Under this model, if the transaction of quality goods happened anywhere, some buyer reached information symmetry. But among the assumptions in the article is that sellers have no alternate market (they just "leave", whatever that means) and there is no credible way to provide information on the quality of goods. But then how do buyers know to lower their prices with what's left in the market?
There're a lot of unreasonable assumptions and maybe that's why the paper was rejected 3 times. You can also run the thought experiment backwards: lemons should be removed from the market first since, as stated, those are the ones that sell, but then you should be left with a market full of peaches.
I really don't like how the OP phrased this one, because it's about more than knowing the value of your car.
This paper was published in 1970, but it demonstrated how markets can fail, as well as a method of correcting that failure. Imagine the following scenario:
There's a used car market of private sellers that is comprised of a mixture of peaches (good) and lemons (bad). To keep it simple, let's assume we're just talking about one model of car.
Additionally, there's no way to identify which car is a lemon, but it's known that they're worth much less than a peach because of the much higher cost of maintenance.
If you have a market where the above conditions exist (only seller knows if car is lemon/peach, and a mixture of lemons/peaches), you'd potentially end up with a market failure.
This is because sellers of peaches can't get the price they want for their car, whereas sellers of lemons can profit over the expected value of theirs.
The problem with assuming that lemons would be removed from the market is that any buyer of a lemon would want to sell it once they've realized what they purchased, putting it back on the market. This effect compounds to where a greater percentage of cars being sold on the market are lemons, further depressing the price and removing peaches from the market.
Akerlof's solution to fix the market was to introduce warranties. Owners of peaches would be willing to offer warranties, because they trusted the quality of the cars they were selling. Eventually, buyers would see the lack of a warranty as the indication of a car being a lemon, forcing the sellers of lemons to either offer a warranty or lower their asking price below the market price of the vehicle.
His work applied to the function of other markets, like insurance (older people are the costliest for health insurance companies) and employment markets (Certain classes of people have difficulty finding a job despite similar skills), as well as the institutions that have formed (Medicare, professional licensing) to improve the functioning of these markets.
There're a lot of unreasonable assumptions and maybe that's why the paper was rejected 3 times. You can also run the thought experiment backwards: lemons should be removed from the market first since, as stated, those are the ones that sell, but then you should be left with a market full of peaches.