Setting prices in the chaos of the market

To get from here to there, we need to understand where we are. And where we are is an economy of markets and prices.

Previously, we defined a simple monetary economy, where private economic units specialise in the production of a particular commodity, and pay for the inputs they need with money. We saw that, with a set of (arbitrarily selected) prices and activity levels, the economy crashed: the workers ran out of money. So the economy was unbalanced and uncoordinated.

But market economies are coordinated. And we should be far more surprised by this fact than the recurring examples of breakdown and crisis. Market economies regularly coordinate millions of independent production activities on a massive scale. The coordination is neither perfect nor equitable but nonetheless effective.

Radical critics of capitalism are quick to emphasise the disorderly and crisis ridden nature of the system. But capitalism is a complex social system with many contradictory properties. Some of its social practices are stabilising and others destabilising. A scientific approach attempts to understand both kinds of practice, and how they interact. Counterfactually, capitalism — if it were purely an anarchic system of production — would have already abolished itself .

Marx describes the “competition between capitalists”, where they withdraw investment from loss-making ventures and invest in profit-making ventures, as a “movement toward equilibrium” (Capital, Vol 3). And Marx’s famous “law of value” is — despite what you may have heard — a direct descendant of Adam Smith’s earlier, and more famous, coordination theory known as the “invisible hand”.

In this post, we’ll examine the first component of the law of value (or, if you prefer, the invisible hand), which is the price setting behaviour of economic units in competition with each other.

As before, imagine a simple monetary economy, consisting of a corn-producing firm, and iron-producing firm, and — to keep things simple — a single worker.

Figure 1. A simple monetary economy featuring a corn-producer, an iron-producer and 1 worker. Each unit produces with its own technology. The technologies compose to form the technology graph for the economy as a whole.

Note, from Figure 1, that the starting price of corn is $3 (per bushel) whereas the initial price of iron is $2 (per ingot).

At this point we make an important simplification (which we’ll relax later). Assume that each firm represents the aggregate of a collection of firms that compete with each other in a given sector. For example, we suppose that the corn-producing firm, shown in Figure 1, actually represents, say, five different firms that compete for buyers in the market. Similarly, the iron-producing firm in Figure 1 represents the iron-producing sector, which is populated by multiple competing firms. So the price of corn is the “average” price charged by the competing firms, and the stock represents the aggregate stocks of the competing firms etc.

Imagine you control the decisions of one of the corn-producing firms. Assume you wish to operate the firm such that, at the very least, it continues as an ongoing concern. Then ask yourself: How would you set the price of corn?

You could sell corn at a high price in order to maximise the firm’s income. The problem with this strategy is that you operate in a competitive environment. Set your prices too high then your competitors may sell lower and capture market share.

Alternatively, you could sell corn at a low price in order to maximise sales volume. The problem with this strategy is that you need to cover your input costs. If your prices are too low then the firm will go bankrupt and not be able to produce at all.

A more reasonable, and balanced strategy, is to adjust prices up and down according to the level of demand in the market. But how do you know the level of demand for your corn?

You don’t directly, especially since business conditions are continually changing in the chaos of the market. But you can observe the level of your stocks of corn. If your stocks are falling then you are selling more than you produce; conversely, if your stocks are rising then you are producing more than you sell.

Assume, therefore, that firms raise prices when inventories shrink since competing buyers will outbid each other to obtain the scarce product, and firms lower prices when inventories grow since competing firms underbid each other to sell to scarce buyers.

We need to translate this price adjustment strategy into something a bit more precise. Let Δs be the change in the stock of corn (during a short period of time). And let Δp be the change in the price of corn. We want to define Δp (the price adjustment strategy) in terms of Δs (the indicator of market demand relative to our level of production).

Clearly, if our prices are huge, in absolute terms, we should make bigger price adjustments compared to when our prices are tiny. So we want Δp to be proportional to p. We write this as (i) Δp ∝ p.

And, if our stock decreases then we should raise our prices (and vice versa); or, in other words, (ii) Δp ∝ -Δs.

Finally, we should set the price of corn astronomically high if we’re completely running out of stock; that is, (iii) Δp ∝ 1/s. (This implies that, in the hypothetical situation that our stock reaches zero, then the price of corn is infinity — meaning, quite correctly, that no amount of money can buy corn.)

Putting (i), (ii) and (iii) together we get the price adjustment equation:

Δp = -η Δs (p/s)

where η is a constant of proportionality. We should give η a name. Call it the elasticity of price with respect to excess supply (feel free to forget this immediately). Put simply, η controls how quickly we change the price of corn.

The representative iron-producing firm set its prices in the same way. In fact, if our simple monetary economy was composed of n sectors then we’d have n price adjustment equations.

OK. We’ve defined a price adjustment strategy for the firms in our simple monetary economy. Previously, in the numbers in our pockets, the firms had fixed prices. Now let’s see what happens, in each sector, when firms continually adjust their prices.

Figure 2. The change in stock levels: over production of corn, and under production of iron.

As before the economy is unbalanced. Too much corn is being produced, and too little iron. How are prices changing?

Figure 3. The change in price levels: the price of corn is falling, but the price of iron is rising.

As Figure 3 shows, market prices are now adjusting. And we see that the price of corn is falling because the supply is too high relative to the demand in the market (from worker households). And the price of iron is rising because its supply is too low relative to demand (from the corn-producing sector).

What about the money stocks held in each sector of production?

Figure 4. The corn and iron firms are losing money, but the single worker earns more than they spend.

In summary, this economy is completely uncoordinated. In fact, at around t = 200 the corn and iron firms run out of money, and endure periods where they cannot pay for their inputs, and so production is repeatedly interrupted.

There’s a simple moral to this story: price adjustment alone does not solve the coordination problem. The reason is straightforward: coordinating an economy means operating at the right activity levels that meet final demand. But adjusting prices merely changes money flows. So an individual firm that follows a price adjustment strategy might increase their income and market share. But they may do so while the whole economy crashes to the ground. Something more is needed for market-based coordination.

(Note that market prices are adjusting in historical time. This framework is quite unlike the supply and demand curves you find in economic textbooks).

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