1. _In isolated exchange, where only two traders engage in barter, their estimates give respectively the upper and the lower figures of the ratio at which the trade can take place._ Let us recall the fact that a difference in the _relative_ estimates that men place on goods is the first essential of exchange. Those estimates may be expressed in a ratio; we may say that A will give four apples for one orange, would be glad to give fewer, but will not give more; while B will give one orange for three apples, would be glad to get more apples, but will not take fewer. The outside limits of the ratio at which the exchange must take place will, therefore, be one orange for three or four apples. A, seller of apples, offers 4 (or fewer) apples for 1 orange. B, buyer of apples, demands 3 (or more) apples for 1 orange. There is, in entirely isolated exchange, therefore, a lack of definiteness in the price, much depending on what Adam Smith called the "higgling of the market." In the old-time American horse trade much depended on "bluff"; in such cases it was as important to be able to judge character as to judge horses. A thorough analysis of the trade, however, would probably show that the bargain is concluded at a point which exactly balances the hopes of gain and fears of loss of one of the parties. [Sidenote: Competitive bidding narrows the limits of price] 2. _Where one-sided competition exists, the ratio of the exchange will be somewhere between the estimates of the two buyers most eager for the last portion offered_. By competition is here meant the independent seeking of the same thing at one time by two or more persons. Where there is one market price paid by a number of buyers, it may be that no two of the subjective estimates are alike; the exchange value may differ from all of their estimates, and yet must correspond closely to two. Auction sales well illustrate the principle. If there is one ax to be sold and ten possible buyers for an ax, and there is no combination among them, the bidding will go on until the estimate of the buyer next to the most eager, has been reached. The most eager buyer can then secure the ax by bidding just a little above his next competitor. But if there are ten axes and ten buyers who know that there will be ten axes offered, the more eager buyers will refuse to bid much above the less eager ones. A shrewd auctioneer, therefore, often conceals the fact that there is more than one of an article, and having sold it off, brings out a second or a third one of the same kind, thus keeping the buyers in ignorance of the supply and getting somewhere near the estimate of the most eager buyer in each case. Advertisements of "a limited supply," "the last chance," "positively the last appearance," are meant to stimulate the demand of the patrons, and to lead them to buy at once. In general, therefore, where competition exists on one side, price is fixed with greater definiteness than in isolated exchange.