The theory of the firm and industry equilibrium

4.1 Competitive equilibrium in an exchange economy

How can we model the outcome of exchange in a market? We could model all the details of the market. In some markets, sellers set prices and buyers find sellers and decide whether to purchase at the posted price. The organization of other markets is closer to that of a double auction: first someone—perhaps a seller—announces a price, then either another seller announces a lower price, or a buyer makes a bid, and the bids and offers continue until a deal is struck.

A model that captures all the details of such markets is complicated. As a first approximation, we use a very simple model. (Recent research, both theoretical and experimental, has investigated more complex models with the aim of trying to understand under what conditions the simple model is a good approximation.)

Model:

• For every price, find the number of buyers whose reservation prices exceed the price (so that they are willing to buy, given the price)
• For every price, find the number of sellers whose costs (“reservation values") are less than the price (so that they are willing to sell).
• Find the price at which the number of buyers willing to buy is equal to the number of sellers willing to sell. This price is a competitive equilibrium price.

One market organization under which the outcome is a competitive equilibrium is the following. A market manager announces a price, and each participant indicates whether she wishes to buy or sell at that price. If demand is not equal to supply, then the manager changes the price. No trades take place until a price is found at which demand is equal to supply. A market manager who acts in this way is called a Walrasian auctioneer.

In most markets there is no person who plays the role of a Walrasian auctioneer. Nevertheless, evidence from experiments and actual markets suggests that the competitive equilibrium is a good predictor of the outcome for a range of types of market organization.

Sometimes it is argued that the competitive model works well only if there is a large number of traders. However, some experiments suggest that even if there are few traders the competitive model may perform well.

Note that if the demand and/or supply functions have vertical or horizontal sections then there may be an interval of equilibrium prices or quantities, rather than a single competitive equilibrium price and quantity.