Price Setting in Markets

In Chapter 10 we developed an analysis of trade and prices on a bipartite graph consisting of buyers, sellers, and the edges connecting them. Most importantly, we showed that market-clearing prices exist and that trade at these prices results in maximal total valuation among the buyers and sellers, and we found a procedure that allowed us to construct market-clearing prices. This analysis shows in a striking way how prices have the power to direct the allocation of goods in a desirable way. What it doesn't do is provide a clear picture of where prices in real markets tend to come from. That is, who sets the prices in real markets, and why do they choose the particular prices they do?

Auctions, which we discussed in Chapter 9, provide a concrete example of price determination in a controlled setting. In our discussion of auctions, we found that if a seller with a single object runs a second-price sealed-bid auction – or equivalently an ascending-bid auction – then buyers bid their true values for the seller's object. In that discussion, the buyers were choosing prices (via their bids) in a procedure selected by the seller. We could also consider a procurement auction in which the roles of buyers and sellers are reversed, and a single buyer is interested in purchasing an object from one of several sellers. Here, our auction results imply that if the buyer runs a second-price sealed-bid auction (buying from the lowest bidder at the second-lowest price), or equivalently a descending-offer auction, then the sellers will offer to sell at their true costs.