EX-1

Market for used cars with three quality types — Good (seller value $1,000, buyer value $1,500), Mediocre (seller value $500, buyer value $750), Bad (seller value $100, buyer value $150). Sellers know quality; buyers see only the distribution. Buyers are risk-neutral; trade at a single market price; a seller sells only if price ≥ her valuation.

Suppose there are 30 cars: 10 Good, 10 Mediocre, 10 Bad. Find the rational expectations equilibrium price. Which types are sold? How many cars are traded?

Same setup as (a), but now the market contains 5 Good, 20 Mediocre, and 5 Bad cars. Find the rational expectations equilibrium price. Which types are sold? How many cars are traded?

Briefly explain the economic intuition behind the difference between the outcomes in parts (a) and (b).

Many risk-averse individuals fall into one of three health states: High (H), Medium (M), or Low (L). The table summarises expected medical costs, reservation price for full coverage, and population share:

The insurance market is competitive; risk-neutral insurers offer only full coverage and have no costs beyond paying medical expenses. Each individual's health state is known to both the individual and the insurers.

Risk-based premiums: assume companies can set premiums based on the individual's health state. What is the price each individual pays for full coverage in competitive equilibrium?

Uniform premium (no risk-based pricing): now assume insurers cannot observe each individual's health state and must charge a single uniform price.

• What will the uniform price be in competitive equilibrium?
• Will all individuals purchase insurance at this price? If not, which groups buy and which do not?
• Explain the effect of adverse selection on the quantity of insurance sold and the equilibrium price.

Government subsidy (challenge). Assume the market is in the equilibrium from (b) with the larger number of insured individuals. The government considers a subsidy to increase coverage and can, if it wants, target the subsidy to a specific health state. The goal is to insure the entire population while minimising total subsidy expenditure.

• What is the minimal subsidy that guarantees an equilibrium in which all individuals buy insurance? Which health states should receive it?
• Does providing the subsidy change the welfare (utility) of individuals who do not receive it? Explain.