"The Market for Lemons: Quality Uncertainty and the Market Mechanism" is a paper by George Akerlof written in 1970 that established the fundamentals of asymmetrical information theory. Akerlof, a professor at the University of California, Berkeley, won the Nobel Prize of Economics in 2001 for his research. It describes adverse selection.

The paper describes the second-hand market for used cars. Some cars are in good working order — these are referred to as cherries, peaches, or jewels. Some have hidden defects — these are called lemons. Yet because buyers don't know which cars are the lemons — under asymmetric information —, in an effect that is known as crowding out, the market price of even the good cars decreases. Thus, sellers of the cherries are less inclined to sell their cars, and even a competitive market will only be filled with bad cars.

The term "lemon," meaning a defective (typically used) car, did not enter the language of economics as a result of this paper. Instead, it came from the famous "Lemon" Volkswagen advertisement of the 1960s.

A simple Exposition of the model

Suppose we can use some number, q to index the quality of used cars, where q is uniformally distributed over the interval [0,1]. The average quality of a used car on the market is therefore 1/2.

There are a large number of buyers looking for cars who are prepared to pay their reservation price of (3/2)q for a car that is of quality q. There are also a large number of sellers who are prepared to sell a car of quality q for the price q. If quality were observable, the price of used cars would therefore be somwhere between q and (3/2)q, and the cars would be sold and everyone would be perfectly happy.

If the quality of cars is not observable by the buyers, then it seems reasonable for them to estimate the quality of a car offered to market using the average quality of the cars. Based on this estimation, the willingness to pay for any given car will therefore be (3/2)q.

Now, assume that the equilibrium price in the market is some price, p, where p>0. At this price, all the owners of cars with quality less than p will want to offer their cars for sale. Since quality is uniformally distributed over the interval from 0 to p, the average quality of the cars offered for sale at p will be p/2.

Fine. We know however that for an expected quality of p/2, buyers will only be willing to pay (3/2)(p/2) = (3/4)p. Therefore we can conclude that no cars will be sold at p. Because p is any arbitary positive price, we have shown that no cars will be sold at any positive price at all. The market for used cars collapses when there is asymmetric information.

Reference

Akerlof, G. (1970). The market for lemons: quality uncertainty and the market mechanism. Quarterly Journal of Economics 84 (3), 488-500.