describe verbally the conditions that would have to hold for a private company to enter and make a profit. [3pts]

(f) What would happen to the government provided plan P after the existence of this new private plan? [2pts]

Part C. Short Answer [22 points total]: Provide a brief explanation for each of the following questions. Each question can be succinctly answered in one or two sentences.

9. For each policy, describe how it would affect moral hazard and adverse selection. Your answer should include a direction (positive, negative, or no change) for each of moral hazard and adverse selection. Why? [4pts each]

(a) The ACA mandated that individuals have health insurance or face tax penalties.

(b) The ACA reduced the deductible for preventative care services for Medicare enrollees.

(c) A hypothetical country with a Bismark health insurance system decided to reimburse insurers based on the ex-post realized health costs of enrolled patients, rather than the ex-ante risk assessment of their patients.

(d) The Beveridge model of health insurance implemented gatekeeping, where patients must see a primary care physician in order to get permission to see a specialist.

10. Consider the demand for insurance model from Lecture 14.

(a) Does the willingness to pay for insurance increase or decrease as the probability of becoming sick goes from p=0.5 to p=0.9? Why? [2pts]

(b) In real-world insurance markets, health insurance is normally seen as most valuable to sick people. Explain this result. Is this the same or different from your result in part (a)? Why? [2pts]

11. Have you completed the course evaluation? [2pts]