Marx and Capital: The Problem of Depreciation

One of the things that’s been bugging me about the Marxian value transformation into prices is the term of fixed capital that goes into prices.

It’s bugging me because the simplifying assumption is that this constant capital is thought to be used up in the process, and we know how much it was worth going in so that is easy to track.

The problem is that is a gross oversimplification, and I’m not sure if it is straight from Marx or if it is from Hunt’s editing. In accounting terms there is a way to track this sort of thing. If something is not automatically used up as supplies and will last a while, it is literally “capitalized”. This is done because of the matching principal where expenses need to go with income, and anything longer than a year shouldn’t be directly expensed, but the expense of the purchase applied over time. This shows how the machinery wears out. Then you have on your income statement the depreciation which is an expense but not a cash expense.

The complicating factor is that useful lives of capital equipment are based on convention. Your capital item may have an actual longer or shorter life than you plan for when you buy it. In account terms that’s something you can deal with down the road – write off my supercomputer if Moore’s law makes it obsolete or have a loom that is abnormally long-lasting so you’re getting production from it long after it has been fully depreciated. But in pricing terms, you need to know this beforehand, so that all the labor that went into the capital item is used up in your period however it is defined. I’m LTV until I die, but once you put the microscope on some of these things and start looking they are hard to quantify. I know capital is in itself controversial from Cambridge to the other Cambridge, but is there a place in Marx where he deals with such problems?

Value and Price: Quick Though on the Worth of Marx

One of the main difficulties I find with Marx is the determination of value and price and how they are different. In a way, value seems to be a qualitative subjective thing, but the word we use for it is synonymous with price. At least how much worth something has in relation to price.

Is it even possible to talk about value in the abstract without comparing it to something so that it has more or less value? Or even worse do we just put a number on it in terms of willingness to pay and point at the consumer or producer surplus and say that this was the value realized?

And then this is tangential, but one of the things that struck me when I was first reading on Marxian economics was that Marx himself didn’t have all the charts and graphs I was used to M – C – M’ was well and good but I wanted some of Marshall’s scissors on the page. And that kind of lead to the question in a larger sense about why Marx has been marginalized (pun intended). Is it because there aren’t enough charts and graphs? Is it because Economics has evolved as a British and then American science so the German Jew’s work isn’t important especially in light of the 20^th century and the people he inspired. Or is it just that no one really felt comfortable with the answer to the transformation problem?

Malthus: Not Wrong But Early

If you have any familiarity with the name Thomas Robert Malthus it is probably based on the following assumption.

Draw the first quadrant of the cartesian plane.

Draw two functions. The first being f(x)=x and the second being f(x)=x^2.

Now look and there’s a point where x=x^2.

That point is where growth in the linear function is surpassed by growth in the geometric function.  As a purely mathematical proposition, it’s easy to see that they intersect where x=1.

But to complicated the matters, we have those functions actually stand in for something, then the linear is the growth in production and the exponential is growth in population. Then you have at that intersection point the place where human population exceeds the productions of technology and then people will solve. (I’ll leave his policy prescriptions for another day). As a thought experiment it seems to work, but it rests on two big assumptions.

The first is that production is linear. Malthus was writing at the early stages of the industrial revolution, but we are children of Moore’s law. Technology has increased at the exponential rate in our lifetimes. Perhaps he was just on the point of the curve where the exponential function looks linear. Though this is a gross over-simplification. Moore’s law is just speed of computer chips and we have to ask what the output of the technological revolution is that makes our lives better.

The other assumption, of course is that population growth is exponential. In current times especially in developed economies, that seems the opposite of true, as western nations are worrying about how to deal with the aging of populations as the later generation are not having babies at the replacement rate for the population and countries are making policy to induce people to have kids.

So, in a way, it looks like on the back of the envelope that the prime conclusion is exactly backwards. Though the world population is growing, the rate of growth is slowing and we are on target to peak. Now that peak is so high that in Malthus’s day it would seem that his population growth projection is correct, output is such that we haven’t met that point of intersection point at a large scale.

But just because we haven’t met it yet doesn’t mean we won’t. Though Malthus takes his inevitable meeting of that point as a reason to keep down the working class, it can be a valuable metaphor for the inheritors of his economic though. The entire economic problem is often defined in some way speaking of finite resources and infinite wants, and that to me is trill true. Though we might not seem to have gotten close to carrying capacity there have been scares with mass famines thwarted by the green revolution and worries about peak oil averted by greater drilling technology. These points can serve as a reminder of the original Malthusian hypothesis as we deplete resources and create chaos on the planet. In a way when we look at the most famous conclusion of Malthus the most important the way to really judge him was not if he was right or wrong. It is better to ask: “Was Malthus too early?”