Capital: Fixed or Fair?
In economics, time is divided into two realms: the short term, and the long term. The distinction between the two is that in the long run, everything is variable and subject to change. In the short run, however, some things are fixed and cannot be adjusted. The way that this is often applied in mainstream economics is in examinations of the firm and profit maximization. In the short run, a firm’s capital is fixed, but in the long run, it is variable.
On its surface, this assumption might seem plausible. Much of a firm’s assets, such as their buildings, machinery, equipment, etc. are long-term investments and are not often replaced. Even so, the assumptions we make in our economic models carry great importance. If they are flawed, their output will correspondingly be flawed as well. Thus, no assumption should be left unturned. Are we fair in assumption capital to be fixed? In order to provide an answer, we must first examine the role of capital in production
The production models that underlies many mainstream production functions are simple mathematical formulas like so:
Y = LK
Y = Output
L = Labor
K = Capital
Variations, such as the Cobb-Douglas, are more complex but keep the same idea:
Y = L^aK^(1-a)
Y = Output
L = Labor
K = Capital
a = income share of labor
These models offer relatively simple views of production, where the output is a result of the product of the units of capital and labor employed. However, these offer to us only a mathematized understanding of production. They don’t tell us what production fundamentally is or how it happens. In situations where a mathematical model is appropriate, this doesn’t present any problems. However, for us to fully comprehend the role that capital plays in production, we must dig deeper into the concept itself.
For this more foundational view of production, we turn to Carl Menger and his Principles of Economics, published in 1871. Within it, he forgoes a mathematical model of production in favor of an exposition on how consumers goods are made through the market process:
“For in addition to goods that serve our needs directly (and which will, for the sake of brevity, henceforth will be called “goods of the first order”) we find a large number of other things in our economy that cannot be put in any direct causal connection with the satisfaction of our needs, but which possess goods-character no less certainly than goods of the first order…These considerations prove that the relationship responsible for the goods-character of these things, which we will call goods of the second order, is fundamentally the same as that of goods of first order…At this point, it could be easily shown that even with these goods we have not exhausted the list of things whose goods-character we recognize, and that, to continue our earlier example, the grain mills, wheat, rye, and labor services applied to the production of flour, etc. appear as goods of the third order, while the fields, the instruments and appliances necessary for their cultivation, and the specific labor services of farmers, appear as goods of fourth order. I think, however, that the idea I have bee presenting is already sufficiency clear.” (Principles of Economics, pg. 56–57)
In Menger’s view of production, the goods that we directly consume and enjoy are the goods of the first order. Included here is everything from a sandwich to a car to a television set. These are all goods that we directly use for our own pleasure, making them goods of the first order. All of those goods which produce the goods of the first order are the goods of the second order. The ingredients that were used to make the sandwich, the components assembled into the car, and the parts put into the television are all goods of the second order. Those goods which produced goods of the second order are goods of the third order, so and on and so forth.
It should be noted that there is nothing inherent in the goods themselves that classifies them as belonging to one order or another. Rather, it is the use that individuals attribute to them in within their production plans. This means that the same good can belong to different orders at different times according to how it is utilized. For example, a truck could be used to haul materials used to produce consumers good. This would classify it as a good of the third order. However, one could also drive that same truck around for leisure. It would then be classified as a good of the first order. The truck itself did not undergo any changes, the way in which it was utilized by individuals was shifted.
Menger’s language may seem confusing to those unfamiliar with his view of production. He states that goods of the higher order “appear” as goods of the lower order. This mental picture works for raw materials and unfinished goods, but how is it that fixed capital goods can somehow turn into goods of a lower order? It is because these capital goods are never permanent. They are constantly in the process of depreciating until they become useless for any further production. As a result, over time these goods are turned into the goods they help to produce, even though this is done in a more indirect way than in variable factors. Thus, the higher orders goods are always in the process of being turned into lower order goods. All of production involves this slow morphing of goods down the structure of production until they reach the consumer.
Let us return to our original question: are we safe to assume that capital is fixed in the short run? If we hold a Mengerian view of production, any such assumption is wholly untenable. Capital cannot be fixed in the short run, because nothing is fixed in the short run. All of the inputs that are used in a production process will be transformed into lower-order goods, the only question is the pace at which this happens. For capital goods, it happens much more slowly than for raw materials or other variable inputs. It is true that capital goods will not be consumed quickly, but this does not mean they are fixed. Capital goods depreciate with their use, which means that over time, they will no longer be the same good that they were originally, as the good will be less serviceable than it was before.
Entrepreneurs, if they are to make rational economic decisions with regard to their production, cannot be blind with regards to their capital goods. They must always exercise judgement with respect to the fact that their capital goods will eventually require replacement. If he were actually to behave as if capital actually was fixed, he would undoubtedly use significantly more capital in his production than if his capital goods were not permanent fixtures. If we overlook this fact with the assumption of fixed capital, then we artificially handicap our ability to understand the judgment of the entrepreneur. Businessmen certainly do not behave as if capital is fixed, so why should we?
None of this is to deny the obvious facts that capital goods cannot easily expand or contract. However, it is an unwarranted logical leap to then conclude that capital is fixed in the short-run. Capital goods, just like all aspects of the market, are one piece of an ever-moving and shifting process. At no point are they actually fixed. These goods are more resistant to that force of change than others, but they are affected by it just the same.
In light of Mengerian production theory, how should we alter our assumptions and models of the firm? Do we have to throw out the production function entirely? Not necessarily. The assumption that capital is fixed in the short-run cannot be maintained, but math and modeling isn’t inherently evil in economics. However, we have to keep two considerations at the forefront of our minds. First, our economic models are derivative of economic theory, not vise versa. Secondly, don’t marry our minds to models. Economics is a science of human action, and thus, is not totally congruent with the precision of mathematics. As such, the models we are a tool of economics, but one that is limited. If we are not careful about the assumptions that we make, then we can fool ourselves in manufacturing models out of alignment with reality. Unsound models might not prove all that troublesome in the short term, perhaps, but the long run will always catch up to us.