Gross Domestic Product (GDP) and Consumer Price Index (CPI)

# Consumer Price Index (CPI)

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## Consumer Price Index (CPI)

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so a good way to track inflation is to pick some goods and see how their prices change over time. Let's check out the C. P. I. Calculation. So the consumer price index CPI i what the government does basically is they pick a typical basket of goods that a family buys during a year and they track what the prices of those goods are from year to year. And by seeing how the prices go up or down of these goods they can track the inflation rate. Okay so let's go through a simple example here and let's calculate a consumer price index in a simple situation and then we'll talk about it a little more at the end. So the first step is for the government to decide what is the typical basket of goods. So the government at least in the us what we do is we survey households they actually take a survey and say what are the things that you buy this and that and they see what type of goods are typically purchased and they make that into the basket right this basket of goods that gets purchased. So in our example we've got a typical family in simple land purchases these items during a given year 50 jugs of water. TM. And £75 of food. Tm. Okay so a typical family that's what their purchases are during the year. They buy some food and they buy some water. In our example. Obviously in the real world it's much more complicated calculation but for our purposes this is good enough so that's the first step is to find out what is actually in this basket of goods. So once they create the basket they go ahead and they find the prices of those goods from year to year. So the second step is to get the prices from year to year. And this is this type of information would have to be given to you. And the problem obviously you we're not gonna know what the prices are of whatever they're talking about. So this is generally where the problem will start. They'll they'll tell you the basket of goods has this much stuff in it, and this is the prices of those goods in each year. So let's go ahead and in step three, we're going to calculate the cost of the basket and each year. So the cost of the basket, we said they were gonna, there was remember 50 so what we said up here in step one, we said 50 jugs of water and £75 of food. So we're gonna calculate for 50 jugs and £75 here for each year. Okay, so let's start in 2017, and the cost of the basket was 50 jugs of food. Excuse me. 50 jugs of water times the price of water was $5 in 2017. Right $5 here, and we're gonna add to it, the price of the food. So £75 of food, times $20 and we'll get that total here. So 50 times five is 2 50 plus 75 times 20 is 1500. We had that together. And the price of the basket of goods was 1750 in 2017. Cool. Let's go on to 2018 and we'll do the same calculation. Alright, so let's go ahead in 2018 again, we've got the same basket, right? 50 uh 50 jugs of water, but they've got a new price. Now the price has gone up to $5.05 plus the £75 of food times the price of $22 right? So we can clearly see inflation is going on because the prices are going up right? Um But how much is the inflation? We'll get to that in a second. So 50 times 5.5 comes to 2 50 to 50 plus the price of the food, 75 times 22 is 1650. We add that together to get our price of the basket. So 2 50 to 50 plus one, is 19 oh two and 50 cents. 1900 to 50 cents. Cool. And last but not least let's do 2019. So in 2019, same thing 50. And now what price are we gonna use in 2019? The 2019? Price right $5.20. And then we'll do £75 of food times $25. Cool. So let's add that up. 50 times 5.2 is 260 plus 75 times $25 is 1875. So the cost of our basket in 2019 is 2135. Cool. Let's pause here and then we'll continue with steps four and five where we're gonna use this information to calculate CPI I. And then use the C. P. I. To calculate inflation. Cool. Let's do that in the neck.

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## Consumer Price Index (CPI)

