In the world of vintage car collecting, a frequent topic of discussion is whether prices for a particular model or type are rising or falling. Answering this question is made more difficult by the fact that very few transactions are documented. We know that a given car was listed for price X, but we don't know what price it actually sold for, or to whom.
Does economics provide any model by which one can infer anything about actual selling prices for something, based only on data obtained from published asking prices? For example, if we had a data set of ~3000 sales over 20 years, and we knew that asking prices in real dollars were basically flat, would that tell us anything about the selling prices? Would they also be flat? Or maybe instead would they be gradually approaching the asking price? I have no idea.
The question you are asking is about the bid-ask spread. The bid is what a buyer wants to pay for an item. The ask is what the seller wishes to receive. You know the ask, you want to know the bid. The bid would be demand, the ask would be supply (see, Ask an Economist any question and eventually you'll get "Supply & Demand" as an answer). For example, a December gold futures contract today had a spread of about 20 cents per ounce. Apple's stock at the same time had a spread of just 3 cents. Throughout the day you can check back to see how the spread is converging or diverging. In your specific example of vintage cars without an established exchange, I can certainly see cases where there might be a very small supply of a particular car, say, an unrestored 1957 Ferrari Testa Rossa, what should you bid? Selling through an auction house (which is all a stock market really is) that brings buyers and sellers together will reveal the bids converging on the ask as other bidders see they might be outbid before the gavel comes down. In each example (gold, Apple stock and a particularly rare auto), both sides of the market benefit from an auction-type setting where everyone sees bids and asks converging because that is revealing a lot of information. It also helps to see how many buyers and sellers there are (the volume). You would expect the bid and the ask to be pretty close, at least by the end of repeated rounds of bidding if there are a lot of buyers, a lot of sellers or both. What about the case you are describing where there is an ask, but nobody ever sees the bid? In that case you have no way of really knowing the spread. But, you can infer the bid was close to the ask if the car sells quickly or if you think there are a lot of people interested in that type of car. Usually, the bid-ask spread is smaller if there are lots of buyers and sellers and it is larger when there are only a few buyers and a few sellers, what is called a thin market. There are statistical techniques that can be used to help see what factors affect the spread and they could be applied in your case if you could get data on a lot of cars. If you could find similar cars somewhere else where you do know the price, add to your spreadsheet variables like brand, year, mileage, condition and then look for correlations between the actual prices and those variables, you could then make more of an educated guess about how, say, mileage of the vintage car will impact the bid. This is called hedonic modeling. It is used in trying to guess how much you should pay for items in thin markets, say, a house. Like vintage cars, all houses are a little different and while the market for houses is big, the market for any particular house is thin. But, other than supply and demand guesswork coupled with some hedonic modeling, without actually seeing the bid, determining the spread from just the ask is tough--especially for a good that is so connoisseur specific.