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Example calculating real GDP with a deflator

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Video transcript

let's say the 2011 nominal GDP is fifteen thousand two hundred ninety four point three billion dollars and I didn't just make this number up this is actually the advanced estimate of what 2011's GDP was in the fourth quarter and now this isn't just the fourth quarter number they took the fourth quarter number and then they annualized this to get to this fifteen thousand billion which is essentially fifteen point two nine four three trillion dollars of GDP now let's say the GDP deflator relative to 2010 you always have to know what you're taking your deflator relative to is a hundred and two point five and this is once again this is the 2011 this is the 2011 GDP deflator and one way to interpret this is if the base year is 2010 that means that prices in 2010 could be viewed as being at a hundred and that now that we are in 2011 we are at a hundred and 2.5 or another way to think about it is that the general level of prices and we've already talked about this this is not an easy thing to measure but they've attempted to do that the general level of prices has gone up by two and a half percent went from one hundred to one hundred and two point five now that out of the way we know the nominal GDP is the GDP measured in 2011 dollars often called the current dollar GDP we know what the deflator is can we figure out the real GDP in 2011 and it will be the real GDP in 2010 dollars when we have the 2002 flater relative to 2010 so to do that we just have to remember that the ratio between our nominal GDP nominal GDP and our real GDP is going to be the ratio it's going to be the ratio you could view it as our current dollars versus 2010 dollars or another way of viewing it is it's the ratio between our deflator our deflator which is 100 and 2.5 and 100 which is essentially you could view that as kind of the deflator in 2010 or we're just setting that level of prices to be a hundred our prices now are the hundred and two point five so thinking of it that way our our nominal current dollar GDP is fifteen thousand two hundred ninety four point three billion dollars or you could view that it's fifteen point two nine four three trillion either way our real GDP is what we want to figure out we do not know what this is and we know our deflator we know that things have gotten two-and-a-half percent more expensive or that our deflator is a hundred and two point five one hundred and two point five and then we can just solve for we can just solve for the real GDP and 102.5 over one hundred you might be able to do this one in your head this whole expression right over here just becomes one point zero two five and so you have this fifteen trillion fifteen point something trillion divided by the real is equal to 1.0 to five or you can divide both sides by 1.0 to five and multiply both sides by the real GDP so let's do that we scroll over to the left a little bit so I'm going to multiply both sides by the real GDP so I'm going to multiply both sides by the real GDP I'm going to divide both sides by 1.0 to five 1.0 to five 1.0 to five now of course this cancels with that that's why I multiplied both sides by the real and then this cancels with that and we get our real GDP I'll just swap well I'll leave it over here are real let me do it in that same blue color our real GDP is equal to our current dollar GDP fifteen thousand two hundred ninety four point three billion dollars divided by essentially the ratio between our deflator and one hundred divided by 1.05 if I were in charge of naming macroeconomic concepts I would have actually made this the deflator I would have set this at one and I would have called this 1.0 to five because then you wouldn't had all this silliness of multiplying and dividing by 100 you just say let's take our current dollar GDB divide it by the deflator i guess you could say we're going to deflate it to get the real GDP you just make a lot more sense to me but either way that's essentially what it simplified to this is our current dollar GDP our nominal GDP dividing it by what I would have preferred to call the deflator but you could do this as a deflator divided by 100 and that gives us our real GDP we're just a flood we're deflating the card dollar 1 and I'm going to need a calculator to figure this one out so let's get the calculator out so we're just do everything in billion fifteen thousand two hundred ninety four point three this is in billions tah or / so our answer is going to be in billions one point zero two five gives us 14 thousand nine hundred twenty-one point three so let me take that off the screen so I can remember what that says I have a bad memory all right so this is our real GDP our real GDP is equal to fourteen thousand two hundred oh no 921 921 0.3 so I'm rounding billion dollars that is equal to our real GDP 1414 thousand billion or fourteen point nine thousand billion is the same thing you could also write this this is same thing as fourteen point nine two one three trillion trillion trillion dollars