Thursday, April 14, 2011

"Equilibrium" in an Economy is Really a Strange Attractor

If we take seriously the idea that an economy is a process, then we cannot take seriously the idea of equilibrium, as equilibrium cannot be reached in a process.

Supply and demand are usually described using supply and demand curves, and the place where they cross over is described as the equilibrium price. As Israel Krizner argues,

“As soon as we draw the cost and revenue curves facing the firm, no matter what their shape, we have created a theoretical case in which all competitive behavior has by definition been ruled out.” (1973, p. 108).

In other words, once everything is known, no discovery can take place. And competition is a discovery process (Hayek). If you can draw the curves, you have made the false assumption that costs and revenues are static. Neither is true. Drawing a supply and demand curve a) suggests you know how each actually curves, meaning b) if either supply or demand changes by a known amount, you will know the exact price to charge and the demand or supply that will result. I suspect that a) is in fact impossible. And if a) is possible, then b) is possible and if b) is possible, then 1) socialism is possible, and 2) entrepreneurship is unnecessary, as there is nothing to discover. In other words, one must assume an equilibrium point that does not and cannot actually exist. More than that, since any creative process has to be in a far-from-equilibrium state to be creative, an equilibrium state implies creativity has ceased. (Please keep in mind that far-from-equilibrium does not mean wild fluctuations, but is merely the discontinuous region between two (momentary) equilibria. Of course, what we are here calling equilibria may not in fact be anything of the kind, as we will soon see.

In any case, here's the best anyone can do for any given firm:

1) look at the costs and revenues over the lifetime of the firm
2) draw upper and lower limits over varying time scales (say, yr 1, yr 2, etc.)
3) conclude that a bunch of stuff happened between the upper and lower limits that drove entrepreneurial discovery

The space between the upper and lower limits, or equilibria, is the far-from-equilibrium state where creativity can occur. If costs and revenues hung out at an equilibrum point for a while, nothing was happening. That's what happens at equilibrium points: nothing. Why? Because you are finished discovering.

Let us apply this to a larger system, like a city. Let us say you have a city where apples are cheaper on one side of the city than the other. Someone discovers this is the case, and finds that transportation costs are such that it makes it worth it to move apples from the cheaper to the more expensive location. Before the entrepreneurial discovery, we had two local equilibria. This creates the condition for a far-from-equilibrium state where one can discover new knowledge. Once the discovery is made, one has a situation of disequilibrium, because the entrepreneur will now work to try to move the city toward apple-price equilibrium. Will he actually achieve it? Probably not, because there may be others who make the same discovery, more apples may be coming into the city, people may want more or fewer apples, etc. Thus, the system always has multiple potential equilibria popping up, keeping the overall system in a far-from-equilibrium state.

Now one can solve the problem by pointing out that the curves can never be drawn accurately, as they can never be discovered. Thus we are talking about a point -- the supply-demand equilibrium point, or the clearing price. If nothing changes in the economy -- if there are no more customers entering, no more producers entering, tastes do not change, etc. -- then in theory this point can be reached. But this requires our theorizing a non-existent economy, one that can never exist. This suggests that even the idea of supply=demand as a point is wrong. So how should we imagine this entity that everyone talks about, but which cannot exist, but which seems to have some value for theorists? Even Kirzner argues that the entrepreneur is trying to move prices toward equilibrium from a state of disequilibrium.

So what is the answer. Let us answer that by first beginning with a given set of inventories. When sales go up, how do the companies producing the good know? Depletion of inventory. So there must be a change in inventory -- at least enough to tell the producers to produce more to restock the inventory. If sales continue to increase, a general trend may be noted, and production adjusted appropriately, but even with a general increase in sales, there will be fluctuations in the rate of change, and that will affect inventory and, thus, production. The companies are trying to discover the right production level and right price throughout this process, and this is changing throughout. What are we in fact seeing here? An equilibrium? Or a constant chasing after a constantly shifting supply-demand point? If we view this in with rough-enough grain, we will see supply=demand; but the finer-grained we view the process, the less aligned supply and demand are. In fact, they have to be if the business is going to adjust production to try to make supply=demand. In reality, what we see is fluctuation around supply-demand point, where inventories are slightly depleted or slightly increased over regular inventory levels relative to the ideal point. That ideal point is rarely if ever reached, and if it is reached, reached but momentarily. From this perspective, the supply-demand point is acting more like an ever-moving strange attractor -- which is what you would expect to find in a far-from-equilibrium self-organizing process. Thus one can look at the relatively inventories of each firm in question as being in a steady-state -- but each firm is ni turn responding to a strange attractor, not an equilibrium point.

Thus, when supply = demand, we do not have an equilibrium; rather, we have a description of a strange attractor, since one is always approaching, but rarely ever (never?) reaching the supply-demand point.

Whether this makes a difference in understanding Kirzner's point, I don't know. I doubt it. However, it does change the way one understands what is going on in an economy. With the concept of equilibrium, you cannot theorize an economy as a process; with the concept of strange attractors, you cannot have anything but a process.
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