Duncan Foley criticizes Walrasian equilibrium theory

Duncan Foley is an astute critic of Walrasian general equilibrium theory in economics. He knows the theory deeply, having made seminal contributions as early as 1970 to its extension to incorporate public goods and to the limits of using Walrasian equilibrium prices, in the presence of transaction costs, to reflect the present value of future commodities. In a recent paper in the Journal of Economic Behavior and Organization (What’s wrong with the fundamental existence and welfare theorems? volume 75, 2010, 115-131), he makes a strong attack on the reverence with which economists hold Walrasian theory.

I agree with Foley’s criticisms but they do not imply that we should abandon Walrasian equilibrium altogether. Let me discuss the criticisms and my reaction.

At the heart of the matter is the assumption that all trades happen at equilibrium prices. For this to happen, we have to imagine that every trader somehow anticipates which equilibrium will occur (it is not too hard to write down a model economy with many Walrasian equilibria) and treats all transactions that are predicated on different prices as tentative.

This is similar to the logic of Nash equilibrium; Foley does not bring in this connection, but I want to do so. Here’s how the story goes for Nash equilibrium. In a normal form game, each player is supposed to guess which of (the, again, potentially many, depending on the game) Nash equilibria will occur and then chooses a strategy that is a best response to the strategies the other players would play at this Nash equilibrium. Relaxing this rather extreme coordination assumption on the beliefs of players about the strategies of the other players is possible; it has been done in developing the theory of rationalizable strategies. The trade-off is that rationalizability has gained a more reasonable assumption on beliefs but has lost predictive acuity; it is easy to find games in which all strategies are rationalizable, so the theory makes no useful prediction.

Foley proposes an equilibrium concept he calls exchange equilibrium. This notion envisions people making mutually advantageous trades at disequilibrium prices; these prices then converge to a small set, in terms of size, but still a continuum set. Which exact equilibrium is reached in this set depends on the time path of transactions. Foley suggests that this is the correct equilibrium notion for a competitive marketplace, but it implies that preferences, endowments, and technology are not, taken together, enough information to pin down the equilibrium. Furthermore, in an exchange equilibrium agents with the same preferences need not be treated equally, unlike the situation in Walrasian equilibrium. Foley shows that, under general assumptions on an exchange economy, the set of exchange equilibria is non-empty and also that it has a stability property. His main conclusion is that Walrasian equilibrium has blinded economists from the aforementioned realization that the triumvirate of “preferences, endowments, technology” is just not enough to pin down an equilibrium. This is worth repeating, as economists, especially theorists, too often take the view that the triumvirate explains well enough what needs explaining in terms of economic exchange.

I suspect that Walrasian equilibrium can still serve as an approximation of the exchange equilibrium set. To the extent it is easier to compute Walrasian equilibria, this is useful. But I find Foley’s critique compelling, and wish that theorists will examine the properties of exchange equilibrium more intensively, extend the concept to production economies, and think about was of incorporating uncertainty without ending up with an equilibrium notion that yields a huge set of predictions or relies hugely on the time path of transactions. My hunch is that the time path of transactions is not powerful enough to completely obliterate the equilibrating tendency in markets; in Foley’s exchange equilibrium it does no such thing, but I can imagine a very weak predictive performance in domains with production and uncertainty. Still, exchange equilibrium is worth taking very seriously, and we should be teaching this paper of Foley’s to our graduate students.

I would love to see Foley move on to the multiplicity of equilibria problem in game theory, but I will not hold my breath for it to happen.