The Market for Lemons

Ernie Kovacs in a comedic used car skit

Akerlof's paper uses the market for used cars as an example of the problem of quality uncertainty. A used car is one in which ownership is transferred from one person to another, after a period of use by its first owner and its inevitable wear and tear. There are good used cars ("peaches") and defective used cars ("lemons"), normally as a consequence of several not-always-traceable variables, such as the owner's driving style, quality and frequency of maintenance, and accident history. Because many important mechanical parts and other elements are hidden from view and not easily accessible for inspection, the buyer of a car does not know beforehand whether it is a peach or a lemon. So the buyer's best guess for a given car is that the car is of average quality; accordingly, the buyer will be willing to pay the price of a car of known average quality. This means that the owner of a carefully maintained, never-abused, good used car will be unable to get a high enough price to make selling that car worthwhile.

Therefore, owners of good cars will not place their cars on the used car market. The withdrawal of good cars reduces the average quality of cars on the market, causing buyers to revise downward their expectations for any given car. This, in turn, motivates the owners of moderately good cars not to sell, and so on. The result is that a market in which there is asymmetric information with respect to quality shows characteristics similar to those described by Gresham's Law: the bad drives out the good. (Although Gresham's principle applies more specifically to exchange rates, modified analogies can be drawn.) [3]

Akerlof considers a situation in which demand D for used cars depends on the cars price p and quality µ = µ(p) and the supply S depends on price alone.[4] Economic equilibrium is given by S(p) = D(p,µ) and there are two groups of traders with utilities given by:

${\displaystyle U_{1}=M+\sum _{i=1}^{n}x_{i}}$

${\displaystyle U_{2}=M+\sum _{i=1}^{n}{\frac {3}{2}}x_{i}}$

where M is the consumption of goods other than automobiles, x the car's quality and n the number of automobiles. Let Y_i, D_i and S_i be income, demand and supply for group i. Assuming that utilities are linear, that the traders are Von Neumann–Morgenstern utility maximizers and that the price of other M goods is unitary, the demand D₁ for cars is Y₁/p if μ/p > 1, otherwise null. The demand D₂ is Y₂/p if 3μ/2 > p, otherwise null. Market demand is given by:

${\displaystyle D(p,\mu )={\begin{cases}\left(Y_{2}+Y_{1}\right)/p&p<\mu ,\\Y_{2}/p&\mu <p<3\mu /2,\\0&p>3\mu /2,\end{cases}}}$

Group 1 has N cars to sell with quality between 0 and 2 and group 2 has no cars to sell, therefore S₁ = pN/2 and S₂ = 0. For a given price p, average quality is p/2, and therefore D = 0. The market for used cars collapses when there is asymmetric information.

The paper by Akerlof describes how the interaction between quality heterogeneity and asymmetric information can lead to the disappearance of a market where guarantees are indefinite. In this model, as quality is indistinguishable beforehand by the buyer (due to the asymmetry of information), incentives exist for the seller to pass off low-quality goods as higher-quality ones. The buyer, however, takes this incentive into consideration, and takes the quality of the goods to be uncertain. Only the average quality of the goods will be considered, which in turn will have the side effect that goods that are above average in terms of quality will be driven out of the market. This mechanism is repeated until a no-trade equilibrium is reached.

As a consequence of the mechanism described in this paper, markets may fail to exist altogether in certain situations involving quality uncertainty. Examples given in Akerlof's paper include the market for used cars, the dearth of formal credit markets in developing countries, and the difficulties that the elderly encounter in buying health insurance. However, not all players in a given market will follow the same rules or have the same aptitude of assessing quality. So there will always be a distinct advantage for some vendors to offer low-quality goods to the less-informed segment of a market that, on the whole, appears to be of reasonable quality and have reasonable guarantees of certainty. This is part of the basis for the idiom buyer beware.

This is likely the basis for the idiom that an informed consumer is a better consumer. An example of this might be the subjective quality of fine food and wine. Individual consumers know best what they prefer to eat, and quality is almost always assessed in fine establishments by smell and taste before they pay. That is, if a customer in a fine establishment orders a lobster and the meat is not fresh, he can send the lobster back to the kitchen and refuse to pay for it. However, a definition of 'highest quality' for food eludes providers. Thus, a large variety of better-quality and higher-priced restaurants are supported.

