[SOUND] In the previous video, we examined how we can compare GDP of two different years using the constant price GDP measure. But we also saw that that measure has problems because realty prices change over time, and the weaknesses in comparing one year with another year. Especially, when you think about the different results that you get if you use different years as the base year. So, what's the solution? And here's the solution that seems to be working and seems to produce better results. You could keep changing the base year. For each year, you use the previous year as the base year and calculate the GDP level of each year in a way that is very closely comparable with the previous year, and then do this for every single year. Find a series of growth rates from one year to the next. That could help reduce the error because the base prices are changing. But then we face a problem. How to compare years that are not consecutive. While using the previous year as the base here, we're reducing, we're diminishing the errors that we cause, especially over long periods of time, but we need to figure out how to compare two nonconsecutive years. And we do this by using this chain of growth rates that we found from one year to the next and building on it. For example, starting from GDP of one particular year, let's say 2015. Finding out how much real GDP increased in 2016 compared to 2015. And once we find out what's the GDP of 2017 compared to 2016, we can then figure out how much growth we've experienced in two consecutive years. And find out what the GDP of 2017 is compared to 2015. Let me show you this with an example. Let's go back to the example we had before, the economy with beer and pizza, and we've calculated this nominal GDP. Now, we want to find the real GDP using the chain rule measure, the way I described to you calculating GDP of each year based on the prices of the previous year. So we start with 2013 in this example. We take those prices, calculate the GDP of 2014 using the base year prices, we get, in this example, we get $100 as GDP. This number that we've found here, the 100, is comparable to the nominal GDP of 2013, because both are based on the same set of prices. So, we can actually find out how much the economy grew between these two years using the same set of prices, because there are fewer changes in one year compared to a longer period, the error is minimized here. You can actually do this quarterly and reduce the error even further. So when you want to calculate real GDP of 2015, we start by first calculating nominal GDP of 2014 in its own prices calculating the GDP of 2015. In the prices of 2014, we get two comparable numbers. We compare the growth rate in that period and then use it for comparing with GDP of 2015 with other years. Which, I'm going to show you how that can be done. Same thing for 2016. Now, how to calculate GDP growth over many years. Here, I've highlighted different numbers that are comparable over the years so we can calculate growth rate. For example, growth rate over time. For example, we have growth rate of GDP in 2014, being equal to 0 based on comparing nominal GDP of 2013, and GDP of 2014 calculated in 2013 prices. We do the same thing for 2015. Here is the number. We've taken the GDP of 2015, calculating the previous year prices, compared it with the nominal GDP of the previous year, come up with a growth rate of 6.7% and then we do the same thing for 2016. If you want to compare everything over longer period of time, we start with our base here, in this case we have 2013. We get GDP of 100, we know that there was 0 growth in 2014, so we increase this $100 at growth rate of 0, we get $100. Then we increase the GDP of 2014 by the 6.7% growth that we saw in 2015, and then we get the number here 106.70. And finally, we use the GDP of 2015 times the growth rate that we experience in 2016 and find out what the GDP should be in 2016. Now, we have a series of numbers here, down here that are comparable. They are all in terms of the dollars of 2013, and only increase by the real growth rates from one year to the next, or one period to the next. This new measure is called, GDP in constant dollars, as opposed to constant prices. You're keeping the processing power of the dollar equal to what it was in 2013 in our base year, and calculate the GDP of every year in terms of those dollars. In terms of the purchasing power of the dollar in that base year.