Do I use base-year or current-year quantities when computing the CPI?

Always use the fixed base-year quantities in both years. The CPI holds the basket constant so that changes in its cost reflect only price changes. Using each year's own quantities would be a different, changing-weight index like the GDP deflator.

Why is the base-year CPI always 100?

Because the CPI divides the current-year cost of the basket by the base-year cost, then multiplies by 100. In the base year you divide the base-year cost by itself, giving 1, and multiplying by 100 gives exactly 100.

What is the difference between the price level and the inflation rate?

The price level is measured by a single CPI value relative to the base year. The inflation rate is the percentage change in that price level between two periods. One CPI number tells you the price level; you need two to compute an inflation rate.

When should I use the CPI versus the GDP deflator on the exam?

Use the CPI when a question mentions a fixed basket, the cost of living, consumers, or imported goods. Use the GDP deflator when it mentions all domestically produced output or the ratio of nominal to real GDP. Coverage and weighting are the deciding clues.

AP-MACRO-2.4

U2.4 Price Indices and Inflation

Learn to compute the CPI from a market basket, calculate inflation rates from CPI changes, and tell the CPI apart from the GDP deflator for AP Macroeconomics.

What you'll do in this lesson

A voice-first session with the Crimsora tutor on U2.4 Price Indices and Inflation, then targeted practice and FRQs — with the tutor adapting to where you get stuck.

Start U2.4 Price Indices and Inflation free

What this lesson covers

Prices move every year, but by how much? Topic 2.4 gives you the tools to measure that movement precisely. The Consumer Price Index (CPI) tracks the cost of a fixed basket of goods that a typical household buys, and comparing CPI values over time gives you the inflation rate — a number that shows up constantly on the AP exam and in the real world.

In this lesson you will build a CPI from raw prices and quantities, convert CPI changes into an inflation rate, and learn exactly how the CPI differs from the GDP deflator you will meet again in U2.6. Master these calculations now: they are quick points on the multiple-choice section and a common FRQ setup.

What the CPI Measures

The Consumer Price Index measures the average change over time in the prices paid by urban consumers for a fixed market basket of goods and services. The key word is fixed: the basket's contents and quantities stay the same from year to year so that any change in the basket's total cost reflects price changes alone, not changes in what people buy.

The formula is

CPI = \frac{\text{cost of basket in current year}}{\text{cost of basket in base year}} \times 100.

The base year is a reference year chosen by convention; its CPI always equals 100 because you are dividing the base-year cost by itself. A CPI of 115 means prices are 15 percent higher than in the base year; a CPI of 90 would mean prices are 10 percent lower.

To cost the basket in any year, multiply each good's price that year by its fixed quantity, then sum. Notice that quantities never change between years — only prices do. This is what makes the CPI a fixed-weight index. A common misconception is that you re-survey what consumers buy every year; in the CPI's core calculation you do not. That fixed basket is exactly what distinguishes it from the GDP deflator, discussed below.

Computing the Inflation Rate

Once you have CPI values for two years, the inflation rate is the percentage change in the CPI between them:

\text{Inflation rate} = \frac{CPI_{\text{new}} - CPI_{\text{old}}}{CPI_{\text{old}}} \times 100.

For example, if the CPI rises from 120 to 126, inflation is

\frac{126-120}{120}\times 100 = 5\%

. Always divide by the earlier year's CPI, never the later one — putting the wrong number in the denominator is the single most common error on this calculation.

A positive result is inflation (prices rising). A negative result is deflation (prices falling). A positive but shrinking inflation rate is disinflation — prices are still rising, just more slowly. The AP exam loves to test whether you can tell disinflation from deflation.

Term	What is happening	Sign of inflation rate
Inflation	Prices rising	Positive
Deflation	Prices falling	Negative
Disinflation	Prices rising more slowly	Positive but decreasing

Remember the inflation rate is a rate of change, so it depends on two CPI values. A single CPI number tells you the price level relative to the base year, not the inflation rate.

CPI vs. GDP Deflator

Both the CPI and the GDP deflator measure the price level, but they cover different goods and use different weighting. The GDP deflator equals

\frac{\text{nominal GDP}}{\text{real GDP}} \times 100

and covers everything counted in GDP — all final goods and services produced domestically.

Feature	CPI	GDP deflator
Coverage	Fixed basket bought by consumers	All domestically produced final goods
Weights	Fixed (base-year basket)	Changes with current output mix
Imports	Included (consumers buy them)	Excluded (not domestically produced)
Capital goods	Not directly	Included

Because the CPI includes imported consumer goods, a jump in the price of imported oil or foreign-made electronics raises the CPI but not the GDP deflator. Conversely, the price of a domestically produced machine tool affects the deflator but not the consumer basket. The CPI uses fixed quantities, while the deflator's weights shift as the economy produces different amounts of each good. On the exam, a question that mentions imported goods or a fixed basket is pointing you toward the CPI; one that mentions all output or nominal versus real GDP points to the deflator.

How the Exam Tests This Topic

Multiple-choice questions typically give you a small basket — two or three goods — with prices in two years and ask for the CPI or the inflation rate. Practice doing these fast: cost the basket each year, divide, multiply by 100, then take the percent change if inflation is asked.

Conceptual questions test whether you know the base-year CPI is always 100, whether you can distinguish inflation from deflation and disinflation, and whether you can tell the CPI from the GDP deflator based on coverage and weighting. FRQs may hand you a table of prices and quantities and ask you to compute step by step, showing work.

