A price index like the consumer price index (CPI) tracks what a fixed market basket of goods costs over time, compared with a base year set to 100. The inflation rate is the percent change in that index. Edit the basket, pick a base year, and follow every step of the work, then convert nominal dollars into real dollars.
Three formulas do all the work.
Type any quantity or price. The base-year column is highlighted; its CPI is always 100.
A nominal value is in current dollars. Divide by the price index and multiply by 100 to get a real value in base-year dollars: Real = Nominal ÷ price index × 100
A price index compares the cost of the same market basket in each year with its cost in the base year. In the base year the index is always 100. An index of 125 means the basket costs 25% more than in the base year.
The CPI prices a fixed basket bought by a typical urban household, including imports. The GDP deflator covers all final goods and services produced in the country: nominal GDP ÷ real GDP × 100. It leaves out imports and has no fixed basket.
Inflation is a rising price level (positive inflation rate). Deflation is a falling price level (negative rate). Disinflation is a falling inflation rate while prices still rise, such as 6% down to 2%.
Substitution bias: people switch away from goods that get pricier, but the basket stays fixed. New goods: new products enter the basket late. Quality changes: some price increases pay for better products, not just higher prices.
Nominal values are in current dollars. Real values remove price changes so you can compare what money buys across years. If your nominal wage rises 3% and prices rise 5%, your real wage falls about 2%.
Demand-pull inflation comes from aggregate demand rising faster than output can keep up. Cost-push inflation comes from higher production costs, such as wages or oil, that shift short-run aggregate supply left.
These are the calculations AP asks most often. Memorize the formula column and always write it before you plug in numbers.
| Question | Formula | Work | Answer |
|---|---|---|---|
| A basket costs $200 in the base year and $240 this year. Find the CPI. | Cost this year ÷ cost in base year × 100 | 240 ÷ 200 × 100 | 120 |
| The CPI rises from 120 to 126. Find the inflation rate. | (New − old) ÷ old × 100 | (126 − 120) ÷ 120 × 100 | 5% |
| The CPI falls from 125 to 120. Find the inflation rate. | (New − old) ÷ old × 100 | (120 − 125) ÷ 125 × 100 | −4% (deflation) |
| Inflation was 6% last year and 2% this year. What happened? | Compare the two rates | The rate fell but stayed positive | Disinflation; prices still rose |
| A worker earns $45,000 when the CPI is 150. Find the real wage. | Nominal ÷ price index × 100 | 45,000 ÷ 150 × 100 | $30,000 in base-year dollars |
| Nominal GDP is $1,100 billion and real GDP is $1,000 billion. Find the GDP deflator. | Nominal GDP ÷ real GDP × 100 | 1,100 ÷ 1,000 × 100 | 110 |
| The CPI is 80 in a year before the base year. What does that mean? | Index ÷ 100 | 80 ÷ 100 = 0.8 | The basket cost 20% less than in the base year |
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 2.4. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 2 terminology guide.