§ 6. The sale at auction. Let us now approach the price problem as it presents itself when groups of traders come together, and where bids are expressed in some common unit of price. "We will consider first the simplest case of price fixing in a group, that of the auction sale. In auctions on the Dutch plan the auctioneer first names a high price and then successively lowers the price until some buyer takes it. Balancing his hopes and fears, some one bids it in, because he fears that when a lower price is named some one else will take it. In auction sales on the English plan the auctioneer asks, "What am I bid?" and after getting "a starter" he stimulates the desire of the bidders by praise of the sale-goods, keeps the crowd good natured and optimistic by artful story telling, arouses the spirit of rivalry in the bidders, and excites their fears by skilful threats of "going, going," until, shrewdly watching their faces, he feels that the limit is reached. Then he lets fall the hammer, "knocking the article off" to the "lucky buyer." The auctioneer in all this is himself under some pressure, and the success of the sale as a whole depends much on his skill. He dare not delay long for a higher bid on any one article, for unless the bidders continue to believe that things can be had at low prices (i.e., at less than new goods will ordinarily bring) the interest flags and the crowd melts away.

§ 7. Bids in relation to valuations. Note how the prices paid are related to the valuations of the bidders. Suppose that an ax is to be sold at auction, and each one of the ten prospective buyers as he comes to the market has his outside valuation, as follows:

B

10

will

bid

at

highest

20.

B

9

"

"

"

"

25.

B

8

"

"

"

"

30.

B

7

"

"

"

"

35.

B

6

"

"

"

"

40.

B

5

"

"

"

"

45.

B

4

"

"

"

"

48.

B

3

"

"

"

"

50.

B

2

"

"

"

"

53.

B

1

"

"

"

"

60.

When B 3 has bid 50 he has reached his limit and only two other bidders remain. B 2 may then hope to be successful at 51, but B 1 "goes one higher" at each bid until the bid of 54, at which point B 2 drops out. The price in an auction sale is the next unit above the next to the highest bidder's maximum valuation.2 "When there are several urgent bidders for a single article, or for a number of articles less numerous than the bidders, the price sometimes goes considerably above what is "normal." For example, if several farmers in the neighborhood have lost or sold horses and a horse is offered at auction just as the spring plowing needs to be done, they may bid so eagerly as to carry the price above that for which an equally good animal could be bought in the next county, or in a near-by city. The buyer can afford to pay as< much more as the cost to himself of a few days' delay and loss of his time when "time is money." If the normal price is 60, the actual price, which is the market price at that time and place, might be 70 or 80.3

2 This may be called the theoretically exact price, under the assumed conditions. Of course inattention, forgetfullness, etc., on the part of the bidders alter the conditions and therefore the price (both theoretical and practical).

§ 8. Effect of multiplicate units of supply. Suppose that instead of one ax, there were ten axes, all of about the same quality. At rural auction sales in America, those present look over the articles before the sale begins, and try to find who has come to buy, what they would like to get, and what they are likely to bid. If every prospective bidder judged the situation with entire accuracy, then when there were nine axes the exact price would be 21, just enough to exclude the lowest bidder; if there were eight axes the price would be 26 (and so on up to 54 if there were but one ax).

What would happen if there were ten axes offered to ten bidders and no one else would be tempted to bid at any price, however low (i.e., complete inelasticity of demand at prices below 20) ? The first thought may be that the price may be twenty. But we are here coming to the margin of satisfaction of desires where values disappear. If the more eager bidders know the situation and refrain from bidding, each buyer might in turn get an ax for one unit, the smallest possible bid. This is the case when things sell for a "song." On Saturday-nights at the produce markets such goods as strawberries, vegetables, and fish will be sold at any price. In fact, it rarely happens that demand is entirely inelastic, for at an abnormally low price each of the more eager bidders may be tempted to get more of the sale-goods than he had expected, and still others who had no thought of buying will do so if only with the purpose of selling later. The man who bought a cheap coffin at an auction because "it would be handy to have in the house" was a bit of an extremist, yet it is proverbial that anything can be sold if the price is low enough.

* Let the buyers be arranged in order of the amount of their maximum valuations, from left to right from the intersection of the coordinates. The dotted horizontal lines represent the successive levels of the bids, rising until the price is fixed at 54, just above the next to the highest bid.

3 This is a case of complementary goods (see above, Chap. 5), the horse being needed to make use of other goods. It also evidently involves time-value, which see later, Part IV.

Auction Sale of One ArticleAuction Sale; Numerous Like Articles

§ 9. Successive price levels through uncertainty. It is evident that a mistake in the judgment of traders must alter the price somewhat with any number of sale-goods. There may be a succession of price levels. When there were ten axes, the first five might sell at close to 40, the next three at close to 30, and the last two at 20; the more eager bidders being uncertain of the number of other bidders and afraid to risk waiting for the lower price. This drop in price is a very