Asymmetric Information

The market for lemons

Sometimes one side of a trade knows more than the other. Akerlof’s used-car market is the classic case: sellers know each car’s quality; buyers only know the distribution. That asymmetry can make a market unravel.

Set it up. Car quality \(q\) is spread uniformly on \([0, q_{\max}]\). A seller values a car of quality \(q\) at exactly \(q\) (their reservation price). A buyer values the same car at \(\beta\,q\) with \(\beta>1\) — buyers get more out of a car, so trade should happen for every car.

But buyers can’t see \(q\). At a market price \(p\), which cars get offered? Only those a seller is willing to part with — cars with \(q \le p\). So the cars on the market are the worse half at that price, with average quality \[ \bar q = \frac{p}{2}. \] A buyer will pay at most their expected value, \(\beta\,\bar q = \beta p/2\). They’re willing to buy only if that covers the price: \[ \beta\,\frac{p}{2} \;\ge\; p \quad\Longleftrightarrow\quad \beta \ge 2. \] If \(\beta < 2\), buyers won’t pay what sellers of decent cars require, the good cars withdraw, average quality falls further, and the market collapses toward \(p=0\) — even though every trade would have been mutually beneficial. Adverse selection in one inequality.

Try it. Set how much more buyers value quality (β) and a candidate price. The sim shows which cars are offered (quality ≤ price), their average quality, and whether buyers are willing to pay. Below β = 2 the market unravels.

What to notice

  • Because only cars with quality ≤ price are offered, the average quality on the market is always just half the price — raising the price attracts better cars, but buyers still face the worse half of those.
  • Set β ≥ 2 and buyers’ willingness to pay keeps up with the price — the market holds together.
  • Set β < 2 and no positive price works: WTP always falls short, good cars exit, and the market unravels despite every trade being mutually beneficial. That’s adverse selection.