- Before proceeding to determine just where the price would be fixed, it will simplify matters to eliminate those buyers and sellers who clearly have no chance to participate in the auction - that is, those buyers who cannot possibly have a demand and those sellers with minimum prices above the maximum price of the highest bidder among the buyers. Buyer G, whose maximum price is 11, cannot have a demand, for the lowest minimum price among the sellers is 17. For the same reason, F must withdraw from the auction. Similarly, sellers W and Z must withdraw, for the minimum price of either exceeds the maximum price of any one of the buyers. There remain, then, five buyers and five sellers, who, so far as we have determined up to this point, will assist to fix the market price. We are now ready for the auction to open.

Fig. 5.

Buyer A announces, let us say, that he will pay 30 for one bicycle. Immediately five sellers each offer him a bicycle at that price. Seeing that he may be able to get a better bargain by holding off, A refuses to buy. The sellers then begin to reduce their prices. When they drop to 28 a second buyer (B) comes into the market. We then have five sellers and two buyers. Prices will continue to fall. When they pass below 28, V will drop out, leaving two buyers and four sellers. At 27 a third buyer's desire becomes a demand. Then we have four sellers and three buyers. Clearly, no one of the four sellers would permit the downward movement of the price to stop at this point if it resulted in his making no sale, and that is exactly what would happen. One bicycle would remain unsold. At 26 the same condition remains; so also at 25. When 24 is reached, however, a fourth buyer (D) cries out that he will take a bicycle at that price. Now we are near the market price, which is likely to be found anywhere between 24 and 23, the exact point being determined largely by the ability of either group to bargain successfully. With the market price established between these two limits, 23 and 24, we find that three of the seven buyers do not have a demand for bicycles, and that three of the seven sellers are unwilling to furnish any of the supply at that price. We find also that the market price is that which produces the greatest number of sales.

Fig. 6.

To make the matter clearer let us bring Figs. 4 and 5 together in Fig. 6. Here we see that buyers A, B, C, and possibly D, have a buyers' surplus. A's surplus is represented by the vertical distance from A on the demand curve to the horizontal line marked PP'. Similarly, the surpluses of B, C, and D may be determined. To express the same thing mathematically, we say that the surplus of each buyer is the difference between his maximum price and the market price. Likewise, the surplus of any one of the sellers is the difference between his minimum price and the market price.

In the above assumptions the simplest condition possible has been chosen, though the conclusion reached holds true for the most complex condition in fixing market price. It is conceivable, first of all, that any one of the buyers might have had a desire for more than one bicycle. If, for example, A had been willing not only to pay 30 for one but also to pay 29 for each of two, the market price would have been fixed between 23 and 27 instead of between 23 and 24. Second, the three sellers who found the market price below their minimum prices might, in a moment of panic, have thrown their bicycles on the market at a sacrifice rather than to hold them. In this case the market price would have been fixed still lower. Third, under actual business conditions it is improbable that the bicycles would have been exactly alike. Such complexities, however, merely complicate the fixing of market prices under free competition, and do not, as one might think at first glance, run contrary to the principle we have worked out under simpler conditions.