Simple model to understand r and g relationship

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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%, and 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.

And 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.

So this is year one, year two, and then maybe we can go, let's see, maybe we can go up to year, let's go to year 15 just for good measure.

Now we can think about what our national capital is, or should I say total capital.

So the capital in our economy.

Now we'd also want to think about the national income.

So we could do this as the output of the economy, national income.

And now we can think about the split of the income between capital and labor.

So income to capital, and income to labor.

And now let's just think about 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 4000.

And if we're talking about millions of dollars then this would be 4 trillion dollars.

But I'm being currency agnostic right over here.

So let's just say it's 4000.

If this was in millions it would be 4 trillion.

But let's just say 4000 for now.

And let's say our national income is 1000, and we've seen charts already, at least for the U.S., that national capital as a percentage of national income has been about 400 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.

And 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 to 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.

And notice, I had the dollar signs in the B1, because I always want to refer to this, but I didn't put the dollar signs in the B5, because as I drag this down, I always want this cell, say when I drag it down here, I want it to refer to that same 3%.

That's why I kind of anchored it there with the dollar sign.

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 is 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%.And we're also going to assume that every year that income to capital all gets re-invested 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 capital from last year plus the new income to capital.

That income to capital is going to get re-invested 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 one 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%.

And then these two over here, actually all three of these over here, we can just drag down.

And now hopefully you see the value of what I did when I put the dollar signs here.

Because now when I dragged it down, this is still referring to B1, because it has the dollar signs there.

It's just taking the 3% times B6. So B6 is this.

It's looking at the B column, but in its row now.

And that's one of the really useful things about spreadsheets.

And 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? And actually let me get rid of some of the decimal places here.

It's making it a little bit messy. 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, decile, qauartile, however you want to define it.

But once again, this is just a proxy.

And the other thing you have to keep in mind is inequality is a natural byproduct of a capitalistic market economy.

And even though more and more of the income is going to the owners of capital, the labor, 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 a per capita income to labor or kind of a proxy for how much the individual person working is making, then even if this is going up and the population is growing faster than that, that might not be a good thing.

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 kind of 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 the disparity becomes much, 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, this is a fairly extreme situation we have right over here, now all of a sudden the income to labor, and 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 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 or I'll give you the link to this model as well, and play with these numbers and just try to get a better understanding for 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.

번역 0%

Simple model to understand r and g relationship발음듣기

다른 번역문 등록

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.발음듣기

다른 번역문 등록

So let's just say R is 3%, and we can change that assumption later, so that's the return on capital that we're assuming.발음듣기

다른 번역문 등록

We're assuming it's just going to be fixed at that constant rate.발음듣기

다른 번역문 등록

And let's say that economic growth is 2%.발음듣기

다른 번역문 등록

So we're assuming a scenario where R is greater than G.발음듣기

다른 번역문 등록

Now this column, let me write the year.발음듣기

다른 번역문 등록

So this is year one, year two, and then maybe we can go, let's see, maybe we can go up to year, let's go to year 15 just for good measure.발음듣기

다른 번역문 등록

Now we can think about what our national capital is, or should I say total capital.발음듣기

다른 번역문 등록

So the capital in our economy.발음듣기

다른 번역문 등록

Now we'd also want to think about the national income.발음듣기

다른 번역문 등록

So we could do this as the output of the economy, national income.발음듣기

다른 번역문 등록

And now we can think about the split of the income between capital and labor.발음듣기

다른 번역문 등록

So income to capital, and income to labor.발음듣기

다른 번역문 등록

And now let's just think about percentage of total.발음듣기

다른 번역문 등록

So capital as percent of total.발음듣기

다른 번역문 등록

So let's come up with some assumptions right over here.발음듣기

다른 번역문 등록

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 4000.발음듣기

다른 번역문 등록

And if we're talking about millions of dollars then this would be 4 trillion dollars.발음듣기

다른 번역문 등록

But I'm being currency agnostic right over here.발음듣기

다른 번역문 등록

So let's just say it's 4000.발음듣기

다른 번역문 등록

If this was in millions it would be 4 trillion.발음듣기

다른 번역문 등록

But let's just say 4000 for now.발음듣기

다른 번역문 등록

And let's say our national income is 1000, and we've seen charts already, at least for the U.S., that national capital as a percentage of national income has been about 400 or 500%.발음듣기

다른 번역문 등록

It's kind of oscillated in that range.발음듣기

다른 번역문 등록

So it's been about four or five times national income.발음듣기

다른 번역문 등록

So this is kind of a not unreasonable ratio.발음듣기

다른 번역문 등록

And now what's the income to the owners of capital?발음듣기

다른 번역문 등록

Well, we're saying that the return on capital is 3%.발음듣기

다른 번역문 등록

So this is going to be equal to this 3%.발음듣기

다른 번역문 등록

I'm going to press F4 to put those dollar signs and we'll see why that's valuable to make sure that we stay referenced to that cell as we drag this down later on.발음듣기