The article draws some conclusions about the cost of dishonesty in markets in general:

The cost of dishonesty, therefore, lies not only in the amount by which the purchaser is cheated; the cost also must include the loss incurred from driving legitimate business out of existence.

Libertarians, like William L. Anderson, oppose the regulatory approach proposed by the authors of the paper, observing that some used-car markets haven't broken down even without lemon legislation and that the lemon problem creates entrepreneurial opportunities for alternative marketplaces or customers' knowledgeable friends.[9]

It is possible to generalize the reasoning in Akerlof's paper.[10] Suppose that there are two populations of cars: the peaches ${\displaystyle {\mathcal {P}}}$ and the lemons ${\displaystyle {\mathcal {L}}}$, where we assume that the quality ${\displaystyle \mu (\cdot )}$ of peaches is always greater than the quality of lemons:

$${\displaystyle \mu (\rho )>\mu (\ell ),\quad \forall \rho \in {\mathcal {P}},\;\ell \in {\mathcal {L}}}$$

Accordingly, the utility ${\displaystyle U(\cdot )}$ and the price ${\displaystyle p}$ of the peaches will also always be greater than that of the lemons. Let ${\displaystyle \eta }$ be the probability of a buyer encountering a peach in the used car market. Then the expected utility for the buyer ${\displaystyle U_{e}}$ from purchasing a used car is:

$${\displaystyle U_{e}=\eta U\left({\overline {\rho }}\right)+(1-\eta )U\left({\overline {\ell }}\right),\quad U'(\cdot )>0,\;U''(\cdot )<0}$$

where ${\displaystyle {\overline {\rho }}}$ and ${\displaystyle {\overline {\ell }}}$ represent the mean peach and lemon respectively. The expected utility for the buyer will always increase - for a monotonic, positive utility function - as the probability of encountering a peach increases.

$${\displaystyle {\partial U_{e} \over {\partial \eta }}=U\left({\overline {\rho }}\right)-U\left({\overline {\ell }}\right)>0}$$

Furthermore, the equation for a buyer's expected utility implies that the equilibrium price in an informationally symmetric market is:

$${\displaystyle p_{\text{sym}}^{*}=\eta U\left({\overline {\rho }}\right)+(1-\eta )U\left({\overline {\ell }}\right)}$$

However, the used car market is not a symmetric market: the sellers know which cars are peaches and lemons, while the buyers cannot distinguish between the two. Depending on the type of car he owns, the seller has a differing decision rule based on the offer price ${\displaystyle O}$:

$${\displaystyle {\text{Sell}}\implies {\begin{cases}O\geq p_{\rho },\quad &({\text{Peach}})\\O\geq p_{\ell },\quad &({\text{Lemon}})\end{cases}}}$$

with ${\displaystyle p_{\rho }>p_{\ell }}$ by definition. It is also assumed that, for both peaches and lemons, sellers are willing to accept a price lower than the full value of the car:

$${\displaystyle p_{\ell }<U\left({\overline {\ell }}\right)<p_{\rho }<U\left({\overline {\rho }}\right)}$$

However, if ${\displaystyle p_{\text{sym}}^{*}<p_{\rho }}$, then the sellers possessing peaches will not put them on the market and the equilibrium price will drop. This occurs when:

$${\displaystyle \eta <{p_{\rho }-U\left({\overline {\ell }}\right) \over {U\left({\overline {\rho }}\right)-U\left({\overline {\ell }}\right)}}}$$

with the associated asymmetric information price equilibrium:

$${\displaystyle p_{\text{asym}}^{*}=\eta \left[U\left({\overline {\rho }}\right)-U\left({\overline {\ell }}\right)\right]\mathbb {I} (p_{\text{sym}}^{*}\geq p_{\rho })+U\left({\overline {\ell }}\right)}$$

where ${\displaystyle \mathbb {I} (\cdot )}$ is the indicator function. Once lemons saturate the market, the peaches are driven out of the market because their sellers cannot be matched with buyers to meet their selling price in equilibrium. The beauty of this example is that it illustrates how product quality can collapse in a market with asymmetric information.