# Calculate the size of the deadweight loss from adverse selection in the insurance market.

Health Economics

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

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

## B. Analytical Problems

**4. 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=500*H.

a) [3 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) [4 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=9) and right (H=0) sides of the graph.

d) [4 points] What is the equilibrium price p* of the insurance plan in this market?

e) [4 points] Which consumers will purchase the insurance plan in equilibrium? (Your answer should depend on H.)

f) [6 points] Calculate the size of the deadweight loss from adverse selection in the insurance market.

g) [4 points] Now suppose an individual insurance mandate is imposed that forces all consumers to purchase insurance or else pay a tax of $1500. What will the insurance mandate do to the equilibrium price of insurance?

h) [3 points] What is the smallest mandate tax penalty that will completely eliminate the deadweight loss from adverse selection in this market?