Supply and demand in historical time

My love of economics as an object of science is tempered only by the iniquities of capitalism and the profound dullness of the majority of academic writing on it.

Perhaps the dullest feature of economic analysis is the ubiquitous supply and demand curve. As soon as one appears prepare for the dynamic splendour of economic life to be nailed onto a static cross.

Joan Robinson distinguished economic analysis in “logical” versus “historical” time. Most economic analysis, as of today, occurs in logical time: the variables of interest are equilibrium values, and the “dynamics” turn out to be a sequence of equilibrium states. Economic theorists, confident in the robustness of market coordination, assume markets instantaneously clear, and happily abstract from the messy process of price formation that occurs in historical time. In consequence, disequilibrium prices are simply absent, and they model a clock without a spring. (I state that all swans are white. Yes, a few are black, but pointing that out proves the point).

Supply and demand curves throw away historical time. So they are not only dull, but misleading, and set students of economic science on the path to thinking purely in terms of equilibrium.

I think it’s worthwhile, then, to look again at the price adjustment process we previously introduced, in order to emphasise its dynamic nature. Currently, the dynamics are simple. But they will eventually become richer and more interesting.

Recall that, in our simple example of a monetary economy, too much corn and too little iron is produced. We can see this by tracking the change in their stock levels over time:

stocks1
Figure 1. Over production of corn. Under production of iron.

The underlying reason for this imbalance is a mismatch between supply and demand. Let’s look more closely at this mismatch.

Figure 2, below, tracks the production levels of corn and iron over time. Production levels are different from activity levels. The activity level defines the quantity of output that an economic unit (say a corn-producing firm) plans to produce per unit clock time. The production level, in contrast, is the actual quantity produced. These can differ for many reasons (e.g., the corn-producing firm cannot acquire sufficient inputs in the market). A production level is a flow of output from a a production process. Here are the output flows from the corn and iron-producing sectors:

production1
Figure 2. The quantity of corn and iron produced over time.

Notice that the production levels start at zero then immediately ramp up as production begins.

Figure 3, below, tracks the consumption levels of corn and iron over time. Note that there may be multiple sources of demand for a given commodity. For example, corn is demanded both by the corn sector (as seed to sow) but also by worker households (as bread to eat). In consequence, the consumption plots include multiple lines that track consumption by the different sectors of production:

consumption1
Figure 3. Consumption of corn over time: (a) by the corn sector (blue line) and by workers (orange line). Consumption of iron over time: (a) by the corn sector (blue line) and the iron sector (orange line).

The total actual demand for each commodity, at any given time, is then the sum of all the individual consumption levels.

In Figure 3 we see that the actual demand for corn is constant at 0.002 + 0.0023 = 0.0043 units, and for iron, 0.0095 + 0.001 = 0.0105 units. But in Figure 2 we see that the actual supply of both corn and iron is a constant 0.01 units of each. Hence there is over supply of corn and under supply of iron, which cause the change in stock levels we saw in Figure 1.

The mismatch between actual supply and demand manifests in increasing or decreasing stocks. The corn and iron-producers then react to these signals and adjust their prices accordingly:

prices1
Figure 4. The price of corn decreases (because it’s over supplied), and the price of iron increases (because it’s under supplied).

The meaning of these market prices is clear: they are indices of abundance and scarcity. The more corn available for sale in the market, the lower its price; the less iron available, the higher its price.

Recall the price adjustment equation we previously introduced:

[1] Δp = -η Δs (p/s)

Δp is the change in price, Δs the change in stock level, p is the current price and s the current stock level (and η controls the speed of adjustment). We can solve this equation to get p as a function of the stock level:

[2] p = k (1 /sη)

Here k is a constant that depends on the initial prices and stock levels at an arbitrary point in the past (e.g. at t = 0).

Equation [1] is a dynamic equation that talks about change over time. Equation [2], in contrast, is a static equation that talks about an invariant relationship between stock levels and prices. To get a better idea of what [2] says let’s plot of it (I’ve arbitrarily set k = 1 and η=2):

ps-plot
Figure 5. A typical relationship between the stock level (x-axis) and the price level (y-axis).

Figure 5 shows that as stocks increase (as we move to the right on the s axis) the price falls. Abundance implies lower prices. On the other hand, if the stocks decrease (as we move to the left on the s axis) then the price increases. Scarcity implies higher prices. In the limit, at zero stocks, the price shoots off to infinity (no stock can be bought at any price).

The market prices induced by price setting strategy [1] are therefore relatively simple functions of the current mismatch between actual supply and demand.

In this example, actual supply and demand is constant over time. So the price trajectories are currently quite simple. However, this example already demonstrates that market prices are not fully determined by the current state of supply and demand (e.g., Figure 2 and 3 show constant supply and demand but Figure 4 shows varying prices). In other words, market prices are historical, not equilibrium, variables.


 

(A surprising number of people, lacking knowledge of the primary sources, believe that the existence of scarcity prices, determined by supply and demand, immediately invalidates the classical labour theory of value. One wonders how such great thinkers, such as Smith, Ricardo and Marx, could have been so stupid.

Of course, they were not so stupid. All these classical thinkers knew that market prices, determined by supply and demand, are a necessary condition of the labour theory of value. I’ll develop this point in a later post).

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