Consumer Price Index (CPI): Videos & Practice Problems

Inflation is tracked using the Consumer Price Index (CPI), which measures price changes in a typical basket of goods over time. The CPI is calculated by dividing the current year's basket cost by the base year's cost and multiplying by 100. For example, if the basket cost in 2017 is $1,750 and in 2018 it rises to $1,902.50, the CPI for 2018 is $\frac{1902.50}{1750}*100$ = 108.71. Inflation rates are derived from CPI changes, indicating how prices fluctuate annually.

Consumer Price Index (CPI)

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 CPI calculation. The consumer price index, or CPI, is what the government uses to track inflation. They choose a typical basket of goods that a family buys during a year and track the changes in the prices of these goods. By observing these price changes, they can monitor the inflation rate. Let's go through a simple example here and calculate a consumer price index in a simple situation, and then we'll discuss it a bit more at the end.

The first step is for the government to decide what constitutes the typical basket of goods. In the US, for example, the government surveys households to determine the goods typically purchased and uses this information to construct the basket. In our example, we have a typical family in Simple Land purchasing 50 jugs of water and 75 pounds of food during a given year. This is a simplified representation, but it suffices for our purposes.

The next step involves creating the problem scenario based on the basket of goods. You generally wouldn't know the prices beforehand; these would be specified in the problem. Let's calculate the cost of the basket for each year.

Starting in 2017, the basket cost calculation would be: 50 jugs of water at $5 each plus 75 pounds of food at $20 per pound. Therefore, \(50 \times 5 = 250\) and \(75 \times 20 = 1500\). Adding these, the total price of the basket in 2017 is $1750.

In 2018, the price of water rose to $5.50 per jug, and the price of food increased to $22 per pound. So, the calculation is \(50 \times 5.50 = 275\) and \(75 \times 22 = 1650\). Therefore, the total is $1925 for the basket.

For 2019, the price of water is $5.20 per jug and $25 per pound for food. The calculations are \(50 \times 5.20 = 260\) and \(75 \times 25 = 1875\). The total cost of the basket in 2019 is $2135.

Let's pause here, and then we'll continue with steps to calculate the CPI and use this information to measure inflation in steps 4-5. We'll see how the CPI can help us determine inflation over these years.

Consumer Price Index (CPI)

Alright. Let's continue here, and we're going to use the cost of the basket that we calculated in the previous video, and we're going to use those costs of the basket to calculate CPI for each year. Okay? So when we calculate CPI, just like we had when we were calculating GDP, nominal GDP, real GDP, what we're going to use, as in real GDP, we had the base year. Right? We're going to pick a year as our base year. And in this question, they don't mention what the base year is. So we're going to assume that the oldest year, which is generally what you're going to do, is the base year. 2017 is going to be the base. If they don't tell you otherwise, if they don't specify which year is the base year, you're just going to use the oldest year, 2017 in this case. Cool? So let's go ahead and use our formula here to calculate CPI in each year. So we're going to take the basket cost in the current year divided by the basket cost in the base year times a hundred to get the CPI. 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 CPI is going to be in the base year? We're going to take the current cost in 2017 of $17.50 and divide it by the base year, which is also 2017. So guess what? It's also $17.50, and multiply it by a hundred. Well, guess what? $17.50 divided by $17.50 is just 1, times a hundred. We're going to get a hundred for our CPI here. And that's always going to be true for the base year. The base year is going to be a hundred because that's how the calculation works. Right? Where the division of the basket is always going to give us 1 in the base year and our CPI will always equal a hundred in the base year. So let's go ahead to 2018 and let's calculate the CPI there. So what's going to be our numerator in the basket cost? We're going to use the current year. So in 2018, the basket cost of the basket was $1,902.50 and we'll divide that by what? We'll use the base year. Right? The bottom is always going to be the base year which is $17.50. So that $17.50 is not going to change in any of our calculations. It's always going to be the base year cost of the basket. So we'll multiply that by a hundred to get our CPI. $1,902.50 divided by $17.50 times a hundred and we'll go to 2 decimal places here. That's generally what we do with CPI, we'll go to 2 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 practices. 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 CPI. So what's going to be our numerator? We're going to use the 2019 basket cost, $2,135 divided by the base year, 1750. Notice, it's not the previous year. We still use the base year which is 2017, and we multiply that by a hundred. So let's go ahead and, excuse me. Do that calculation. $2,135 divided by $17.50 times a hundred and we get exactly $122.00 there. So $122 is the CPI 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 CPI figures. 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 going to 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 going to 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 the percentage change? The percentage change is 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 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 prices changed. So we're going to take our CPI, which was in 2018, 108.71. We're going to subtract the previous year of 100 and divide it by a 100. And then obviously, we'll multiply it by a hundred to get a percentage, but to save space, I'm not going to put the multiply times a hundred. We're just going to go $108.71 minus $100 divided by $100 and then times a hundred. So obviously, we're going to end up getting 8.71% and that's always going to be like that in the year after the base year because the base year has that $100 CPI. It makes the calculation a little simple there. You could 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. All right? So, pause real quick. I'm guessing you guys gave it an attempt, and now we're going to follow through here and finish up if the inflation for 2019. So what are we going to do here? We're going to take the current year in 2019, which was $122 CPI, minus the previous year. Notice the difference here. When we are calculating the CPI, 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. The previous year CPI was 108.71, and we're going to divide it by 108.71. Right? New minus old divided by old. Cool. $122 minus $108.71. So let's go ahead and do that math. $122 minus $108.71, So that's our numerator divided by $108.71, and that gives it to us as a decimal. So we multiply by a hundred, and we're going to get a CPI to 2 decimal places of, 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 CPI to help us calculate the inflation rate, and this is generally how it's done. We're going to have a CPI, and we use it to calculate inflation. Sometimes, a question will give you the CPI numbers and then just ask you to calculate inflation. A more complicated question might ask you to use the basket cost to calculate CPI and then use those CPIs to calculate inflation just like all the steps we went through here. So one last thing about CPI is what we have here is the actual basket of goods that is used in the US survey. 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 those prices over time. So you'll notice that housing is generally the biggest spending bucket that we have, then food and beverages, and then we've got all these other things here. Education, other, medical, transportation. Oh, it looks like transportation is just about as big as food and beverages there. Cool. So you don't need to know this. 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. Generally, in this class, when you have to solve these problems, they're not going to have you do a giant basket of goods. It'll generally be one, two or three products being tracked in the CPI. Cool? Let's pause here and let's move on to the next video.

