My last post on this topic was a bit technical, so let me break it down a bit. This post will still probably only appeal to actual economists, whether professional or amateur, because these issues get so nuanced. But I will try to keep the discussion in plain English.
The claim I want to establish is that it is bad economics to walk around thinking that “wages are to labor, as interest is to (physical) capital.” Because of certain modeling conventions in mainstream economics, most economists think this statement is true, but they’re wrong.
Before diving in, let me be clear that throughout this post, I’m talking about real wages and the real rate of interest, as defined in terms of consumption goods. So you pick a basket of consumption goods, and then define the real wage rate as how many such baskets a worker can afford to buy, after selling a time-unit (an hour, say) of his labor. The (gross) real interest rate measures how many baskets of consumption goods in one year you can buy by selling one basket of consumption goods today, and the net real interest rate is just the gross rate minus one.
==> First of all, without workers, there can be no wages, period. So that’s a pretty good reason to think they are intimately related concepts. Yet without physical capital goods, you can still have interest. For example, if there’s an island with coconut trees and no production at all (we’re just harvesting nature’s gifts), people can still say, “Hey, I’ll give you 11 of my coconuts next year, if you let me have 10 of your coconuts right now.” If coconuts are the only consumption good, then the real interest rate is 10%, even though there’s no such thing as “the marginal product of capital” in this scenario.
==> Now the defender of the orthodox treatment might say, “OK sure, in a world without capital goods, you’d still have interest. But all we’re saying is, when you do have capital goods–and where there’s a choice between using the capital to produce consumption goods versus more capital goods–then in equilibrium, the physical ability of the capital good to reproduce itself ends up equaling the real rate of interest measured in consumption goods. For example, suppose there’s only one good, sheep, and you can either consume 1 sheep today, or let it reproduce and turn into 2 sheep next year. This clearly pins down the equilibrium real interest rate at 100%, and this is because of the physical facts concerning the production of sheep.”
==> The above retort is correct, as far as it goes, but I think 99% of professional economists would not see how the rabbit got into the hat. It wasn’t a harmless, simplifying assumption to assume that the same good (sheep) served as consumption and capital good; that was a critical move that guaranteed the result.
==> To see why, consider a slightly more general scenario, where I can use 1 machine today to produce 1 unit of food today, or to produce 2 machines in one year. (In other words, it takes the machine 12 months to make a physical copy of itself. Furthermore, the machines are perfectly durable physically; the owner just performs routine maintenance on them to keep them indefinitely usable.) Now most economists would probably think, “Well, in this case the physical facts pin down the equilibrium real interest rate at 100%. The machine today can produce either 1 unit of food today, or two machines next year, which at that time have the option of producing 2 units of food. So it must be that 1 unit of food today trades for 2 units of food next year, for a 100% real rate of interest.”
==> Not so fast. We are leaving out the fact that the machine can be sold for food on the spot market. I didn’t tell you in the above reasoning what the food-price of a machine was in period 1 versus period 2. Suppose in period 1, the machine could have been sold for 100 units of food, but in period 2, each machine fetches only 49.5 units of food. That means the guy in period 1 can use his machine to produce 1 unit of food and then sell it for 100 more units, for a total of 101 units of food. Or, he can use his machine to produce two machines next period, when he can use them to produce 1 unit of food each, and then sell them both for 49.5 each. This gives him a total of 101 units of food in period 2. Thus the equilibrium interest rate must be 0%, because the owner has to be indifferent between producing 101 units of food in period 1 versus 101 units of food in period 2.
==> The above example shows that when there is a distinct capital and consumption good, you can’t derive the equilibrium real interest rate just by thinking about physical production. You also have to worry about the spot market price of the capital good, measured in terms of the consumption good. If it’s the same forever, then this subtlety falls away. This automatically has to happen in a one-good economy, which is why those models are awful ways to think about capital & interest theory. It can happen too in a “steady state” of a model with distinct capital and consumption goods. But notice that it is a lot more restrictive than mere equilibrium; it has to lock in the real prices of all the capital goods, forever.
==> If people still think “meh” about the above, consider this: I can come up with a model involving robots where, in a steady-state equilibrium, it must be the case that the real rate of interest equals the marginal product of labor. But surely we can agree it would be crazy for me to walk around thinking, “Interest has to do with the marginal product of labor.” Well, the exact same reasoning applies to people thinking, “Interest has to do with the marginal product of capital.”