Saturday, 15 November 2008

If GE is the answer, what was the question

That's an interesting question. Or at least one I have been asked - close enough. General equilibrium theory, or for that matter partial equilibrium theory, does seem a bit strange in the sense that it doesn't obviously relate to the the "real world" of markets we see around us. Who has ever seen a market in equilibrium? But this does raise the issue of why then did the model develop the way it did. What was the question that GE was trying to answer.

The thing that the standard GE model tries to model is the price system. As has been pointed out by Demsetz (1982, 1988 and 1995) the fundamental preoccupation of economists, right up until the 1930s and beyond in many cases, was with the price system. The interest in the price system, culminating in the "perfect competition" model, has its intellectual origins in the eighteenth-century debate between free traders and mercantilists. This debate was, at its simplest, about the proper scope of government in an economy, and the model it gave rise to reflects this. The central question of the debate was, Is central planning necessary to avoid the problems of a chaotic economic system? Adam Smith famously answered no.

For Smith, markets are one very prominent mechanism for solving the problems of coordination and motivation that arise with interdependencies of specialisation and the division of labour. Market institutions leave individuals free to pursue self-interested behaviour, but guide their choices by the prices they pay and receive. The 200 hundred years following Smith amounted to a closer examination of the conditions necessary for the price system alone to be able to avoid chaos.

The formal model that arose from this examination is one which abstracts completely from any form of centralised control in the economy. This is an abstraction Smith myself would have argued was going too far. Smith knew of the importance of institutions to the proper functioning of the market economy. But the point of the modelling was to remove those very institutions so that the price system is the only mechanism available to coordinate and control the economy. It is a model delineated by "perfect decentralisation", to use Demsetz's term. Authority, be it in the form of a government or a firm or a household, plays no role in coordinating resources. The only parameters guiding decision making are those given within the model - tastes and technologies - and those determined impersonally on markets -prices. All parameters are outside the control of any of the economic agents and this effectively deprives all forms of authority a role in allocation. This includes, of course, the government, the firm and the household. We are left with a world only controlled by the price system.

The amazing thing is that it can be shown that chaos does not result in such a system. This is what the standard results on the existence, uniqueness and stability of equilibrium in the general equilibrium model tell us. See, for example, Debreu (1959) if you must.
  1. Debreu, Gerard (1959). Theory of Value, New York: Wiley.
  2. Demsetz, Harold (1982). Economic, Legal, and Political Dimensions of Competition, Amsterdam: North-Holland Publishing Company.
  3. Demsetz, Harold (1988). 'The Theory of the Firm Revisited', Journal of Law, Economics, and Organization, 4(1) Spring: 141-61.
  4. Demsetz, Harold (1995). The Economics of the Business Firm: Seven Critical Commentaries, Cambridge: Cambridge University Press.


Gabriel M said...

But G.E. as found in A-D is a model of centralized exchange, i.e. it assumes the existence of an "Auctioneer".

Also, I'm not sure how I am supposed to go about asking the question whether markets I observe are or are not in equilibrium. I might as well assume that they are, since it's a very convenient and productive assumption...

Even when we have agents choose prices, and the motive there must be some sort of market power/positive profits, markets still provide a huge degree of coordination, probably lots more than we could really achieve.

Paul Walker said...

But an auctioneer who mimics the role of prices in the system. He adjusts prices with regard to excess demands. In a sense he is the price mechanism in the model.

Gabriel M said...

Yes, but that's a centralized model, an agent collecting information on excess demands from all market participants... it's not agents "on the ground" quoting prices.

Also, the results on stability and uniqueness are not all that encouraging either.

Paul Walker said...

The auctioneer could be replaced by a central planner but there is no need for him to be a planner. He can just respond to what he is told without actually trying to direct what is happening. As Ross Star put it in his GE book "There it is in modern mathematical form - just what Adam Smith (1776) would have said. The competitive market can work effectively decentralize efficient allocation decisions."

Gabriel M said...

I understand what you mean but I don't buy it. G.E. theorists always say that they formalized what Adam Smith said and Adam Smith/HET scholars always deny it.

If you agree that the auctioneer CENTRALIZES excess demand information, by quoting prices, than that's a centralized process.

Paul Walker said...

Fair point on the Adam Smith bit. This is why I said "This is an abstraction Smith myself would have argued was going too far. Smith knew of the importance of institutions to the proper functioning of the market economy." I would argue that the GE approach to economies isn't the Smith approach. The Austrian School may be closer to Smith than the GE school.

Even if you accept that the auctioneer does centralise, Walras's use of him was with regard to stability not existence. As Arrow and Hahn write

"Walras went further and discussed the stability of equilibrium, essentially for the first time (that is, apart from some brief discussions by Mill in the context of foreign trade) in his famous but rather clumsy theory of tatonnements (literally "gropings" or "tentative proceedings"). Suppose, as Walras did, a set of prices arbitrarily given; then supply may exceed demand on some markets and fall below on others (unless the initial set is in fact the equilibrium set, there must be at least one case of each, by Walras' law). Suppose the markets are considered in some definite order. On the first market, adjust the price so that supply and demand are equal, given all other prices; this will normally require raising the price if demand initially exceeded supply, decreasing it in the opposite case. The change in the first price will change supply and demand on all other markets. Repeat the process with the second and subsequent markets. At the end of one round the last market will be in equilibrium, but none of the others need be because the adjustments on subsequent markets will destroy the equilibrium achieved on anyone. However, Walras argued, the supply and demand functions for any given commodity will be more affected by the changes in its own price than by changes in other prices; hence, after one round the markets should be more nearly in equilibrium than they were to begin with, and with successive rounds the supply and demand on each market will tend to equality."

Walras's approach to existence was to argue that there was an equality between the number of prices to be determined and the number of equations expressing the equality of supply and demand on all markets.

So even in Walras you can argue that an equilibrium exists which decentralises efficient allocation decisions even if stability can't be determined.

Gabriel M said...

I think we've pretty much converged on some sort of common understanding :-)

Also, FYI, Robert has some comments on this post here.

YouNotSneaky! said...

Actually the answer to the question of whether the Auctioneer is a central planner or a decentralized system mimicking what an all wise central planner would do is ... "in between".

She's not quite a decentralized system because she still needs to know the data on excess demand for each good.

She's not quite the central planner because she ONLY needs to know the data on excess demand for each good rather than the actual preferences/endowments of each agent.

So yes, the Auctioneer economizes on the necessary informational input. But no, the Auctioneer is not firms setting prices in response to market conditions "on the ground".

At the end of the day, she's a modeling device. Which both the pro-decentralized markets folks and the pro-central planner folks try to hitch to their wagons.

This, by the way, is pretty close to the argument made by Market Socialists in the Socialist Calculation Debates - if all we need is knowledge of excess demands then we can set up a centrally planned system that does that and then we can mimic the market and more - which is why until Hayek busted out the 'tacit knowledge' business they were winning that debate.

Michael Greinecker said...

The Arrow-Debreu model doesn't include an mechanism of price making (only their proof does). What they do have is an equilibrium notion. Wether this equilibrium notion can be the outcome of some price adjustment process is a different question.

Such processes exist, even though they are hard to interpret economically. They have to include information on all excess demand function simultaneouslythough, as Saari and Simon have shown.

Ostroy and Makowski have built an GE model in which agens can basically set prices. But perfectcompetition forces them basically to choose the right prices, so they don't get around the problem of information.