Why Good Used Cars Never Show Up

See why good used cars never show up on the market.

Only the seller knows the quality. Buyers set their price by the average of whatever shows up. A low average makes good-car owners give up selling. So the average sinks further, and the price spirals down to zero. The same structure wears three faces: hidden quality, adverse selection, and moral hazard. In health insurance, healthy people leave first and premiums climb again. Banks trusting deposit insurance turn reckless after the deal. The average-quality formula is below.

For example, a 🧑 classmate offers a used game console for 50,000 won. Only the seller knows whether it is broken. The nervous buyer offers just 30,000. Owners of working consoles will not sell at that price. Only the broken ones stay on the market.

E[\theta \mid \theta \le p] = \frac{p}{2}

p_{\text{next}} = \frac{k}{2} \cdot p

Part of these learning paths

Intro Track: First Steps in Microeconomics

Examples & Exercises

🚗 Used cars have quality spread evenly from $0$ to $100$ .

Buyers value a car at $1.5$ times its quality ( $k = 1.5$ ).

Since $k > 1$ , every trade should make both sides better off — so why does the market disappear?

k = 1.5

, top quality

100

— the spiral runs to the floor.

Show proof

At price $p$ only cars of quality at most $p$ are offered — better cars are not worth selling that cheaply.
So the average quality offered is just $p/2$ .
At the first price $75$ , the average is $37.5$ .
Buyers pay at most $1.5$ times that average, $56.25$ . Once the price drops to $56.25$ , only quality $56$ and under remains and the average halves again: $42.2$ , $31.6$ , ... each round multiplies by $0.75$ .
The spiral converges to $0$ . The gains from trade that full trading would have created, $(1.5 - 1) \times 50 = 25$ , evaporate entirely — a loss caused by missing information.

Now buyers value a car at $2.5$ times its quality ( $k = 2.5$ ).

Does the market survive? Where exactly is the borderline?

k = 2.5

, top quality

100

— the spiral never starts.

Show proof

The first candidate price is $2.5$ times the average quality $50$ : $125$ . That exceeds the top quality $100$ , so at that price every car comes to market — the average stays $50$ .
Willingness to pay for the average car, $125$ , covers the price. With no reason to bid down, the only-lemons-remain spiral never starts, and the gains from trade of $75$ are fully realized.
The borderline is exactly $k = 2$ . Since the average is always half the price, willingness $k \cdot \frac{p}{2}$ can only keep up with the price $p$ when $k \geq 2$ .

1. Intro to Microeconomics