Walras’ Law

I now move closer to modeling the interaction of agents, building on the theory of the individual agent set forth in the previous two chapters. I begin with a consideration of Walras' Law. Certainly, one expects to find some version of Walras' Law holding for this economy, and, indeed, some version does hold; however, there are some points of special interest as to just what that version is.

Walras' Law in its usual form states that the total value of all excess demands is zero. Here, the excess demands involved will be those for commodities (including bonds), shares, and money. But it is not so clear precisely how the result will turn out. To begin with, demands in this model are distinguished by the dates at which agents expect to exercise them; they are not static. Will Walras' Law hold as a statement about the demands planned for any future moment or only as a statement about the value of all future plans? In fact, the result applies to either case; this is because agents expect at every instant to exchange commodities or shares for money of equal value.

Second, Walras' Law requires that we value all excess demands. In more primitive models, this is straightforward. Such valuation simply uses the common prices. In the present model, however, individuals can have different prices for the same commodity. Even without the individual price offers considered in the preceding chapter, this is true of the prices which agents expect. Not surprisingly, therefore, Walras' Law requires us to value each agent's excess demands at the prices at which that agent personally expects to (or actually does) act on them.