Simple model to understand r and g relationship

What I want to do in this video is to create a simple spreadsheet to help us understand why, if R is greater than G, why that might lead to more and more of national income going to the owners of capital as opposed to labor.

So, let's just say R is 3%. We can change that assumption later, so that's the return on capital that we're assuming. We're assuming it's just going to be fixed at that constant rate.

Let's say that economic growth is 2%. So, we're assuming a scenario where R is greater than G. Now, this column—let me write the year: this year, one year, two, and then maybe we go, let's see, maybe we can go up to year—let's go to year 15, just for good measure.

Now, we could think about what our national capital is, or I say total capital, so the capital in our economy. Now, we'd also want to think about the national income. So, you could view this as the output of the economy: national income.

Now we could think about the split of the income between capital and labor, so income to capital and income to labor. Now, let's just think about the percentage of total—so capital as percent of total. So, let's come up with some assumptions right over here.

So, let's say that our aggregate capital, and I'm just going to throw out a random number here, let's say it's 4,000. If talking about millions of dollars, this would be $4 trillion. But I'm being currency agnostic right over here, so let's just say it's 4,000. It could be—if this was in millions, this would be four trillion, but let's just say 4,000 for now.

And let's say our national income is 1,000. We've seen charts already that at least for the US, capital as a percentage of national income has been about 4 or 500%. It's kind of oscillated in that range, so it's been about four or five times national income. So, this is kind of a not unreasonable ratio.

Now, what's the income to the owners of capital? Well, we're saying that the return on capital is 3%, so this is going to be equal to this 3%. I'm going to press F4 to put those dollar signs, and we'll see why that's valuable.

Make sure that we stay referenced to that cell as we drag this down later on. It's going to be that times the amount of capital that we have in the economy, so it's going to be 120. Notice I had the dollar signs on the B1 because I always want to refer to this, but I didn't put the dollar signs on the B5 because as I drag this down, I always want this cell to say—when I drag it down here, I want it to refer to that same 3%.

So, that's why I kind of anchored it there with the dollar signs, but I want it to be times the capital in that row. So, we'll see how that happens in a second. Now, what's the income to labor?

Well, it's going to be what's left over: national income minus the income to capital. And then capital as a percentage of total; the income to capital is a percentage of total income. Well, that's just going to be equal to—I can select income to capital, D5, divided by national income.

And so, it's 12%. We're also going to assume that every year that income to capital all gets reinvested as capital, so it doesn't get consumed in some way. So, the year two, the capital that we start off with is going to be the capital from last year plus the new income to capital. That income to capital is going to get reinvested as capital; that's just going to be my assumption there.

And national income—well, we know it's growth. It's going to be the previous year's national income plus, I guess we could say, times 1 plus this number plus our economic growth.

So, there, and I'll press F4 because I want to stay referencing that. And so, notice we grew by 2%. Now, these two over here—actually, all three of these over here—we can just drag down. Now, hopefully, you see the value of what I did when I put the dollar signs here because, now, when I drag it down, this is still referring to B1 because I have the dollar signs there.

So, it's taking the 3% times B6. So, B6 is this, so it's looking at the right at that B column but in its row. Now, that’s one of the really useful things about spreadsheets.

Actually, this column—let me make this a percentage just so it becomes a little bit cleaner. Okay, there you go, and then we can just keep on going.

So, let's just keep on going down, and what do we get? Actually, let me get rid of some of the decimal places here; it's making a little bit messy. So, let me—so, there you go; that actually makes it a little bit cleaner.

And so, what do we have going on over here? Well, we see that when R is a fixed rate of return on capital that is greater than growth, we see that capital, the income going to capital as a percentage of the total national income is increasing.

Now, this could be used as a proxy for inequality because, as we've said before, capital does tend to be concentrated amongst the upper percentile, desile, quartile—whatever you want to define it. But, once again, this is just a proxy.

The other thing you have to keep in mind is inequality is a natural byproduct of a capitalistic market economy. Even though more and more of the income is going to the owners of capital, the income going to labor is also increasing.

Now, that by itself doesn't necessarily say it's a good thing. For example, if the population were increasing faster than this, then the income to labor divided by the population—which would be kind of the per capita income to labor, or kind of a proxy for how much the individual person working is making—then if that—even if this is going up, with the population growing faster than that, that might not be a good thing.

That’s because that means per capita income might not be where it needs to be. But if we assume the population is stable or it's not growing as fast as this—even though we see inequality, or at least this measure of inequality going up—more and more of the income is going to capital. These people still might be better off in this reality.

But to test the sensitivity of this model that we've created, we can actually try different things. So, if the return on capital is much larger—say it's 5%—we see that the disparity becomes much more significant.

And let's say if it was 10%, now you see a situation that could get not so pleasant because, in this situation—and this is a fairly extreme situation—we have right over here, now all of a sudden the income to labor, and absolute—not even on per capita terms—is actually decreasing.

So, it really does matter a lot where these two numbers are. But, of course, if economic growth was also pretty robust, now all of a sudden—well, this is still decreasing—but if economic growth was 9%, now all of a sudden this could be a pretty good scenario for everyone involved.

You do have, at least, this is kind of a proxy for increased income to capital, which could be a proxy for inequality. But maybe the economy is growing fast enough that everyone is benefiting.

So, I encourage you to either build a model like this—and I'll give you the link to this model as well—and play with these numbers. Just try to get a better understanding of if we assumed R and G were constant and we made some assumptions about starting capital and national income, how that ends up breaking down as we go further and further into the future.