Econ 5860: Health Economics

Professor Tamar Oostrom

Ohio State University

Spring 2021

Problem Set 4

Due Date: Apr 19, 2021 by the beginning of class

Please submit assignments on Carmen.osu.edu


A. True/False Explain. Indicate whether each of the following statements is true or false and then explain why you think this. Include in your explanation any pertinent institutional details and economic reasoning (including appropriate graphs and equations). Please provide concise, clear answers with minimal irrelevant detail. Explanation is required.

1. Policymakers in at least 14 states in the US have in recent history passed laws called “community-rating” laws. The idea of these laws is that, since individual private health insurance markets don’t seem to function very well, leaving many older and sickly people unable to purchase affordable insurance, community rating laws impose restrictions on prices that insurance companies are allowed to charge. Consider a community rating law that forces insurance companies to charge the same price to all individuals (and forces insurance companies to sell insurance to anyone who is willing to pay the chosen price).

[5 points] True or false: the Rothschild-Stiglitz model suggests that this law will help old and sickly people gain access to insurance.

2. [5 points] In the Rothschild-Stiglitz model, more risk averse consumers have flatter indifference curves, all else equal.


B. Analytical Problems

3. Consider the figure below



a. [2 points] Explain why UH is not a valid indifference curve.

b. [3 points] Draw a new version of the diagram with the same indifference curve. On the new diagram, label two insurance contracts, A and B, such that A provides more income in both states of the world but the individual with the indifference curve in the diagram nonetheless prefers contract B over contract A.

c. [2 points] Draw a new diagram with a version of the indifference curve that represents valid preferences

d. [3 points] Is the set of contracts (F, H) a valid separating equilibrium if the high risk individuals have preferences as you have drawn them in part c?

4. Consider the basic Rothschild-Stiglitz model with asymmetric information and two types on consumers. A policymaker who has taken this class suggests that is might be beneficial to impose a flat tax on healthy people and distribute the tax revenue to sick people, providing partial insurance to people.

a. [3 points] Since the tax will only offer partial insurance, there will still be a private competitive market for additional insurance. Will a separating equilibrium be possible in the insurance market if this tax is implemented? Draw a diagram to justify you answer.

b. [3 points] After the tax is implemented a recession hits and a new policymaker decides to make up for a tax revenue shortfall by expanding the tax to include sick people as well as healthy people. Will a separating equilibrium be possible in the insurance market under this policy.

5. Individual Health Insurance Mandates and Adverse Selection

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 9. The marginal cost of medical care depends on an individual’s health H, and is characterized by the function MC=1000+1000*H (notice that a higher value of H corresponds to a sicker person, with higher marginal costs, so the left edge of the graph corresponds to the sickest person with H=9, and the right edge of the graph corresponds to the healthiest person with H=0). Individuals are risk averse, there is a single insurance plan available for purchase (as in the Akerlof model, NOT the R-S model), and individuals have utility functions for this insurance plan that result in a risk premium equal to RP=1000*H.

a) [2 points] Write down the equation describing the demand function for this insurance plan. (Hint: the demand function 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) [3 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=9) and right (H=0) sides of the graph.

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

e) [2 points] Which consumers will purchase the insurance plan in equilibrium? (Your answer should depend on H.)

f) [3 points] Calculate the size of the deadweight loss from adverse selection in the insurance market.