Main takeaways
Explain, using a graph, how unraveling could occur in a market with adverse selection.
Discuss and show graphically how an individual mandate or subsidies could help to alleviate or minimize the adverse selection problem.
Adverse Selection and Pricing
Ian McCarthy | Emory University
Motivation
In practice, people know more about their health than insurers. This is a form of asymmetric information.
Here’s a good example, Costs during special enrollment periods.
Motivation
- This creates adverse selection: higher-risk individuals are more likely to buy/keep insurance than lower-risk individuals.
- Consequences: risk pool becomes sicker on average → higher costs and potential market instability.
- Intuition: enrollment decisions reflect private expectations about future costs (e.g., sign-ups during special enrollment periods often follow new health needs).
Today’s Roadmap
- Adverse Selection
- Partial vs Full Unraveling
- Adverse Selection in Practice
Adverse Selection
Description of graph
- Demand (willingness to pay) for health insurance (downward sloping)
- Average cost (AC): average healthcare costs incurred by all enrollees
- Marginal cost (MC): additional healthcare costs incurred by one more enrollee
- Downward sloping because healthier individuals (lower cost) are willing to pay less for health insurance
Description of graph
- \(D>MC\) because willingness to pay is expected costs plus risk premium
- As price falls, additional—typically healthier—individuals enroll (move downward along demand).
- AC declines as healthier entrants join.
- MC tracks the cost of the next (healthiest) entrant and lies below AC.
Competitive Equilibrium with Community Rating
- With sufficient competition and a single premium for all (community rating), equilibrium occurs where Demand = AC.
- At this point the premium exactly covers expected costs → zero-profit condition.
- Use this stylized benchmark to isolate the role of adverse selection (abstracting from imperfect competition, risk adjustment, etc.).
Types of Equilibria
- Full Insurance
- Under-insurance (Partial Unraveling)
- Full Unraveling
1. Full insurance
2. Under-insurance (partial unraveling)
3. Full unraveling
Understanding Unraveling
For any amount of unraveling, we need at least two features in the market:
- Individuals select plans based on health needs (which is private information)
- Common price to all enrollees of a given plan (community rating)
Understanding Unraveling
Think in periods: if initially \(AC > p\), insurers incur losses and raise \(p\).
- Higher \(p\) moves the market up the demand curve; healthier enrollees drop coverage.
- The pool becomes sicker → AC rises, prompting further premium increases.
- Process converges to a smaller, high-cost pool (partial unraveling) or collapses altogether (full unraveling).
Numerical Example
Assume the insurer’s cost function is \(C=100q - 2q^{2}\), where \(q\) denotes the number of people enrolled in the plan. Further assume that demand is given by \(D=140-4q\). Assuming the insurer enters the market with \(p_{1}=40\),
- What is the next year’s price (if profits are $0 based on period 1)?
- What is the equilibrium price?
Answer
- To solve this, we need to first calculate the marginal cost curve, \(mc=100-4q\), and the average cost curve, \(ac=100-2q\).
- At a price of \(p=40\), we know that quantity demanded will be \(q=25\). At that point, the average cost is then $50
- Since \(AC>p\), the firm is losing money.
- If they set prices to break-even, then next period’s price would be set to their observed AC, \(p_{2}=\) $50.
- We can find the equilibrium price as the point where the AC and D curves intersect, which occurs at \(q\) of 20 and price of $60.
In-class Problem: Adverse selection
Assume that the insurer’s cost function is given by \(C=100q - 2q^{2}\), where \(q\) denotes the number of people enrolled in the plan. Further assume that the inverse demand function takes the form, \(D=110 - 3q\), and that there are 20 individuals total in this market.
- If the insurer enters the market at a price of $65, what is the insurer’s profit (or loss)?
- What price does the insurer set next year if they set price equal to average cost in the prior year?
- What is the equilibrium price in this market?
- What if there is a $10 penalty imposed for those that do not purchase health insurance?
Adverse Selection in Practice
- How does adverse selection in real-life environments?
- How might we help curb its effects?
Death spiral!
Death spiral!
So, are the exchanges in a “death spiral”?
Standard & Poor’s writes: “The ACA individual market is not in a ‘death spiral.’ However, every time something new (and potentially disruptive) is thrown into the works, it impedes the individual market’s path to stability.”
Some potential policy solutions
- Subsidize consumers
- Subsidize insurers
- Mandate purchases
Can you examine each of these policies graphically? How do they differ from the patient’s or government’s point of view?
Other related issues
Effects from other insurance markets
Based on our discussion of adverse selection and health insurance markets, what would you expect to happen if we increased the Medicare age from 65 to 70 years old?
Advantageous selection
What if individuals who are high risk are also less risk-averse? In this case, individuals who are willing to pay the most for health insurance (the most risk averse) are actually less risky and therefore the cheapest to insure. Very different policy implications (e.g., individual mandate is bad in this case).