A frequent trap: the exam gives quantities that differ between years and hopes you will use each year's own quantities. For the CPI you must use the fixed base-year quantities in both years. Another trap is asking for the inflation rate when you only computed a CPI — read carefully. Finally, know that the CPI is used to measure the cost of living and to adjust nominal values (like wages) into real terms, a link you will use in U2.5 and U2.6.

Key terms

Consumer Price Index (CPI).: A measure of the average change over time in prices paid by consumers for a fixed market basket of goods and services, set to 100 in the base year.
Market basket.: A fixed set of goods and services, with fixed quantities, whose total cost is tracked across years to measure price changes.
Base year.: The reference year against which prices are compared; its CPI equals 100 by definition.
Inflation rate.: The percentage change in a price index from one period to the next, calculated as the change in CPI divided by the earlier CPI, times 100.
Deflation.: A sustained decrease in the overall price level, shown by a negative inflation rate.
Disinflation.: A decrease in the inflation rate while prices are still rising; the rate stays positive but falls.
GDP deflator.: A price index equal to nominal GDP divided by real GDP times 100, covering all domestically produced final goods with changing weights.

Worked example

A simple economy's consumer basket contains 4 loaves of bread and 2 gallons of milk. In the base year (Year 1), bread costs 2 dollars per loaf and milk costs 3 dollars per gallon. In Year 2, bread costs 2.50 dollars per loaf and milk costs 3.50 dollars per gallon. Compute the CPI for both years and the inflation rate from Year 1 to Year 2.

Start by costing the fixed basket in the base year. Bread:

4 \times 2 = 8

dollars. Milk:

2 \times 3 = 6

dollars. Total base-year cost is

8 + 6 = 14

dollars.

Because Year 1 is the base year, its CPI is

\frac{14}{14}\times 100 = 100

.

Now cost the same fixed basket at Year 2 prices, keeping quantities fixed at 4 and 2. Bread:

4 \times 2.50 = 10

dollars. Milk:

2 \times 3.50 = 7

dollars. Total Year 2 cost is

10 + 7 = 17

dollars.

Year 2 CPI is

\frac{17}{14}\times 100 \approx 121.4

.

Finally, find the inflation rate using the earlier year in the denominator:

\text{Inflation} = \frac{121.4 - 100}{100}\times 100 = 21.4\%.

So prices rose about 21.4 percent between Year 1 and Year 2. Notice the quantities 4 and 2 were used in both years — that fixed weighting is what makes this a CPI calculation.

Practice questions

A country's CPI rises from 150 in 2022 to 156 in 2023. What is the inflation rate for 2023?

3 percent
4 percent
6 percent
56 percent

Answer: 4 percent

Use the percent-change formula with the earlier year in the denominator:

\frac{156-150}{150}\times 100 = \frac{6}{150}\times 100 = 4\%

. The trap answer 6 percent comes from forgetting to divide by 150; 56 percent comes from misreading the CPI as a percentage itself.

Explain two reasons the CPI and the GDP deflator can move differently in the same year, and identify which index would rise more if the price of imported oil spiked while domestic output prices were flat.

Answer: The CPI would rise more than the GDP deflator.

First, the CPI covers only a fixed basket of consumer goods, while the GDP deflator covers all domestically produced final goods, including capital goods not bought by consumers. Second, the CPI includes imported goods that consumers buy, whereas the GDP deflator excludes imports because they are not domestically produced. An oil price spike raises the cost of the consumer basket (which includes imported oil and fuel), pushing up the CPI, but since the oil is imported and domestic output prices are unchanged, the GDP deflator barely moves. Therefore the CPI rises more.

In an economy the CPI was 110 in Year 1, 121 in Year 2, and 127 in Year 3. Did the economy experience inflation, deflation, or disinflation from Year 2 to Year 3? Support your answer with the inflation rates.

Answer: Disinflation.

Year 1 to Year 2 inflation is

\frac{121-110}{110}\times 100 = 10\%

. Year 2 to Year 3 inflation is

\frac{127-121}{121}\times 100 \approx 4.96\%

. Prices are still rising (positive inflation rate), so it is not deflation, but the rate fell from 10 percent to about 5 percent. A falling but still-positive inflation rate is disinflation.

FAQ

Do I use base-year or current-year quantities when computing the CPI?: Always use the fixed base-year quantities in both years. The CPI holds the basket constant so that changes in its cost reflect only price changes. Using each year's own quantities would be a different, changing-weight index like the GDP deflator.
Why is the base-year CPI always 100?: Because the CPI divides the current-year cost of the basket by the base-year cost, then multiplies by 100. In the base year you divide the base-year cost by itself, giving 1, and multiplying by 100 gives exactly 100.
What is the difference between the price level and the inflation rate?: The price level is measured by a single CPI value relative to the base year. The inflation rate is the percentage change in that price level between two periods. One CPI number tells you the price level; you need two to compute an inflation rate.
When should I use the CPI versus the GDP deflator on the exam?: Use the CPI when a question mentions a fixed basket, the cost of living, consumers, or imported goods. Use the GDP deflator when it mentions all domestically produced output or the ratio of nominal to real GDP. Coverage and weighting are the deciding clues.

Learn this with a teacher, not a page

The Crimsora tutor teaches U2.4 Price Indices and Inflation live — explaining on a whiteboard, asking you questions, and adapting to where you get stuck.

Try a live session free