An addendum to the posts on Walrasian equilibrium

An addendum to the posts on Walrasian equilibrium

After writing the posts on Walrasian equilibrium, I realized I should have written paragraphs connecting my first post on Walrasian equilbrium with the second post on it. While responses to No-trade theorem(s) are definitely all sensible, one response should have been much more common: trade occuring on disequilibrium basis.

That is, ex-ante Pareto optimal situation is already hard to occur, and thus every market movement is essentially moving along disequilibrium. This is not saying that people do not realize the ex-ante Pareto optimal situation is required for some of No-trade theorems — people DO. It is more that we do not realize truly embrace starting from disequilibrium condition and ending with possibly disequilibrium.

Does this mean humans are less than “full rationality”? (For now, forget about what it means to be “fully rational”) This is so, in some way. Even with incomplete ex-ante information, agents can engage in a series of exchange contracts so that they do not suffer from disequilibrium problems.

However, and this will connect to some of the upcoming posts, money and modern price-based markets appeared because there are costs to writing contracts and negotiation processes (and I will discuss while-mentioned-often-forgotten costs too in some of the upcoming posts). Furthermore, we can simply assume market structure as being institutional, and assume that agents are doing the best inside that structure.

Of course, as we have seen, disequilibrium inside general equilibrium is troubling, as this does not give us proper allocation, unless we assume that agents can be satisfied with saving money they could have spent to buy something to improve their utility. And excess supply also means “budget/endowment value re-calculation” problem, as some of the assumed budget are not actually available in disequilibrium (but note below). This thus may require a series of re-calculating general equilibrium for agents.

To fix these problems — though eventually one will see, in the upcoming posts and possibly this post also, that there are other possibly more natural options in addition to these — “debts” and “default” arise out naturally, though debts and default do exist in equilibrium models, so some of what appears is really a generic explanation. And this requires modelling expenditure-planning stage, what agents believe as their expected budget, how agents hedge against different possibilities and so on. In expenditure-planning stage, as agents do not have all budgets available to buy things in markets that will open, they will have to take some debts to optimize decisions. In case “price vector” is wrongly set with some agents left with excess supply, agents come to carry “debt” and may have to repay next period (but usually, debt is not re-paid immediately at one time period anyway).

These processes create what Hayek would have called as disequilibrium business cycle (though I am not supporting Austrian business cycle approach here — more of mentioning Hayek because he was one of the first people that discussed disequilibrium-based business cycle approach), with financial sector and real sectors connected tightly.

As said in the previous post, however, some sectors, and here that would be financial sector, are best to be modeled as non-Walrasian. Or this is what many macro models do these days — financial sector thinking “cleverly,” not just relying on price vector for decisions, but relying on prediction models and different information for their operation. Combined with firms also having some thought on how their price vector must be set, this completes a Walrasian disequilibrium picture.

An alternative approach, and this seems justified if one wishes to keep some parts of disequilibrium, while adhering to equilibrium approach in some ways, is to assume that demand drives the economy. This is most represented, at least in mainstream economics, in New Keynesian economics models, even if practitioners may not actively realize the consequences of this. If, for “effective modeling” purposes, firms can be thought of as listening passively for demands, supplying what is demanded, then one can eliminate “excess supply” from the model entirely. One can notice that in “very traditional” sense, this is disequilibrium — however, we can now make use of equilibrium tools.