How to Calculate the Consumer Price Index (CPI) and Inflation Rate

[00:00:00] Speaker 1: Hello, in this video we're going to look at how to calculate the consumer price index and the inflation rate. So we'll start here with the definition of the consumer price index, which is technically the CPIU. It's a measure of the overall cost of goods purchased by people living in metropolitan urban areas. The CPIU is used to calculate inflation, which is just an increase in the average level of prices in the economy. Let me present the formula for the annual inflation rate. We'll be doing this at the end of this presentation. The annual inflation rate is the percentage change in the CPI from its preceding year using this formula right here. So it would be the CPI, say, in 2017, minus the CPI in 2016, divided by the CPI in 2016. All multiplied by 100 would give us the inflation rate for 2017. All right, let's begin here. We have a simple economy. This economy has three goods that consumers buy: soccer balls, shoes, and concert tickets. We have data for three years. In the base year, in 2016, we have the price of each item and the quantity that consumers purchased. In 2017, we have the prices. And in 2018, we have the prices for those three items. We do not need quantity data for any other year but the base year. So I do not need quantity data for 2017 or quantity data for 2018. So an important point to keep in mind: we only need quantity data from the base year. So the first step in calculating the consumer price index is to calculate the total cost of purchasing the base year fixed basket, which I highlighted in red. We are going to call that the fixed basket. And we are going to assume that consumers keep buying that same quantity year in and year out. So for 2016, what is the cost of that basket, that fixed basket? So in 2016, it is just the price times the quantity. And we are going to just sum those up and we get $5,000. 10 times 100, 50 times 40, and 100 times 20. So the quantities never change. The prices will change, but the quantities from the base year, the fixed basket, will not change. And finally in 2018, we are going to evaluate that fixed basket at 2018 prices. 18 times 100, 56 times 40, and 110 times 20. Here is the calculation down here. Adding that up, the cost of that fixed basket in 2018 is a little over $6,000. So just rewriting our findings from the last screen. Noting that the base year is 2016. We are going to construct the CPI index. Here is the formula, the all-important formula. So in general, the CPI in year X is going to be the cost of that fixed basket in year X divided by the base year cost of the fixed basket. So here is our calculation in 2016. In 2016, the cost of the fixed basket is $5,000. What is the base year cost? Well, the base year cost, since the base year is 2016, it is also $5,000. So the CPI in the base year is going to be 100, and it will always be 100 in the base year. The CPI in 2017 is going to be the cost of the fixed basket in 2017, which is $5,660 up here. The base year cost doesn't change. The base year cost doesn't change. It's $5,000. So the CPI in 2017 equals $113.2. The CPI in 2018, the cost of the fixed basket in 2018, $6,240. That goes in the numerator, dividing once again by the base year cost of the fixed basket, which is $5,000. We get a CPI of $124.8. Rewriting those CPIs for each year, and now it's time to calculate the inflation rate, the annual inflation rate in 2017, and the annual inflation rate in 2018. Here again, I'll rewrite the inflation rate formula. So we're going to use that to guide us in calculating the inflation rate. So in 2017, the inflation rate is the CPI in 2017 minus the CPI in the preceding year in 2016, all divided by the CPI in 2016. This gives us an inflation rate of 13.2%. On average, prices rose 13.2% in 2017. And in 2018, we're going to take the CPI in 2018 minus the CPI from 2017. Divided by the CPI in 2017, we get an annual inflation rate here of 10.25% in 2018. All right, that's it. I hope you found this video helpful.