If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Simple model to understand r and g relationship

Use a simple spreadsheet model to understand how a higher return on capital (R) than economic growth (G) might lead to more national income going to capital owners instead of labor. Explore different scenarios and how they affect income distribution and inequality. Created by Sal Khan.

Want to join the conversation?

  • duskpin ultimate style avatar for user tuannb1997
    Is the government capable of controlling the R-and-G relationship so as to set it at a proper level at which both Capital as % of Total Income and Income to Labor tend to rise ?
    (12 votes)
    Default Khan Academy avatar avatar for user
    • male robot hal style avatar for user kokemoor
      The government has some limited controls on R; in the USA, there is a Capital Gains tax. Increasing this tax would decrease R, but may also decrease G. Generally, the primary goal of fiscal/monetary policy is to maximize G, though there are many differing approaches to that end.
      (34 votes)
  • orange juice squid orange style avatar for user thawryluk11
    I understand this spreadsheet is an oversimplification and there are many variables that aren't factored in but I see an inherent problem with this model. Using the same number's as Sal I also made the chart and extended it much further than 15 years. Upon doing so I discovered that, with the r=3% and g=2%, at Year 177 Income to Labour peaks and begins to decline until Year 224 when it reaches 0.
    Am I misunderstanding or is our current economic system inherently flawed?
    (8 votes)
    Default Khan Academy avatar avatar for user
  • mr pants teal style avatar for user Wrath Of Academy
    At it's interesting to see how with a high enough r that the cost of labor goes negative in year 14. So people are paying money in order to work? Clearly this is nonsense, so what assumption or assumptions in the model broke down there? And what does it say about the model in general?
    (5 votes)
    Default Khan Academy avatar avatar for user
  • male robot donald style avatar for user Jeremy s
    how is national income measured?
    (3 votes)
    Default Khan Academy avatar avatar for user
  • piceratops seedling style avatar for user Robert Polster
    Are there models that predict a higher g if the ratio between national capital and national income is lower ? I could imagine that if more money flows through the economy instead of lying around on bank accounts the entire economy should grow faster ? Are there arguments against it ? Are there policies that try to make that happen ?
    (3 votes)
    Default Khan Academy avatar avatar for user
    • ohnoes default style avatar for user Tejas
      There are arguments that claim that, namely Keynesian economics, but there are a few problems with it. First, it doesn't take into account the role of savings in the economy. Contrary to popular thought, when your money gets put in a bank account, it doesn't just sit there. Instead, your money gets loaned out. For every dollar you put in the bank, your bank loans out nine dollars. So, in effect, your money is circulating far faster while sitting in a bank than if you had actually spent it. Secondly, there is no guarantee that faster circulation will lead to growth in the long term. In fact, economic thought suggests that faster circulation in the long term only leads to inflation.

      But, whether it is right or wrong, there are policies that do make that happen. The central bank prints more money, trying to force inflation so that it would disincentivize saving. The government lowers taxes and increases spending in order (forcing it to borrow from the pool of savings) to get people to spend more than they otherwise would. There have been proposals to do more. Piketty himself in this book proposed a wealth tax to do pretty much the same thing as inflation: disincentivize saving.
      (7 votes)
  • leafers seedling style avatar for user David Larisch Frazer
    Is return on capital necessarily positive? Can it be a negative percentage?
    (2 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user Stefan van der Waal
      I don't entirely agree with Tejas here. It is possible the return of capital is negative. Let's say I have an apple tree that's worth $1000 and produces apples worth $150 every year. However, the tree needs to be watered, fertilized and harvested. The costs of water, fertilizer and labor are $200 every year. So every year I lose $50 with this apple tree while it's worth $1000. That's a return on capital of -5%.

      I also googled and found this: http://www.advisorperspectives.com/commentaries/images/Capture_545.JPG
      According to this graph the return on capital in Japan was negative for a short time.

      I have to agree with Tejas on one thing: a negative return on investment for a long time is unlikely, because people will then start to realize it's better to get rid of your assets you're making a loss on so over time only assets you DO get a positive return on will remain.
      (5 votes)
  • primosaur ultimate style avatar for user Nathan Foster
    When you make g greater than r, the capital as % of total decreases. Is there a real-world scenario for this- and if so, what would that be?
    (4 votes)
    Default Khan Academy avatar avatar for user
  • starky tree style avatar for user mk
    Just got to the end of this Macro series, and realized there aren't any practice problems or exercises included to demonstrate the skills that Sal is teaching. Are there any plans to add in practice exercises similar to the math section?
    I think this would be beyond useful, as a lot of the time for this Econ stuff, or most, students cannot make up their own data or graphs to practice questions from.
    (3 votes)
    Default Khan Academy avatar avatar for user
  • piceratops sapling style avatar for user Yolanda Wei
    Should inflation rate be taken into account when we talk about income of labor?
    (2 votes)
    Default Khan Academy avatar avatar for user
  • leaf red style avatar for user Julian Delgadillo Marin
    Why he doesnt just write the formulas of r and g, it would be so much easier to understand, what im missing?
    (2 votes)
    Default Khan Academy avatar avatar for user

Video transcript

- [Instructor] What I wanna do in this video is to create a simple spreadsheet to help us understand why if R 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 and let's say that economic growth is 2%. So we're assuming it's an area where R is greater than G. Now in this column let me write the years. There's Year One, Year Two, and then we would 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 could say Total Capital. So the capital in our economy. Now we'd also want to think about the national income. So we could view this as the output of the economy. National income. And now we could 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 gonna throw out a random number here. Let's say it's 4,000 and if we're talking about millions of dollars, then this would be four trillion dollars, but I'm being currency agnostic right over here. So let's just say it's 4,000. It could be, this could, if it 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 and we've seen charts already that, at least for the U.S., capital, the 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 the return on capital is 3%. So this is going to be equal to this 3%, I'm gonna press F4 to put those dollar signs and we'll see why that's valuable. It'll make sure that we stay referenced to that cell as we drag this down later on. It's going to be that times, 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 on the B1 because I always wanna 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, say that 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 gonna 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, 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 reinvested as capital. So it doesn't get consumed in some way. So, then 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 capital, that income to capital's going to get reinvested as capital is just going to be my assumption there. And national income, well we know its growth. It's going to be the previous year's national income plus, I guess we could say times, times one plus this number, plus our economic growth. So there and I'll press F4 because I keep, I wanna 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 'cause it had the dollar signs there. So it's taking the 3% times B6. So B6 is this. So it's looking at the right, at the B column, but in its row now. That's what's one of the really useful things about spreadsheets and actually this column, let me make this. 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 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, decile, quartile, 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 by-product 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 the per capita income to labor. A kind of a proxy for how much the individual person working is making, then if that, even if this is going up but 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, 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 that the disparity, 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. 'Cause 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 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 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.