Financial Mathematics Text

Tuesday, March 26, 2013

Adam Smith on Equilibrium

The neoclassical conception of "equilibrium" is actually somewhat different than Adam Smith's characterization. In spite of that, neoclassical reasoning often (implicitly) assumes that their equilibrium  has the same implications as Adam Smith's. I would like to briefly describe Adam Smith's notion of equilibrium and would suggest that his notion is far more useful than the neoclassical market clearing equilibrium.

In  An Inquiry into the Nature and Cause of the Wealth of Nations (or simply Wealth of Nations),  Smith described two kinds of prices for commodities. This is all laid out in Chapter VII of Book I. Smith described the Natural Price and the Market Price of commodities. I will begin by looking at the latter as it's the closest concept to the current neoclassical understanding of equilibrium.

The Market Price of Commodities

Smith distinguishes what he calls demand and effectual demand. The former is more of a general want or desire for a particular commodity whereas the latter includes the fact that the demander must have sufficient means to realize the commodity desired. Someone may have a desire for the best home theater system available on the market, but may not have an effectual demand for that being either unwilling or unable to pay the going price for it.

Now there are three scenarios Smith lays out. They all begin with the firm (or firms within the industry producing a specific commodity) bringing a quantity of goods and making them available for a specified price. This supply of goods can be broadly thought as inventory.

It first should be noted that this supply is already somewhat different than the neoclassical representation of supply. The neoclassical characterization, found in any economics textbook, represents supply as an upward sloping curve.

Figure 1

With Adam smith's characterization we have, instead, a fixed quantity of goods available (which could be represented as a vertical curve.)

Figure 2

In both figures, I have drawn a downward sloping demand curve. I suspect Adam smith has something like this in mind as I'll show in a moment here. Like the neoclassicals, Adam Smith considers three possible scenarios (recall that we are assuming both the quantity is given and that the price is specified.

Scenario 1: Quantity Supplied > Effectual Demand

If producers set the price too high (above the neoclassical equilibrium), they will be unable to liquidate their supply. As a result, they may have to lower their price to sell their goods.

Scenario 2: Quantity Supplied < Effective Demand

Here the price is set lower than the above "equilibrium" (in the neoclassical sense). In this case, the supply is liquidated and there ends up being a shortage of goods. The only way to remedy this, in the short term, is to raise the price.

Scenario 3: Quanity Supplied = Effective Demand

Here the price is set at the "equilibrium". In this case, the number of goods supplied are all sold at the price which was set. There's no left over goods and there are no other individuals who have an effective demand for the product at the given price.

Now as I've alluded to with my scare quotes, this is not Adam Smith's notion of equilibrium. This is what is often referred to as the market clearing price. This is a very short-term price phenomenon that concerns itself with a given supply (inventory). It doesn't tell us much about the broad considerations of a firm and how it produces and what quantities it produces. So let's get to the second price Adam Smith discusses.

The Natural Price of Commodities

The natural price of commodities is probably the closest the thing in Adam Smith to a stable equilibrium price. I emphasize stable because many economists talk about equilibriums as if they are all stable. Anyone who has studied mathematics knows that some equilibriums are not stable. To quote Smith:
The natural price, therefore, is, as it were, the central price, to which the prices of all commodities are continually gravitating. Different accidents may sometimes keep them suspended a good deal above it, and sometimes force them down even somewhat below it. But whatever may be the obstacles which hinder them from settling in this center of repose and continuance, they are constantly tending towards it.
The idea that the natural price is the price which "all commodities are continually gravitating" indicates that Smith considers this to be a stable equilibrium. So what is this natural price? Let's take a closer look.

First we need Smith's notion of ordinary rate of rent or profit. This he says varies dependent on a number of factors including the society and so on. In modern language, this is known as the cost of capital (COC).

The easiest way to understand this is in terms of interest (although it doesn't have to be restricted to debt financed capital; we can finance capital with equity as well). The idea here is that we employ capital to earn a rate of return (appropriate for the risk being undertaken). This allows us to see what Smith termed as the "natural price".
When the price of any commodity is neither more nor less than what is sufficient to pay the rent of the land, the wages of the labour, and the profits of the stock employed in raising, preparing, and bringing it to market, according to their natural rates, the commodity is then sold for what may be called its natural price.
In modern language, we use the term return on capital (ROC) or return on invested capital (ROIC). For our purposes, we'll define return on capital (or ROC) as:
$$ROC = \frac{P \times Q - E(Q)}{C}$$
where P is the price of the good, Q is the quantity of goods sold, E are the expenses (as a function of quantity) and C is the capital which is invested.

With that we can now define Smith's natural price as the price in which return on capital is equal to cost of capital or $ROC = COC$.

From the firm's perspective, the strategy is to set a price in such a way that the firm can sell an adequate quantity of goods at that price to achieve an adequate return on capital. This means that the firm is in the situation of having to predict effectual demand for their product at the price they set so they bring the correct quantity of goods to market.

Smith then notes of the natural price:
Though the [natural] price, therefore, which leaves him this profit, is not always the lowest at which a dealer may sometimes sell his goods, it is the lowest at which he is likely to sell them for any considerable time; at least where there is perfect liberty, or where he may change his trade as often as he pleases.
It is at this point that Smith goes into market prices. If the firm misjudges the effectual demand, as stated above, then we get either scenarios (1) or (2) as discussed above which result either in an oversupply or a shortage.

When a firm earns a lower than adequate rate of return, eventually the firm may decide to exit that particular market. While they will consider a lower rate of return for a short time, it wouldn't make economic sense to remain in that business.

On the other hand, if a firm earns a higher than adequate rate of return, others will be attracted to the return and will consider investing in that line of business. This can place competitive pressure on prices so as to lower them down enough that the return on capital equals cost of capital.

In markets with "perfect competition", that rate of return will decline over time. However, as I noted in my post on competitive advantages, some firms are able to earn a high rate of return for long periods of time, an indication that the markets in the real world are not "perfectly competitive".

While I'm not necessarily endorsing Smith's view, I do think it's better than the neoclassical obsession with market clearing price. And I believe it's fundamental to the way that many people in business actually think about prices.  For those reasons I think it should be given further consideration.

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