Example question calculating CPI and inflation | AP Macroeconomics | Khan Academy

The CPI, or Consumer Price Index, is used to measure the cost of a typical basket of goods the typical household in the nation of Jacksonia buys. Four loaves of bread, three pounds of cream cheese, and eight books are purchased each week. The prices of these goods in the years 2015, 2016, and 2017 are given in the table below, and then they ask us some questions: calculate the CPI in 2017 using 2016 as the base year; calculate the CPI in 2015 using 2016 as the base year; calculate the rate of inflation between 2015 and 2016; calculate the rate of inflation between 2016 and 2017; and then describe a reason why the inflation rate between 2016 and 2017 might overstate the changes in cost of living.

So, pause this video and see if you can work through it before I do it with you. Alright, now let's just do it step by step.

So this first two letters, they want us to calculate the CPI's in 2017 and 2015 using 2016 as a base year. The way I'm going to do it, I'm going to set up a new column here which is the cost of the weekly basket. Because they tell us how much they buy each week: cost of weekly basket.

Let's see, in 2015 they buy four loaves of bread at a dollar each, so it's going to be four times one, plus they buy three pounds of cream cheese at three dollars a pound, plus three times three, plus they buy eight books a week. These people like to read, and so, and each book in 2015 is ten dollars, so eight times ten. Eight times ten, and this is going to be equal to four times one is four, plus nine is thirteen, plus eighty is going to be ninety-three.

Now that same basket, that weekly basket in 2016, well we're buying four loaves of bread at two dollars now, four times two, plus we're buying three pounds of cream cheese at six dollars a pound now, plus three times six, plus eight books per week at twenty dollars per book, eight times twenty. This is going to be equal to eight plus eighteen, which is twenty-six, plus a hundred and sixty is one hundred and eighty.

So this is going to be one hundred eighty-six dollars. And now we're going to do the same thing in 2017. Each week, you're going to get four loaves of bread, now it's three dollars per loaf, plus we're buying three pounds of cream cheese per week. Three, it's still at six dollars per pound, plus eight books per week at twenty-five dollars per book. And so this is going to be equal to twelve plus eighteen, which is thirty, plus two hundred, which is going to be two hundred thirty dollars.

And now we can calculate the CPI's. So the CPI, it's typical that it's going to be 100 in your base year, should be 100, so I could just put that there. And for the other years, you could say the basket cost in a year divided by the cost and base year cost in base year year times 100. So obviously in 2016, that's going to be the cost in 2016 divided by the cost in 2016 times 100; you'll get 100.

But for 2015, it will be the cost of the basket in 2015, which is 93 dollars, divided by the cost in 2016, which is 186 dollars, times 100. This one is actually pretty straightforward. 93 is half of 186, so this is going to be equal to 50.

And then in 2017, it's going to be the cost of the basket in 2017 divided by the cost of the basket in 2016 times 100, which is going to be equal to, I'm going to use a calculator for this one, 230 divided by 186 is equal to approximately 1.24. If we multiply that times 100, we'll say it's approximately, it is approximately 124. So calculate the CPI in 2017 using 2016 as the base year; it would be 124.

Calculate the CPI in 2015 using 2016 as the base year; that is 50. Calculate the rate of inflation between 2015 and 2016. So how much do prices grow if we take this basket of goods from 2015 to 2016? Well, you could look at your CPI; I went from 50 to 100. So prices doubled, and so if something's doubled, you grew by a hundred percent.

The rate of inflation is the growth in prices, and so this is 100 inflation. Things doubled in price, and you can see it here; everything doubled in price right over here. Calculate the rate of inflation between 2016 and 2017. Well, if you start at 100 and you grow to 124, you have just grown by 24. One way to think about it is you multiply by 1.24, which is the same thing as growing by 24. So that 24 growth is the rate of inflation.

Describe a reason why the inflation rate between 2016 and 2017, so that's what we answered right here in part d, might overstate changes in the cost of living. And if you haven't answered that part yet, I encourage you, given all that we've done, to try to pause the video and think about that.

So let's look at what happened from 2016 to 2017. The price of a loaf of bread increases by 50 percent; the price of a book increases by five dollars on a base of 20; that's an increase of 25 percent. But the price of cream cheese does not change, plus zero percent; it experiences no inflation from 2016 to 2017.

And so you could imagine a scenario where if some goods' prices increase a lot while others don’t, the basket of goods might change. People might buy less bread and fewer books and more cream cheese, and so we could say the typical basket might get more weighted to goods that had less inflation. An example in this case would be cream cheese, because they look relatively cheaper to the goods that had more inflation.

And if that happened, you would have a lower actual growth in cost of living. This last question really alludes to the fact that the CPI isn't necessarily a perfect indicator; that as different goods in the basket have a price inflation at different rates, you could have a substitution effect between the various goods.

Now, in countries, they try to rebalance the basket of goods based on a perception of what is typical, but once again that is not necessarily going to be perfect.