Apparently a woman from San Diego has decided to auction off her virginity. She has many takers, and the bid has gotten quite high. There are so many interesting questions raised by this that I don't know where to start.
First, why an auction? Why not a list price? One reason that auctions are used is that many markets are thin, rather than thick. That is, there are so few things for sale that there is no established market price. Auctions allow a seller to discover the best price to charge. Except for illegal prostitution markets, there is no established market price of virginity.
Second, is this legal? The auction is being conducted by a brothel near Carson City, Nevada, where prostitution is legal. If someone within the state is the highest bidder, the transaction could be legal. On the other hand, the auction will be handled through the ranch's website (she tried running the auction on eBay, but eBay removed it). This means that someone from out of state could participate, which brings the Interstate Commerce Clause into play. In this situation I would guess the auction would not be legal. The arrangement could be considered criminal.
Third, should it be legal? An economist's default answer to this question is something like "if both sides enter the exchange fully informed and consenting, then both sides must benefit, and the transaction should be allowed to occur". If there were some third party harmed by the transaction (as in the case of, say, me selling you some gasoline, which you use to produce pollution), an economist might want some form of intervention, but there does not seem to be any such party in this case.
Fourth, leaving aside statutory law, would this be an enforceable contract? Suppose that this woman decides not to go through with it. The court could declare the contract "unconscionable", which means that they find it morally unacceptable or unfair, although I would also guess they would require her to return the money. To do otherwise would basically be court-mandated rape. In any case, even in contracts that are valid, courts rarely require specific performance. That is, if I pay you to paint my house, and you get halfway finished but quit, the court will usually require you to pay me some of my money back, rather than forcing you to finish painting my house. There are two reasons for this. First, you and I probably don't want to deal with each other any more after the unpleasantness of a court case. Second, you are likely to do a sloppy job.
The more interesting question is what would happen if the seller and auction winner had sex, and the auction winner then refused to pay (assuming that pay was not demanded up front). If the court declared the contract unconscionable, the auction winner would not have to pay anything (which seems to be rewarding pretty awful behavior), yet if the court declares the contract valid and enforceable, they are in essence sanctioning future prostitution contracts. I have no idea what they would do.
Fifth, Patrick Gray had a brilliant suggestion. Some pro-abstinence group could bid, win, and then simply hold the option unused. That is, they would in essence own the woman's right to have sex. Granted, this might be difficult for a non-profit, given that the bid is now in the millions of dollars, but it's still an interesting situation. Suppose she breaches the contract, losing her virginity. What damages would the court assign? She would probably have to return the money, plus interest. Ideally the court would assign some form of expectation damages, so that the non-profit would be paid an amount that makes them indifferent between performance and breach, but it is probably impossible to determine what that number would be. That is, what is the value to the non-profit of the woman's virginity staying preserved? It is probably higher than the amount they paid (the difference between their willingness-to-pay and what they actually pay being their "consumer surplus").
Sixth, if one group does this, what would be the long-run result? Many women might choose to sell their right to have sex to such groups, establishing a market price--a price which would surely be lower than that paid to this first entrepreneurial woman. Would these organizations be willing to put their money where their mouths are, and pay many women not to have sex (presumably until marriage)? Such a program would probably not work for men, due to the cost of verifying that a man has not had sexual intercourse.
Suppose that organizations offer a standard price for such contracts, say, $20,000. Some women are considered more attractive than others; they may find that there are men who are willing to pay them more than $20,000 for their virginity. Some might sell to such men, while others refuse and stick with the pro-abstinence organizations. Women who cannot sell their contract to men at this price (due, unfortunately, to unattractiveness) would sell their right to organizations. As a result, pro-abstinence organizations might find themselves overwhelmingly holding the contracts of unattractive women, who might be the least likely to lose their virginity in the first place.
On the other hand, this might not be true at all. I seem to recall from reading The Red Queen that people tend to sort themselves by attractiveness, choosing mates of similar levels of attractiveness. So less attractive women might be no less able to find a mate (a less attractive mate, though) than attractive women.