Market price signals permit dispersed people to synchronize production and consumption activities.*
Broken Symmetry readers know that the aggregate supply and demand curves are cumulative distribution functions that can be derived from the frequency distributions that describe the rhythms of consumption or production for a given good or service. Specifically, the frequency distributions show the patterns of consumption or production for a population of people within a window of time. Within different time windows, the peaks of these frequency distributions may slide left or right, and narrow or fatten. For example, we can observe the supply cycle sliding right to some maximum mean frequency and then sliding left again. As another example, we can observe the demand cycle sliding right to a higher maximum mean frequency when the good consumed is certain kinds of information (such as books or music).
Often, the frequency distributions in supply and demand will take a poissonian shape because the decision by each person within the population to consume or produce will often be uncorrelated with the decisions of other members of the population. Other distribution shapes may arise, especially within smaller populations and shorter time windows.
Both frequency distributions (i.e., both the frequency distribution for supply and the frequency distribution for demand) correspond to a set (or "ensemble") of time-varying functions. These two ensembles of time-varying functions (in supply and demand, respectively) together provide the the information needed to calculate the time-varying function of price. What follows is a plain-English explanation of the dynamics.
Static Theory and the Cobweb Model
To visualize what is happening in time, it helps to start with an easier case, which has already been solved. What I will here call "static theory" obtains at the limit where, for a given population within selected successive time windows, the frequency distributions (and hence supply and demand curves) do not change. More specifically, they vary less from time window to time window than would be required to increase or decrease equilibrium price more than the transactions costs for exchange within that market. In other words, if the supply or demand curves don't shift enough from window to window to increase or decrease equilibrium price more than transactions costs, we're at a "static" limit.
From the cobweb model, we know that when the static limit obtains, price will evolve as a damped, driven oscillation around the equilibrium price. In other words, regardless of where the aggregate quantity of supply or demand begins, the suppliers and producers will eventually (over a succession of time windows) end up exchanging goods at the equilibrium price. This is equivalent to saying that regardless of how many people are producing or consuming within the first time window, price will eventually (after a succession of later time windows) reflect the level corresponding to the point at which the aggregate supply and demand. (Technically, within a price range of that point proportional to the transactions costs.)
The period of time required to reach equilibrium is a function of the frequency of supply, the frequency of demand, and the transactions costs. Higher frequencies and lower transactions costs means faster return to equilibrium.
Non-equilibrium Price as a Phase Synchronization Device
With the static limit picture of a damped, driven oscillation in price in mind, we have our insight into what is causing non-equilibrium dynamics in price. Specifically, it must be a mismatch in phase between supply and demand because, by definition, at the static limit the frequency distributions of supply and demand are not varying in time.
At any given moment, there are some people within the population that have to decide whether to undertake another cycle of supply or demand. To a good approximation, each person within the population decides whether or when to undertake another cycle of supply or demand by asking whether, at the current market price, an additional cycle of supply or demand would be increase wealth. When the current market price is below equilibrium, suppliers will not undertake a new supply cycle. When the current market price is above equilibrium, consumers will not undertake a new consumption cycle.**
In other words, market price is a mechanism for synchronizing the cycles of supply and demand.
At any given moment in time, market price is a combination of the (positive or negative) phase difference (caused by the asynchronicity in supply and demand) plus the equilibrium price.
Beyond Static Theory: Dynamic Market Price
Having seen how market price is a mechanism for synchronizing supply and demand cycles in the static limit, I now ask whether removing the static limiting conditions should have an effect on price.
Not on the synchronization mechanism. Although the "equilibrium" component of price will no longer be fixed in time (because the supply and demand curves may slide left or right or fatten or narrow with time), the phase difference component is calculated the same way by looking at the aggregate lead phase difference between supply and demand cycles.
Conclusions
Price at a moment in time is a function of both the relative aggregate quantity of supply and demand (which are a function of the frequency of supply and demand cycles) and the aggregate difference in phase between supply and demand cycles.
Although the phase of supply and demand cycles may be randomly distributed at an earlier point in time, as time evolves, a population of people will tend to synchronize supply and demand cycles so as to eliminate the phase difference component of price. In the equilibrium limit, this component vanishes as supply and demand become perfectly synchronized.
* In electrical engineering terms, I am toying around with the model of markets as voltage-controlled oscillators, with the voltage being the phase difference signal. VCOs are very useful devices in control theory. When used in conjunction with negative feedback, VCOs can be used to build phase-locked loops.
** Note that the ability to store and use inventory or money
will have important effects on the phase synchronization of the supply
and demand cycles. I'm going to ignore these for now, although I will assert that these effects probably dominated the price dynamics within the subprime mortgage market.
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