#25 - In one-round sealed-bid auctions, each prospective

[ConfusedStudent]

Hi, can someone help explain why E is the correct answer? I had a really hard time both prephrasing and eliminating answer choices on this question, so a fully explanation would be really nice.

Thank you!

[Adam Tyson]

Thanks for the question, ConfusedStudent, and I hope we can get you to change your username before long!

In this Resolve the Paradox question, the stimulus tells us that setting a reserve is especially important when the item being auctioned is extremely desirable. This should seem odd, because one would think that a lot of people would be bidding, and the reserve is there to protect against a single bidder with a low bid. How do we explain the importance of a reserve price for a very desirable item?

The prephrase here would be something that brings two things together in a way that makes sense - a very desirable item but only one (or very few) bidders. An answer that tells us that very desirable items are not bid on by many people would do the job nicely! That is what is happening in answer E, when it tells us that the prospective buyers believe that the only way to win is to make unreasonably high bids. That suggests that a lot of those would-be buyers won't bother to bid, because the amount they think they have to bid is more than they believe is reasonable. "Oh well, I'll never be able to get that item at a price I would be willing to pay, so I won't even bother bidding." Next thing you know, the only person bidding is the one who made the token offer, far below what the item is worth, and boom, that seller needs the protection of the reserve price.

I hope that made sense, and that you are a little bit less of a ConfusedStudent now!

[anureet]

Why is C not the right answer? It says the reserve price is set high enough to yield profit. This shows why and how the reserve price is set. The price is set high enough so the seller can make profit.

[Adam Tyson]

The problem with that answer, anureet, is that it fails to explain why a reserve price is set for very desirable items. Why would we need to ensure that profit if the item is desirable? Won't the bidding be aggressive enough to ensure that the seller makes money? That's the paradox here - you would think that the reserve would only be needed when you are worried about not getting any reasonable bids, just token bids that are unreasonably low.

So answer C explains what a reserve bid can do - it can guarantee a profit - but tells us nothing about why a reserve would be set in this case, where the need for setting it is unclear.

As an extreme example, if I was selling the Mona Lisa, I would expect the bids to be extremely high, because it is such a rare and special item that art collectors all over the world would be falling all over themselves trying to own it. A reserve price seems a little unnecessary, since one would think that the bids will be high just because of what it is. Answer C doesn't address that oddity.

[Morgan2cats]

Hi Powerscore,

How should I understand the question? I think it's asking for an option which explains why it's a paradox, instead of solves the paradox? Thanks in advance.

[Robert Carroll]

Morgan2cats,

This is definitely a Resolve the Paradox. We're not trying to explain why it's paradoxical. It is characterized as such already. We're trying to explain why that apparently paradoxical thing can still be true. That's what the task always is for a Resolve the Paradox question. Note the question doesn't say to explain why it's a paradox, or to explain why it was characterized as such. It's saying to explain why the generalization holds.

Robert Carroll