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### Course: AP®︎/College Macroeconomics > Unit 2

Lesson 4: Price Indices and inflation# Example question calculating CPI and inflation

The Consumer Price Index (CPI) is a measure of the average change in prices of a typical basket of goods and services over time. It is used to gauge inflation and changes in the cost of living. The CPI might overstate changes in the cost of living because it doesn't always account for how people adjust their spending when prices change.

## Want to join the conversation?

- This seems like a different calculation approach than the "percentage of expenditures" approach in the Intro to Inflation video. Here Sal only looks at the changes in the costs of the goods (easier).

In Intro to Inflation, Sal uses the 60%/40% base-year percentages of a household's expenditures on each good to give different weights to the inflated prices.

That method would have required a few more steps than this video took, and it would yield different answers on an exam.

Which is right?(10 votes)- Sal made a mistake in the Intro. The Consumer Price Index (CPI) cannot be calculated using percentages alone; it requires real numbers for the amount of goods in the basket.

It is necessary to have specific quantities or amounts of goods in the basket to calculate the CPI, as the CPI aims to measure the average price change of a fixed set of goods and services over time. Thus, the CPI cannot be derived from 60%/40% base-year percentages.

Please correct me if I am mistaken :)(2 votes)

- My 2016 = 177 and 2017 = 221 why is it different(3 votes)
- Your 2016 should be 100 by definition. The base year is always 100.(7 votes)

- I've been told we're not able to use calculators on the AP Exam, so if a question like the sample problem part a, what do we do?(4 votes)
- On the AP Exam, if calculators are not allowed, you should manually perform calculations, basically, just learn how to preform the calculations.(3 votes)

- For calculating the CPI, shouldn't the entire total cost spent in a year be taken rather than a week?(3 votes)
- Yes that's correct.(2 votes)

- WHO INVENTED INFLATION? he needs to not exist....(3 votes)
- why is the base year 100 dollars(3 votes)
- How does the CPI account for changes in consumer spending behavior due to price fluctuations?(3 votes)
- at7:10Sal says-"inflation lower actual growth in cost of living." So, *I didn't get this point what it means and how it's overstate cost of living?*(2 votes)
- the question was about how the changes in the inflation rate create changes in the cost of living. In this case, since cream cheese is considered cheaper (due to its unchanged rate of inflation comparatively) which means people would buy more of the 'cheaper' good, rather than the bread or books. It does not create growth in the cost of living as the high costs of the book and the bread is sort of balanced out by buying less of it, and rather turning to buy more of the cream cheese.(2 votes)

- why the answer of c is 100, I calculated by 186/93*100=200(2 votes)
- cuz the formula is (CPI of that year/CPI of base year)/CPI of base year, which means the answer is (186-93)/93 = 93/93 = 100%(2 votes)

- 5. Explain the meaning and uses of a pie diagram. Prepare a pie diagram of family expenditure from the following data:

S.No. Items Expenditure (`.)

1.

2.

3.

4.

5. Food

Clothing

Education and Entertainment

Rent

Miscellaneous

Total Expenditure

480

300

330

450

240

1880(2 votes)

## Video transcript

- [Instructor] 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 each week. The prices of these goods in 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. All right, now let's
just do it step by step. So these first two letters,
they want us to calculate the CPIs in 2017 and 2015, using 2016 as a base year. So the way I'm going to do it, I'm going to set up a new
column here, which is cost of the weekly basket, and they tell us how
much they buy each week, cost of weekly, weekly basket. Let's see, in 2015, they buy four loaves of bread at $1 each. So it's going to be four times one, plus they buy three pounds of
cream cheese at $3 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
$10, so eight times 10, eight times 10. And this is going to be equal
to four times one is four, plus nine is 13, plus 80 is going to be $93. Now, that same basket,
that weekly basket in 2016, where we're buying four
loves of bread at $2 now, four times two, plus we're buying three pounds of cream cheese at $6 a pound now, plus three times six, plus eight books per week at $20 per book, eight times 20. This is going to be equal to
eight plus 18, which is 26, plus 160 is 186. So this is going to be $186. 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 $3 per loaf, plus we're buying three pounds
of cream cheese per week, three, it's still at $6 per pound, plus eight books per week at $25 per book. And so this is going to be equal
to 12 plus 18, which is 30, plus 200, which is going to be $230. And now we can calculate the CPIs. 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, cost in year, divided by the cost in 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, divided by the cost in
2016, which is $186, 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 the
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. It went from 50 to 100, so prices doubled. And so if something is
double, it grew by 100%. And the rate of inflation
is the growth in prices. And so this is 100% inflation. Things doubled in price,
and you could 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,
try to pause the video, and try to think about that. So let's look at what
happened from 2016 to 2017. The price of a loaf of
bread increases by 50%. The price of a book increases
by $5 on a base of 20. That's an increase of 25%. But the price of cream cheese
does not change, plus 0%. It experiences no inflation
from 2016 to 2017. And so you could imagine a
scenario where if some goods, their prices increased 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, had less inflation, example, in this case,
would be cream cheese, cream cheese because they look relatively, relatively cheaper to the goods that had more inflation. And if that happened, you would
have a lower actual growth, actual growth in cost of living. And 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.