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Suppose there a three bidders competing in an ascending price auction for a piece of art. Their valuations for the art are $100,$200 and $300, respectively. What is the clearing price of the art. | In an ascending price auction, also known as an English auction, the bidders keep raising their bids until only one bidder remains, and that bidder wins the item at the final bid price. The clearing price is the price at which the winner obtains the item. Given the valuations of the three bidders for the piece of art: - Bidder 1: $100
- Bidder 2: $200
- Bidder 3: $300
In an ascending price auction, the bidders will continue to bid until the price exceeds the valuation of all but one bidder. In this case, the auction will proceed as follows: - The bidding starts at a low price, let's assume $0.
- Bidder 1 will bid up to their valuation of $100.
- Bidder 2 will outbid Bidder 1 by bidding higher than $100, say$101.
- Bidder 3 will then outbid Bidder 2 by bidding higher than $200, say$201.
- At this point, Bidder 1 and Bidder 2 will drop out of the auction since the price has exceeded their valuations.
- Bidder 3, being the last remaining bidder, wins the auction and obtains the piece of art.
The clearing price, which is the final price at which the winner (Bidder 3) obtains the item, is $201. Therefore, the clearing price of the art in this ascending price auction is $201. |

Suppose there a three bidders competing in an ascending price auction for a piece of art. Their valuations for the art are $100,$200 and $300, respectively. What is the clearing price of the art. | Okay, let's think through this step-by-step: -
In an ascending price auction, the price starts low and increases until there is only one bidder left. This last bidder wins the item at the current price. -
The bidder with the lowest valuation will drop out of the auction first. In this case, the bidder with a valuation of $100 will drop out when the price exceeds$100. -
The auction will continue with the remaining two bidders. The bidder with the second lowest valuation will drop out next. In this case, the bidder with a valuation of $200 will drop out when the price exceeds$200. -
The last remaining bidder is the one with the highest valuation, which is $300 in this case. This bidder wins the auction. -
The clearing price (the price at which the auction ends and the item is sold) will be just slightly over the second highest bidder's valuation. This is because the price will have increased just beyond $200 for the bidder with the second highest valuation to drop out.
So, the clearing price will be just slightly over $200. The exact amount depends on the minimum increment of the auction, but it will be less than or equal to$300 (the highest bidder's valuation). |

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- Input ID
- ee93549f-3ff8-4e33-8644-93ae5e93afc4
- Created
- March 6, 2024
- Permission
- Public