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Alright let's continue here. And we're gonna use the cost of the basket that we calculated in the previous video. And we're gonna use those costs of the basket to calculate CPI I. For each year. Okay so when we calculate CPI I just like we had when we were calculating GDP nominal GDP real GDP. Well we're gonna use as in Real GDP we had the base year right? We're gonna pick a year as our base here. And in this question they don't mention what the base here. So we're gonna assume that the oldest year which is generally what you're gonna do is the base year 2017 is gonna be the base here. If they don't tell you otherwise if they don't specify which year is the base year, you're just gonna use the oldest year. 2017 in this case. Cool. So let's go ahead and use our formula here to calculate CPI I in each year. So we're gonna take the basket cost in the current year divided by the basket costs in the base year. Two times 100 to get the C. P. I. Okay so the current year basket cost depends on what year we're talking about in 2017. The current year. Well that's 2017. So guess what the C. P. I. Is gonna be in the base year. We're gonna take the current the cost in 2017 of 17 50 divided by the base year which is 2017. So guess what? It's also 17 50 and multiply it by 100. Well guess what 17 50 divided by 17 50 is just one times 100. We're gonna get 100 for R. C. P. I. Here. And that's always gonna be true for the base here. The base here is gonna be 100 because that's how the calculation works right? Where the division of the basket is always gonna give us one in the base here and r C. P. I will always equal 100 in the base here. So let's go ahead to 2018 and let's calculate the C. P. I. There. So what's gonna be our numerator in the basket cost we're gonna use the current year. So in 2018 the basket the cost of the basket was 1902 and 50 cents. And we'll divide that by what we'll use the base here. Right? The bottom is always gonna be the base here which is 17 50. So that 17 50 is not gonna change in any of our calculations, it's always gonna be the base here cost of the basket. So we'll multiply that by 100 to get our C. P. I. 1902.5 divided by 17 50 times 100. And we'll go to two decimal places here. That's generally what we do with cp I will go to two decimal places so it came out to 108 .71 is where we'll call it right there. Cool. Let's do the same thing for 2019. So why don't you guys try this one pause real quick. Try it and then follow along with me. I'm sure you'll be able to get it after we've done these practice. This isn't too tough of a calculation. So I'm guessing you guys paused it and you started it up again. Let's go ahead and calculate 2019. Uh C. P. I. So what's gonna be our numerator? We're gonna use the 2019 basket cost 2135 divided by the base here. 1750 notice it's not the previous year. We still use the base here which is 2017. And we multiply that by 100. So let's go ahead and excuse me do that calculation uh 2135 divided by 17 50 times 100. And we get 122 exactly there. So 1 22 is the C. P. I. In 2019. Cool. Let's go ahead and use this information to calculate the inflation rate for each year. So let me leave that on the screen. Those C. P. I. Cool. Alright so In 2017 we're not going to calculate an inflation rate because we have to go what is the change from one year to the next since 2017 is our first year. We're not gonna have an inflation rate. What we're going to see is in 2018. How much did the prices rise between 2017 to 2018. Cool. So look at our formula here we're gonna take the current year minus the prior year divided by the prior year. What does this look like to you? This looks like a percentage change formula right? Remember when we talked about percentage change percentage change. The easy way that I like to remember it? It's just the new minus the old divided by the old. Okay. New minus old divided by old. That gives us the percentage change. How much did this change from the previous the old to the new to the new year? The current year. Okay so in 2017 we're not going to calculate an inflation rate because it's the first year there's no inflation from the first year to the first year. Let's see how it goes from 2017 to 2018 how the price has changed. So we're gonna take our C. P. I. Which was in 2018. 108.71. We're gonna subtract the previous year of 100 and divide it by 100. And then obviously we'll multiply it by 100 to get a percentage. But to save space I'm not gonna put the multiply times 100. We're just gonna go one oh 8.71 minus 100 Divided by 100. And then times 100. So obviously we're gonna end up getting 8.71%. And that's always gonna be like that in the year after the base year because the base here has that 100 cp i it makes the calculation a little simple there. You can see that the 8.71 that was the inflation rate. But why don't you guys pause real quick and try the same thing for 2019? You guys try and calculate the inflation rate and then follow along and we'll see how you did. Alright so pause real quick. I'm guessing you guys gave it an attempt and we're gonna follow through here and finish up the inflation for 2019. So what are we gonna do here? We're gonna take the current year in 2019 was 1 22 was our C. P. I minus the previous year. So notice the difference here when we are calculating the C. P. I. We were always doing it by the base year but now we're just going from year to year. What is the inflation from 2018 to 2019? Not from the base year to 2019 from 2018 to 2019. So it's just the previous year and the previous year. Cp I was 108.71 and we're gonna divide it by 108.71. Right? New minus old divided by old Cool 1. 22 minus one. Oh 8.71. So let's go ahead and do that math 1 to 2 minus one oh 8.71. So that's our numerator divided by 108.71. And that gives it to us as a decimal. So we multiply by 100 and we're gonna get a C. P. I. To two decimal places of 12 point excuse me. An inflation rate of 12.23%. So that means that the prices had risen between 2018 prices and 2019 prices by 12.23%. So in that one year the prices went up 12 about 12%. Cool. So that's how we use our C. P. I. To help us calculate the inflation rate and this is generally how it's done. We're gonna have a C. P. I. And we use it to calculate inflation. Sometimes the question will give you the C. P. I. Numbers and then just ask you to calculate inflation. A more complicated question might ask you to use the basket cost to calculate CPI I. And then use those C. P. I. E. S to calculate inflation just like all the steps we went through here. So one last thing about um C. P. I. Is what we have here is the actual basket of goods that is used in in the US survey. Um so you'll see that the government surveys approximately 14,000 households to find their basket of goods to find what they're spending their money on and then they use those spendings to create the basket of goods and track the prices over time. So you'll notice that housing is generally the biggest uh spending bucket that we have. Then food and beverages and then we've got all these other things here, education, recreation, other medical transportation. It looks like transportation is just about as big as food and beverages there. Cool. So you don't need to know these. I just added this in there just so you can see how the actual basket of goods is more complicated than what we did in our example with just two products. But generally in this class when you have to solve these problems, they're not gonna have you do a giant basket of goods. It will generally be 12 or three products being tracked in the C. P. I. Cool. Let's pause here and let's move on to the next video.