A Problem in the Market for Lemons

I’m not convinced the logic actually works

Akerlof’s “Market for Lemons” is an enormously influential paper, highlighting the effects of asymmetric information upon markets. The most famous example in the paper is the titular “market for lemons”. A “lemon” is a low quality car, contrasted with a “plum”. Lemons break down all the time, while plums do not. The sellers of the car know the quality of their cars, while buyers do not. We’re gonna assume that all buyers have the same valuations, and each seller has a private value of 0 (in other words, they have a reserve price of zero). Buyers are willing to pay only the expected value of a car. Knowing this, the owners of “plums” no longer wish to sell at a price below what they know their car could get. The owners of the best cars pull theirs from the market, leaving behind worse cars. Buyers know this, and lower the price that they are willing to pay, inducing more sellers to exit the market. In the limit, no transactions occur, because everyone has left the market, despite everyone preferring a world where transactions occur. This is the death spiral, and in order to avoid it, we have to evolve better institutions. These “institutions” include certifying the car as a certain level of quality, or promising to pay for repairs. 

Yet, there is a serious problem with the logic. If owners of “plums” wish to exit the market, it implies that at some point they will be able to sell the car for the “true value”. But this is precisely what allows people to escape the death spiral. If everyone could reveal their true valuation of the car, then the people with higher values than average reveal, and you have the exact opposite of the death spiral. Thus, there is no reason for people to exit the market at all, unless the way to escape the death spiral already exists.

How can we rescue the model? If we raise the reserve price of sellers, and presume that their reserve price is correlated with the quality of the car, then a death spiral is possible. Let’s say the value of all cars is randomly distributed 0-100, and since people like driving their own car, they have a reserve price three quarters of the car’s value. Buyers are willing to pay 50, leading to a lot of people at the top dropping out to drive their own cars, and then the death spiral comes. So long as people have a reserve price greater than half the true value of the car, and there is no way to show the true value of your car to buyers, then the death spiral will occur. With a reserve price of zero, though, there is no social loss due to incomplete or asymmetric information.

Another way to illustrate this is a different classic example of asymmetric information leading to social loss. Imagine there are two companies, a target and an acquirer. The acquirer knows that they will be able to raise the value of the company by 50%, but does not know the precise value of the company, only that it lies at some random point between 0 and 100. The owners of the target company know its value precisely. Suppose the acquirer offers 50. The expected value of the company, conditional upon the offer being accepted, is 25, so the acquirer will get a company with expected value 37.5. No bid, in fact, is profitable! The problem is that the reserve price is non-zero — were it zero, any finite offer would be rational for the individual to take.

This does not mean that asymmetric information doesn’t lead to social loss. When there is any market power, and sellers are uncertain of buyer valuations, it is optimal to give a take it or leave it offer at the midpoint of each buyer’s distribution of values. (This is just Myerson 1981, by the way). In the prior example, since there’s only one firm, the buyer maximizes profit by giving a take it or leave it offer at 50, accepting that half the time the transaction won’t occur. 

My point is simply that the logic in Akerlof’s market for lemons doesn’t work. Unless sellers have high reserve prices, the market could only break down if the way of fixing the market exists!