Here’s what students ask on this topic:

What is the Consumer Price Index (CPI) and how is it calculated?

The Consumer Price Index (CPI) measures the average change in prices over time that consumers pay for a basket of goods and services. To calculate the CPI, follow these steps:

1. Determine the base year and the current year.

2. Calculate the cost of the basket of goods in both the base year and the current year.

3. Use the formula:

$\frac{\mathrm{Cost} \mathrm{of} \mathrm{basket} \mathrm{in} \mathrm{current} \mathrm{year}}{\mathrm{Cost} \mathrm{of} \mathrm{basket} \mathrm{in} \mathrm{base} \mathrm{year}} \times 100$

For example, if the basket cost $1,750 in the base year and $1,902.50 in the current year, the CPI is:

$\frac{1902.50}{1750} \times 100 = 108.71$

How does the CPI help in measuring inflation?

The CPI helps measure inflation by tracking changes in the cost of a fixed basket of goods and services over time. Inflation is calculated by comparing the CPI of different years. The formula for calculating the inflation rate is:

$\frac{\mathrm{CPI} \mathrm{in} \mathrm{current} \mathrm{year} - \mathrm{CPI} \mathrm{in} \mathrm{previous} \mathrm{year}}{\mathrm{CPI} \mathrm{in} \mathrm{previous} \mathrm{year}} \times 100$

For example, if the CPI in 2018 is 108.71 and in 2017 it was 100, the inflation rate is:

$\frac{108.71-100}{100} \times 100 = 8.71\%$

This indicates that prices increased by 8.71% from 2017 to 2018.

What is a base year in the context of CPI calculation?

A base year is a reference year used in the calculation of the Consumer Price Index (CPI). It serves as a benchmark for comparing the cost of a basket of goods and services in other years. The CPI for the base year is always set to 100. For example, if 2017 is the base year and the cost of the basket in 2017 is $1,750, the CPI for 2017 is:

$\frac{1750}{1750} \times 100 = 100$

In subsequent years, the cost of the basket is compared to the base year to calculate the CPI and measure inflation.

How is the basket of goods determined for CPI calculation?

The basket of goods for CPI calculation is determined through surveys conducted by the government. In the U.S., approximately 14,000 households are surveyed to identify their spending habits. The survey collects data on the types and quantities of goods and services typically purchased by households. This information is used to create a representative basket of goods, which includes categories like housing, food and beverages, transportation, medical care, and education. The prices of these items are tracked over time to calculate the CPI and measure inflation.

What are the limitations of using CPI to measure inflation?

While the CPI is a widely used measure of inflation, it has several limitations:

1. **Substitution Bias**: CPI assumes a fixed basket of goods, ignoring that consumers may substitute cheaper alternatives when prices rise.

2. **Quality Changes**: CPI may not fully account for improvements in product quality, which can affect price comparisons over time.

3. **New Products**: CPI may not immediately include new products and services, potentially missing changes in consumer spending patterns.

4. **Geographical Differences**: CPI is a national average and may not reflect regional price variations.

5. **Expenditure Patterns**: The basket of goods may not represent all demographic groups equally, leading to inaccuracies for specific populations.