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# Simple model to understand r and g relationship

## Video transcript

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 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 is year 1 year 2 and then 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 are our national capital is or going to say total capital so the capital in our economy now we'd also want to think about the national income so because view this is 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 going to throw out a random number here let's say it's 4,000 and if we're talking about millions of dollars and this would be 4 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 we're this it was in millions we would this would be 4 trillion but let's just say 4,000 for now and let's say our national income is 1000 and we've seen charts already that at least for the u.s. the capital national capital as a percentage of national income has been about four or five hundred percent it's kind of oscillated in that range so it's been about four or five times national income so these are this 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% 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 x 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 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 say look when I drag it down here I want 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 is a percentage of total the income to capital as a percentage of total income well that's just going to be equal to I can select income to capital d5 / / 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 the near to 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's that that income to capital is going to get reinvested as capital it'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 x times 1 plus this number plus our economic growth so there and I'll press f4 because I keep 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 drew when I dragged it down this is still referring to B 1 because I have the dollar signs they're just hanging the 3% times B 6 so b6 is this so it's looking at the right at that 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 it actually let me get rid of some of the decimal places here it's making it 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 the upper percentile decile quartile would however you want 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 where 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 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 just 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 so 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 because in this situation and this is a fairly extreme situation we have right over here now sudden the income to labor and apps was 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 was this is still decreasing but if economic growth was 9 percent now 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