Famous hoaxes in economic theory: 1. The market for lemons is inefficient

The celebrated Akerlof paper on the market for lemons – i.e., used cars – analyzes a so-called market inefficiency due to the unobservability of product quality to the buyer. The argument runs as follows: Suppose people know the quality of their car and have the option of continuing to use it rather than sell it. Then the higher the market price, the higher the average quality of the cars sold on the market. Conversely, suppose the welfare of the buyers is increasing in quality and decreasing in price; then they are willing to pay a higher price for cars if the average quality of the cars sold in the market is greater. Thus the demand curve may be increasing in price over some range, and there may be multiple equilibria, or even no equilibrium at all. In particular, we may construct examples where a low-price, low-quality equilibrium is dominated by any other equilibrium with a higher price and a higher quality. For example, assume buyers are willing to purchase any number of cars if they know that their quality on average is greater than their price. The demand curve is such that quality equals price. At a high price, high quality equilibrium, more sellers sell their cars at a higher price. Sellers are strictly better-off than in the low price, low quality equilibrium. Buyers are indifferent, since in both cases they derive a zero surplus from transactions, as price equals quality. Consequently, the higher price equilibrium dominates the low price equilibrium.
Now, what is wrong with this argument?[1] Suppose the economy is in a low price, low quality equilibrium and that there exists a superior equilibrium that it could reach. Suppose people are rational, meaning they know the structure of the economy and in particular the probability distribution of car quality. Then a buyer (or an intermediary) can offer a price slightly lower than the superior equilibrium; almost all the sellers that sell their cars in that equilibrium, including of course those who are currently selling it in the inferior equilibrium, are going to propose their cars to this intermediary. The average quality will be the same as in the good equilibrium, and the buyer will obtain a positive surplus[2]. Clearly, this destroys the initial equilibrium.
The inferior equilibria are based on the assumption that market participants take prices as given and, consequently, the buyers cannot affect the quality of the cars they purchase. It is however not rational for market participants to hold such belief. I know that if I deviate by posting a higher price I will on average get offered higher quality cars. This error comes from a misunderstanding of the real meaning of price taking in Walrasian equilibrium. While this is spelled out mathematically as an assumption in the definition of an equilibrium, in logical terms price taking is not an assumption, it is a result. The actual economic assumption is perfect competition. Perfect competition means that a given firm, if it charges a higher price than the market one, will not sell any good. If it decides to charge a lower price, it will get the whole market. Therefore, if the firm underbids the market price, it is rational for it to pick a price arbitrarily close to it. [To prove this we need to first show that the market price is unique and below the monopoly price, which is true]. Therefore, everything takes place as if market participants took prices as given.
But the conclusion that perfect competition implies price taking no longer holds in markets where the characteristics of the good depend on the price, as is the case with the market for lemons. Instead of a single price, there is an equilibrium price schedule relating prices to the characteristics of the good, and perfect competition means that market participants cannot move this schedule. However they are perfectly free to move along it, which is what one does when offering a price higher than the low equilibrium one in the above example. There are a number of examples where inefficient outcomes do not survive if we view competition that way. Consider for example competition between swimming pools: a cheaper swimming pool will attract more clients and be more congested. Here again, the quality of the good depends on its price. Yet if market participants arbitrage correctly, they will internalize the correct trade-off between price and congestion, and this trade-off will be reflected in an equilibrium price schedule which will allocate people to swimming pools efficiently. The congestion problem is not an externality, as it is internalized by the owners of the pool. The congestion cost of more crowded swimming pools is exactly reflected in their lower price. Indeed nobody ever wrote a paper to show that the market for swimming pools is inefficient. Yet the market for lemons is essentially similar; what drives the action is the relationship between price and product characteristics, not imperfect information, which in this case is just a side show. What imperfect information implies is that the relevant welfare benchmark is a second best constrained optimum where the unobservability of car quality is taken into account.
This fallacy illustrates that mathematical assumptions are different from economic assumptions. There is more economics in a mathematically formulated model than what is just written in the mathematics. It is convenient to define walrasian equilibrium as a system where market participants take prices as given, but some economic reasoning has taken place before one decides to actually make this formal assumption.
One may argue that it is more difficult for the economy to reach the good equilibrium than to attain an efficient Walrasian equilibrium in an economy with observable goods characteristics. This is true. In the latter case, any situation which is not an equilibrium will entail an imbalance between supply and demand. Suppose the price is too high. What do sellers need to know in order to have an incentive to reduce their price? They need to know that they can get an arbitrarily large number of additional customers by charging a price arbitrarily smaller than the market one. That is, they need to know that competition is perfect. Any seller who is rationed and knows that will reduce his price. In the market for lemons case, in order to offer a price different from the “low equilibrium” one, the buyer needs to know the entire distribution of car quality, including those that are not currently for sale. Knowledge of the relationship between price and quality locally around the “low equilibrium” is not enough. If that situation is locally “stable”, meaning that a small increase in price will raise quality by less than the price, no buyer has an incentive to offer a price slightly higher than the equilibrium one. While in a Walrasian economy a disequilibrium with rationing is broken by a slight deviation, here the deviation must be large.
Indeed people need more information to reach the good equilibrium in the market for lemons than in a Walrasian market. But if the economy is stuck at a bad equilibrium because they do not have enough knowledge, we are in a case of cognitive failure, not market failure.[3] Note however that it is probably not difficult for the economy to learn the good equilibrium; all we need is a sufficient inflow of mutants who offer random prices and replicate if their strategies are successful. Clearly a mutant which offers a price in the vicinity of the good equilibrium price will do better than buyers in the bad equilibrium. Thus we can conjecture that the only evolutionary stable outcome is the good equilibrium.

Notes:

[1] What follows is by no means a discovery. The formal treatment of the lemons problem in the textbook by Green, Whinston and Mas-Colell parallels the arguments made here. Yet the view that the market for lemons is inefficient pervades popular wisdom, partly because of the uncritical exposition in many undergraduate textbooks.
[2] In fact the average quality will also be slightly lower, but strictly greater than the price. This requires the good equilibrium to be “stable”, in the sense defined later in the text. It is possible to show that the highest price equilibrium is always stable.
[3] This critique does not apply to all markets with imperfect information. In a Rothschild-Stiglitz insurance market, the incentive compatible contract is subject to some pecuniary externality which may deliver an inefficient separating equilibrium. See Bisin and Gottardi, Journal of Political Economy, 2006.

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