AP® Macroeconomics review sheet from Aim for Five (aimforfive.com/macro/units/2/2-4)
Unit 2 · Topic 2.4
2.4 Price Indices and Inflation
A price index tracks how much a set group of goods costs compared with a base year. The consumer price index (CPI) is the most common one, and the percent change in a price index is the inflation rate. Price indices also let you turn nominal values, like a paycheck, into real values that show actual buying power.
Key terms
- consumer price index (CPI)
- market basket
- inflation rate
- deflation
- disinflation
- substitution bias
Building the CPI
Government statisticians pick a market basket: a fixed list of goods and services a typical urban household buys (food, rent, gas, clothing, medical care and so on). They price that basket every month, and update what's in it only from time to time.
CPI = (cost of the basket in the current year ÷ cost of the same basket in the base year) × 100.
In the base year the CPI is always 100. A CPI of 120 means the basket costs 20% more than in the base year. Put another way, a CPI of 120 says you'd need $120 today to buy what $100 bought in the base year.
You won't be tested on calculating the producer price index (PPI), which tracks the prices businesses receive for what they sell.
Inflation, deflation, disinflation
Inflation rate = (new index − old index) ÷ old index × 100. You can use the CPI or the GDP deflator (2.6) as the index.
Inflation is a rise in the general price level. Deflation is a fall in the general price level (a negative inflation rate). Disinflation is a fall in the inflation rate while it stays positive: prices still rise, just more slowly. If inflation goes from 6% to 3%, that's disinflation, not deflation.
Real vs. nominal values
A nominal value is measured in the dollars of its own time. A real value adjusts for price changes, so it shows buying power.
Real value = nominal value ÷ (price index ÷ 100). This gives the value in base-year dollars.
Real wages are the classic example. If your pay rises 3% but prices rise 5%, your nominal wage went up but your real wage went down. You can buy less than before.
You can also compare two years when neither is the base year. To express an amount from year A in year B dollars, multiply it by (CPI in year B ÷ CPI in year A). If the CPI was 80 when a concert ticket cost $40 and is 120 now, that ticket would cost $40 × (120 ÷ 80) = $60 in today's dollars.
Why the CPI overstates inflation
The CPI isn't a perfect measure of the cost of living. Most economists agree it overstates inflation a little, for three main reasons.
- Substitution bias: the basket is fixed, but when one good gets expensive, people switch to cheaper substitutes. The CPI keeps pricing the expensive good, so it overstates the rise in the cost of living.
- Quality changes: some price increases buy a better product (a phone with a better camera), and the CPI doesn't fully separate that from inflation.
- New goods: products that didn't exist when the basket was set may enter late, missing early price drops.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
CPI and the inflation rate
A simple basket holds 10 pizzas and 5 movie tickets. In the base year, a pizza costs $10 and a ticket costs $10. This year, a pizza costs $12 and a ticket costs $12. (a) Find this year's CPI. (b) Next year the CPI is 124.8. What is the inflation rate from this year to next year?
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- Step 1: Base-year basket cost = 10 × $10 + 5 × $10 = $150.
- Step 2: This year's basket cost = 10 × $12 + 5 × $12 = $180.
- Step 3: (a) CPI = 180 ÷ 150 × 100 = 120.
- Step 4: (b) Inflation rate = (124.8 − 120) ÷ 120 × 100 = 4.8 ÷ 120 × 100 = 4%.
- Step 5: Don't report the change as 4.8%. That's the change in index points, not the percent change.
Answer: (a) CPI = 120. (b) Inflation rate = 4%.
- Example 2Calculator allowed
Is your raise real?
Jordan earned $19 an hour in the base year (CPI = 100). Now Jordan earns $23 an hour and the CPI is 115. Did Jordan's real wage go up or down?
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- Step 1: Convert today's wage to base-year dollars: real wage = $23 ÷ (115 ÷ 100) = $23 ÷ 1.15 = $20.
- Step 2: Compare with the base-year wage of $19. In base-year dollars, Jordan now earns $20.
- Step 3: The real wage rose by $1, so Jordan's buying power increased, though by much less than the $4 nominal raise suggests.
Answer: The real wage rose, from $19 to $20 in base-year dollars.
Common mistakes
- Subtracting index numbers and calling the result a percent. Divide the change by the starting index.
- Confusing disinflation with deflation. Disinflation means prices rise more slowly; deflation means prices fall.
- Multiplying by the price index to get a real value. Divide the nominal value by (index ÷ 100).
- Saying the CPI understates inflation. Substitution bias makes it overstate inflation.
On the exam
- Expect calculations: build a CPI from a basket, find an inflation rate between two years, or convert a nominal wage or price to a real one. Show the setup.
- Watch for questions about which years' prices go in the numerator and denominator. The base year always goes on the bottom.
Connected topics
Videos
Check yourself
4 questions on 2.4 Price Indices and Inflation. Pick an answer to see if you got it, and why.
| Item | Quantity in basket | Price in 2020 (base year) | Price in 2025 |
|---|---|---|---|
| Movie tickets | 10 | $10.00 | $13.00 |
| Pizzas | 15 | $10.00 | $12.00 |
| Gallons of gasoline | 50 | $3.00 | $3.80 |
Hypothetical market basket
What is the consumer price index (CPI) for 2025?
What was the inflation rate from 2020 to 2025, as measured by this CPI?
A worker earned $20.00 per hour in 2020 and $24.00 per hour in 2025. Measured in 2020 dollars, what was the worker's real wage in 2025?
The CPI rises from 240 last year to 252 this year. What is the inflation rate?
0 of 4 answered