Question

A reserve price is a minimum price set by the auctioneer. If no bidder is willing to pay the reserve price, the item is unsold at a profit of $0 for the auctioneer. If only one bidder values the item at or above the reserve price, that bidder pays the reserve price. An auctioneer faces two bidders, each with a value of either $126 or $168, with both values equally probable. Without a reserve price, the second highest bid will be the price paid by the winning bidder. The following table lists the four possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder with and without the stated reserve price. Bidder 1 Value ($) | Bidder 2 Value ($) | Probability | Price Without Reserve ($) | Price with $168 Reserve Price $126 | $126 | 0.25 $126 | $168 | 0.25 $168 | $126 | 0.25 $168 | $168 | 0.25 Without a reserve price, the expected price is $ . With a reserve price of $168, the expected price is $ . Thus, the expected price is larger the reserve price.

          A reserve price is a minimum price set by the auctioneer. If no bidder is willing to pay the reserve price, the item is unsold at a profit of $0 for the auctioneer. If only one bidder values the item at or above the reserve price, that bidder pays the reserve price. An auctioneer faces two bidders, each with a value of either $126 or $168, with both values equally probable. Without a reserve price, the second highest bid will be the price paid by the winning bidder.

The following table lists the four possible combinations for bidder values. Each combination is equally likely to occur.

On the following table, indicate the price paid by the winning bidder with and without the stated reserve price.

Bidder 1 Value ($) | Bidder 2 Value ($) | Probability | Price Without Reserve ($) | Price with $168 Reserve Price
$126 | $126 | 0.25
$126 | $168 | 0.25
$168 | $126 | 0.25
$168 | $168 | 0.25

Without a reserve price, the expected price is $ . With a reserve price of $168, the expected price is $ . Thus, the expected price is larger the reserve price.

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A reserve price is a minimum price set by the auctioneer. If no bidder is willing to pay the reserve price, the item is unsold at a profit of 0 for the auctioneer. If only one bidder values the item at or above the reserve price, that bidder pays the reserve price. An auctioneer faces two bidders, each with a value of either126 or 168, with both values equally probable. Without a reserve price, the second highest bid will be the price paid by the winning bidder.

The following table lists the four possible combinations for bidder values. Each combination is equally likely to occur.

On the following table, indicate the price paid by the winning bidder with and without the stated reserve price.

Bidder 1 Value () | Bidder 2 Value () | Probability | Price Without Reserve () | Price with 168 Reserve Price126 | 126 | 0.25126 | 168 | 0.25168 | 126 | 0.25168 | 168 | 0.25

Without a reserve price, the expected price is . With a reserve price of 168, the expected price is . Thus, the expected price is larger the reserve price.

Added by Paula W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Samriddhi Singh

04/24/2022

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- There are four possible combinations of bidder values, each with a probability of 0.25. Show more…

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A reserve price is a minimum price set by the auctioneer. If no bidder is willing to pay the reserve price, the item is unsold at a profit of $0 for the auctioneer. If only one bidder values the item at or above the reserve price, that bidder pays the reserve price. An auctioneer faces two bidders, each with a value of either $126 or $168, with both values equally probable. Without a reserve price, the second highest bid will be the price paid by the winning bidder. The following table lists the four possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder with and without the stated reserve price. Bidder 1 Value ($) Bidder 2 Value ($) Probability Price Without Reserve ($) Price with $168 Reserve Price $126 $126 0.25 $126 $168 0.25 $168 $126 0.25 $168 $168 0.25 Without a reserve price, the expected price is $. With a reserve price of $168, the expected price is $. Thus, the expected price is larger the reserve price.

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Transcript

0:00 Hello everyone.

00:01 So in this question it is given that the table is given, the bidder 1 value, bidder 2 value and the probabilities are given.

00:09 We have to find the price without reserve and price with dollar 168 reserve price.

00:14 Now a reserve price is a minimum price set by the auctioneer.

00:20 If no, okay, from this, from the definition of a reserve price, that is the minimum price set by the auctioneer, we can write the price without reserve as.

00:31 The minimum of those of that of bidder 1 and bidder 2 value because it will be the minimum amount that a bidder can start with so the minimum amount in this is 126 in second is 126 in third is 126 and in 4th is 168 let us come to price with 168 reserve price it is given that if no bidder is willing to pay the reserve price the item is unsold at a profit of dollar zero for the auctioneer so the reserve price given is 168 no bidder is bidding for 168 so this becomes zero next if only one bidder values the item or at or above the reserve price that bidder pays the reserve price right so in second case we see that one bidder two bids for 168 dollar which is our reserve price so this becomes 168.

01:36 Similarly, in third outcome, bidder 1 values the reserve price and bids for 168.

01:44 So price with reserve price becomes 168.

01:48 Next, it is given that an auctionaire faces two bidders, each with the value of either $126 or $168, with both values equally probable.

02:02 Without a reserve price, the second highest bid will be the price paid by the winning bidder.

02:10 Okay, so in fourth one, as both are the valuing it, so the price remains 168...

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