다른 번역문 등록

It's going to be that times the amount of capital that we have in the economy.발음듣기

다른 번역문 등록

So it's going to be 120.발음듣기

다른 번역문 등록

And notice, I had the dollar signs in the B1, because I always want to refer to this, but I didn't put the dollar signs in the B5, because as I drag this down, I always want this cell, say when I drag it down here, I want it to refer to that same 3%.발음듣기

다른 번역문 등록

That's why I kind of anchored it there with the dollar sign.발음듣기

다른 번역문 등록

But I want it to be times the capital in that row.발음듣기

다른 번역문 등록

So we'll see how that happens in a second.발음듣기

다른 번역문 등록

Now what's the income to labor?발음듣기

다른 번역문 등록

Well, it's going to be what's left over.발음듣기

다른 번역문 등록

National income minus the income to capital, and then capital is a percentage of total, the income to capital is a percentage of total income.발음듣기

다른 번역문 등록

Well that's just going to be equal to, I can select income to capital, D5, divided by national income.발음듣기

다른 번역문 등록

And so it's 12%.And we're also going to assume that every year that income to capital all gets re-invested as capital.발음듣기

다른 번역문 등록

So it doesn't get consumed in some way.발음듣기

다른 번역문 등록

So the year two, the capital that we start off with, is going to be capital from last year plus the new income to capital.발음듣기

다른 번역문 등록

That income to capital is going to get re-invested as capital.발음듣기

다른 번역문 등록

That's just going to be my assumption there.발음듣기

다른 번역문 등록

And national income, well we know it's growth.발음듣기

다른 번역문 등록

It's going to be the previous year's national income plus I guess we could say times one plus this number, plus our economic growth.발음듣기

다른 번역문 등록

So there, and I'll press F4 because I want to stay referencing that.발음듣기

다른 번역문 등록

And so notice we grew by 2%.발음듣기

다른 번역문 등록

And then these two over here, actually all three of these over here, we can just drag down.발음듣기

다른 번역문 등록

And now hopefully you see the value of what I did when I put the dollar signs here.발음듣기

다른 번역문 등록

Because now when I dragged it down, this is still referring to B1, because it has the dollar signs there.발음듣기

다른 번역문 등록

It's just taking the 3% times B6. So B6 is this.발음듣기

다른 번역문 등록

It's looking at the B column, but in its row now.발음듣기

다른 번역문 등록

And that's one of the really useful things about spreadsheets.발음듣기

다른 번역문 등록

And actually this column, let me make this a percentage.발음듣기

다른 번역문 등록

Just so it becomes a little bit cleaner. Okay, there you go.발음듣기

다른 번역문 등록

And then we can just keep on going.발음듣기

다른 번역문 등록

So let's just keep on going down.발음듣기

다른 번역문 등록

And what do we get? And actually let me get rid of some of the decimal places here.발음듣기

다른 번역문 등록

It's making it a little bit messy. So there you go.발음듣기

다른 번역문 등록

That actually makes it a little bit cleaner.발음듣기

다른 번역문 등록

And so what do we have going on over here?발음듣기

다른 번역문 등록

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.발음듣기

다른 번역문 등록

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, decile, qauartile, however you want to define it.발음듣기

다른 번역문 등록

But once again, this is just a proxy.발음듣기

다른 번역문 등록

And the other thing you have to keep in mind is inequality is a natural byproduct of a capitalistic market economy.발음듣기

다른 번역문 등록

And even though more and more of the income is going to the owners of capital, the labor, the income going to labor is also increasing.발음듣기

다른 번역문 등록

Now that by itself doesn't necessarily say it's a good thing.발음듣기

다른 번역문 등록

For example, if the population were increasing faster than this, then the income to labor divided by the population which would be kind of a per capita income to labor or kind of a proxy for how much the individual person working is making, then even if this is going up and the population is growing faster than that, that might not be a good thing.발음듣기

다른 번역문 등록

Because that means per capita income might not be where it needs to be.발음듣기

다른 번역문 등록

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.발음듣기

다른 번역문 등록

But to kind of test the sensitivity of this model that we've created, we can actually try different things.발음듣기

다른 번역문 등록

So if the return on capital is much larger, say it's 5%, we see the disparity becomes much, much more significant.발음듣기

다른 번역문 등록

And let's say if it was 10%.발음듣기

다른 번역문 등록

Now you see a situation that could get not so pleasant.발음듣기

다른 번역문 등록

Because in this situation, this is a fairly extreme situation we have right over here, now all of a sudden the income to labor, and not even on per capita terms, is actually decreasing.발음듣기

다른 번역문 등록

So it really does matter a lot where these two numbers are.발음듣기

다른 번역문 등록

But of course if economic growth was also pretty robust, now all of a sudden 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.발음듣기

다른 번역문 등록

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.발음듣기

다른 번역문 등록

So I encourage you to either build a model like this or I'll give you the link to this model as well, and play with these numbers and just try to get a better understanding for 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.발음듣기

다른 번역문 등록

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