Question

All of the drop downs in the table or for options: $0 dollars, $60, $80

The drop-down for the final question is: with or without

Homework (Ch 18) 3. Individual Problems 18-3 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 $60 or $80, with both values equally probable. Without a reserve price, the second highest bid will be the price paid by the winning bidder The following table lists the four possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder with and without the stated reseve price. Bidder 1 Value Bidder 2 Value Price Without Reserve ($) (s) Probability () Price with $80 Reserve Price $60 $60 0.25 $60 $80 0.25 $80 $60 0.25 $80 $80 0.25 Without a reserve price, the expected price is With a reserve price of $80, the expected price is s .Thus, the expected price is larger the reserve price.

Answer 1

Under Price without reserve :- We will take the price of the second highest bidder.

Under Price with reserve :- We take the highest bid provided it is higher than reserve price, otherwise 0.

Using above equation we can complete the table :-

Bidder 1 value	Bidder 2 value	Price without reserve	Price with $80 Reserve
$60	$60	$60	$0
$60	$80	$60	$80
$80	$60	$60	$80
$80	$80	$80	$80

$\small Expected \; Value (EV) = \sum_{i=1}^{n} x_{i}P(x_{i})$

So, Expected Value of Price without Reserve Price is :-

For all cases we can see Probability is 0.25

So, EV = (0.25*60) + (0.25*60) + (0.25*60) + (0.25*80)

= $15 + $15 + $15 + $20

= $65

Expected value of Price with $80 Reserve price :-

Again for all case probability is 0.25

So, EV = (0.25*0) + (0.25*80) + (0.25*80) + (0.25*80)

= $0 + $20 + $20 + $20

= $60

So,

Expected price without Reserve price ($65) > Expected price with $80 reserve price ($60)

So, Expected price is larger without the reserve price.

Hence, the sentence is

Without a reserve price, the expected price is $65 . With a reserve price of $80, the expected price is $60. Thus, the expected price is larger without the reserve price.

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