For those who really want to understand what all the fuss is about capital & interest, you need to get a cup of coffee, perhaps even a piece of paper and pencil, and spend 20 minutes reading my latest Mises Canada post. You know I don’t often ask these things of you, but this is really tough stuff and it takes a while to free your mind from its shackles.
In this latest post, what I’ve done is tweak my bird economy to show that even if there are physically productive nets which augment output, and even if everybody gets paid his or marginal product, the rate of return on financial capital can still be zero. An excerpt:
Suppose our hypothetical economy only last for 10 periods, and that everybody has perfect foresight of what’s coming. This time, however, the “bird catch” steadily declines each period, in order to perfectly offset the natural “time preference” in people’s subjective preferences. Thus, in equilibrium, a bird in period 1 trades for a bird in period 2, which trades for a bird in period 3, etc. Yes, *other things equal* people would prefer a present bird to a future bird, but other things aren’t equal: There is going to be very little bird consumption occurring in period 10, so a worker even way back in period 1 would be willing to trade away one of his present birds in order to obtain an airtight claim to someone else’s bird to be delivered in period 10.
Now then, the other wrinkle in our hypothetical economy is that a few workers start out in period 1 in possession of nets. A worker with a net can always catch 1 bird per hour more, than a worker who just uses his bare hands. (It’s true that over time it gets more difficult to catch birds per hour of labor, but workers also get more adept at handling the nets. The advantage of having a net in your possession is always 1 extra bird per hour, for periods 1, 2, …, 9, and 10.)
Notice that in this world, capital goods and labor contribute to total output. (When we explained that the real interest rate on birds would be exactly 0% because of the declining bird catch per period, we had already taken into account the fact that workers would be using the nets optimally.) We are assuming standard competitive markets, meaning that each worker earns the marginal product of his labor. The owners of the nets also earn the marginal product of their capital goods: Either they use the nets themselves and reap the extra output, or they rent the net to another person who then hands over the surplus above what that person would have caught with his bare hands. Either way, the earnings of the net owners are 1 bird/hour of usage.
Finally, to keep the math simple, suppose that all the workers just work for 10 hours each period. (If you want, you can suppose that there is only a 10-hour window each period when the birds fly low to the ground. Or, you can assume that the workers’ preferences for leisure just happen to yield the result that everybody always optimally choose to work exactly 10 hours each period, all things considered.) What can we say about the earnings of the capitalists, i.e. the owners of the nets?
Well, it’s clear that the owners of the nets will receive a flow of “real bird income” of 10 birds per period. If they want, the capitalists can thus eat 10 birds per period more than the workers who only have their raw labor power to generate an income. Now in Piketty’s preferred framework where we calculate a distribution of “national income” between “labor and capital” or between “the workers and the capitalists,” clearly we should say that the capitalists are getting some of the output, while the workers are getting the rest. According to Piketty, the share of income going to the capitalists is the real return to capitalr multiplied by the stockpile of capital β. (Remember he uses the formula α = rXβ.) Since the result is positive–we know the owners of the nets are getting birds each period, while the workers aren’t retaining the full catch–it must be the case that the real rate of return on capital is positive.
Oops, except that it isn’t. If we calculate the market price of the nets in each period, we can see that their owners earn a zero return.
It’s easiest to work backwards. At the end of period 10, the market price of the nets will be 0 birds; nobody would trade even a single bird to buy the net from an owner, because the world ends in period 10.
At the end of period 9, people know that a net still has one period left to contribute to physical output. This contribution will be 10 birds (accruing one period in the future). But since (in this contrived example) we’ve adjusted things on purpose to get birds trading at par across time periods, that means a “bird-in-period-9″ has the same market value–trades one-for-one against–claims to a “bird-in-period-10.” Thus, the market price of the net in period 9 is “10 present birds.” In other words, the owner of a net could sell it outright in period 9 to someone who would hand over 10 birds that could be eaten on the spot.
At the end of period 8, similar logic shows that the spot market price of the net must be 20 birds immediately available. At the end of period 7, the market price of the net will be 30 birds, etc. etc., and at the end of period 1 the market price of the net will be 90 birds. Also note that at the beginning of period 1–which is equivalent to the “end of period 0″ before time begins–the net has the full value of 100 birds, which will be its lifetime contribution to physical output.
Now then, suppose the owner of a net asks his accountant to calculate the rate of return on his financial capital from period to period. What will the answer be?
The accountant will say, “At the beginning of period 1, your net had a market value of 100 birds. During that period, you rented it out to earn a gross return of 10 birds. However, even though the net was physically in perfect condition when the worker gave it back to you after his shift, by the end of period 1 the market price of the net had fallen to 90 birds. Thus your total wealth went from 100 birds at the start of the period, to 10+90 = 100 birds at the end of the period. You just treaded water financially speaking; you converted the form of your wealth from being 100% concentrated in a net to being 90% in a net and 10% in a stockpile of birds. But your total wealth–measured in market value–didn’t go up. Your rate of return was zero.”
If you go to the link, you’ll also see I included a quote from Mises on this stuff. I figured if it’s Mises Canada then Bohm-Bawerk shouldn’t be getting all the love.