Questions: Insurance Markets with Adverse Selection

Question 1

An insurer offers a single policy priced at the average-risk premium. Low-risk customers find the price too high relative to their true risk and drop coverage. What happens next, and why?

• A. Premiums fall because fewer claims are made with fewer customers in the pool
• B. The remaining pool becomes riskier on average, forcing the insurer to raise premiums, which drives out more low-risk customers — a spiral toward market unraveling
• C. High-risk customers also drop coverage because the premium becomes unaffordable
• D. Nothing changes; the insurer simply services a smaller but proportionally identical pool

Answer: (B)

This is the adverse selection spiral. When low-risk customers exit, the average risk of the remaining pool rises — because only higher-risk individuals stay. The insurer must raise premiums to cover the now-riskier pool. This makes the insurance even less attractive to any remaining low-risk customers, driving more to exit. The process feeds on itself, potentially until only the highest-risk types remain or the market collapses entirely. The key mechanism is that low-risk exits change the composition of the pool, not just the size.

Question 2

Why does offering a high-deductible/low-premium contract alongside a full-coverage/high-premium contract help an insurer separate risk types without observing their private information?

• A. Low-risk customers prefer the high-deductible plan because their low expected losses make out-of-pocket costs cheap relative to the premium savings
• B. High-risk customers are required by regulation to purchase the higher-premium plan
• C. The deductible reduces the insurer's total payout, making the cheap plan inherently profitable regardless of who buys it
• D. Low-risk customers prefer full coverage but are priced out of the comprehensive plan, so they accept the partial-coverage option by default

Answer: (A)

The deductible is a screening device, not primarily a cost-saving tool. Low-risk individuals expect few claims, so the deductible is unlikely to cost them much — they accept it willingly in exchange for a lower premium. High-risk individuals expect many claims, so a high deductible would be very expensive; they prefer to pay the high premium for full coverage. Neither type wants to pretend to be the other type. This self-selection is precisely what the insurer designed for — the contract menu exploits the fact that the cost of the deductible differs across types.

Question 3

In a pooling equilibrium, high-risk individuals are overcharged because they subsidize low-risk customers who pay less than their actuarially fair premium.

• T. True
• F. False

Answer: False

This reverses the direction of cross-subsidization. In a pooling equilibrium, everyone pays the average-risk premium. Low-risk individuals are overcharged relative to their true risk — they subsidize the high-risk individuals, who are undercharged. This is exactly why low-risk types find the pooling contract unattractive and exit, triggering adverse selection. If high-risk types were being overcharged, they would be the ones exiting — not the mechanism we observe.

Question 4

Mandatory insurance requirements (such as requiring all drivers to carry auto insurance) can prevent adverse selection spiral by keeping low-risk individuals in the pool.

• T. True
• F. False

Answer: True

The adverse selection spiral is triggered by low-risk types voluntarily exiting the pool. A mandate removes that exit option — all individuals must remain in the market regardless of whether the premium exceeds their actuarially fair value. With low-risk types forced to stay, the pool composition remains stable and the premium does not spiral upward. This is the economic rationale behind mandatory insurance and community rating: the mandate does the work that the price mechanism fails to do under information asymmetry.

Question 5

Why is a high deductible described as a 'screening device' rather than simply a cost-saving measure for insurers?

Model answer: A deductible is a screening device because its primary function is to make a contract unattractive to high-risk types, inducing self-selection rather than just reducing insurer payouts. High-risk individuals expect many claims, so a high deductible would cost them a lot out-of-pocket — they prefer to pay a higher premium for full coverage. Low-risk individuals expect few claims, so the deductible is rarely triggered; they happily accept the lower premium. The deductible exploits the fact that the cost of bearing risk differs across types, allowing the insurer to separate them without observing private information directly.

The distinction matters because it explains the design logic of insurance contracts. Deductibles, copays, and tiered plans are calibrated to achieve incentive compatibility — making each type prefer their intended contract. If deductibles were purely about reducing payouts, insurers would just raise them universally. Instead, they're set strategically to deter high-risk types from choosing the cheap plan. This is the Rothschild-Stiglitz insight: contract design substitutes for observability of private information.