17. Auctions - Solutions - Chapter 17 NAME Auctions...

Chapter 17
NAME
Auctions
Introduction.
An auction is described by a set of rules. The rules
specify bidding procedures for participants and the way in which the
array of bids made determines who gets the object being sold and how
much each bidder pays. Those who are trying to sell an object by auction
typically do not know the willingness to pay of potential buyers but have
some probabilistic expectations. Sellers are interested in finding rules that
maximize their expected revenue from selling the object.
Social planners are often interested not only in the revenue generated
from an auction method, but also in its efficiency . In the absence of
externalities, an auction for a single object will be efficient only if the
object is sold to the buyer who values it most highly.
17.1 (1) At Toivo’s auction house in Ishpemming, Michigan, a beautiful
stuffed moosehead is being sold by auction. There are 5 bidders in atten-
dance: Aino, Erkki, Hannu, Juha, and Matti. The moosehead is worth
$100 to Aino, $20 to Erkki, and $5 to each of the others. The bidders do
not collude and they don’t know each others’ valuations.
(a) If the auctioneer sells it in an English auction, who would get the
moosehead and approximately how much would the buyer pay?
Aino
would get it for $20.
(b) If the auctioneer sells it in a sealed-bid, second-price auction and if
no bidder knows the others’ values for the moosehead, how much should
Aino bid in order to maximize his expected gain?
$100.
How much
should Erkki bid?
$20.
How much would each of the others bid?
$5.
Who would get the moosehead and how much would he pay?
Aino would get it for $20.
17.2 (2) Charlie Plopp sells used construction equipment in a quiet
Oklahoma town. He has run short of cash and needs to raise money
quickly by selling an old bulldozer. If he doesn’t sell his bulldozer to a
customer today, he will have to sell it to a wholesaler for $1,000.
Two kinds of people are interested in buying bulldozers. These are
professional bulldozer operators and people who use bulldozers only for
recreational purposes on weekends. Charlie knows that a professional
bulldozer operator would be willing to pay $6,000 for his bulldozer but no

216 AUCTIONS (Ch. 17)
more, while a weekend recreational user would be willing to pay $4 , 500
but no more. Charlie puts a sign in his window. “Bulldozer Sale Today.”
Charlie is disappointed to discover that only two potential buyers
have come to his auction. These two buyers evidently don’t know each
other. Charlie believes that the probability that either is a professional
bulldozer operator is independent of the other’s type and he believes that
each of them has a probability of 1/2 of being a professional bulldozer
operator and a probability of 1/2 of being a recreational user.