Does a bigger paycheck buy more?
Distinguish nominal income from purchasing power and calculate a fixed basket price index.
A fictional weekly basket contains food costing $50, transport costing $30, and other goods costing $20 in Year 0. Income starts at $100. Quantities and quality stay fixed. The same selected inflation rate applies to every item in each of the next two years; income grows at the selected rate each year.
Print creates the fixed example worksheet below. “Print with teacher answers” adds a separate answer page. Use your browser’s Save as PDF option to download it.
Change one assumption.
Predict what will happen, adjust an input, then use the results to check your reasoning. Sliders work with arrow keys.
What the numbers mean
The basket gets more expensive each year. After two years, purchasing power is 8.88% below the starting level. Compare income growth with price growth, not just the size of the paycheck.
Show calculation table
| Year | Basket cost ($) | Income ($) | Income in Year 0 dollars |
|---|---|---|---|
| 0 | 100 | 100 | 100 |
| 1 | 110 | 105 | 95.45 |
| 2 | 121 | 110.25 | 91.12 |
Use the terms precisely.
Open a term to read its meaning, then use it in your explanation.
Price level
The cost of a basket at a point in time. Our Year 0 basket has an index of 100.
Inflation
The percentage increase in the price level over a period. Negative inflation is deflation.
Disinflation
Inflation slows but remains positive, so prices still rise. Compare separate scenarios with lower positive rates.
Nominal versus real income
Nominal income is measured in current dollars. Real income adjusts for the price level; here it is expressed in Year 0 basket dollars.
- Price level
- The cost of a basket at a point in time. Our Year 0 basket has an index of 100.
- Inflation
- The percentage increase in the price level over a period. Negative inflation is deflation.
- Disinflation
- Inflation slows but remains positive, so prices still rise. Compare separate scenarios with lower positive rates.
- Nominal versus real income
- Nominal income is measured in current dollars. Real income adjusts for the price level; here it is expressed in Year 0 basket dollars.
Work through the starting example.
These questions use the default settings, even if you changed the interactive lab. Show your calculations and explain one assumption behind your answer.
Starting inputs: Annual basket inflation: 10%; Annual income growth: 5%.
Name: __________________________ Date: ______________
- At the default settings, calculate the basket cost and income in Year 1 and Year 2.
- Calculate Year 2 income in Year 0 dollars. Can the household buy more or less of the basket than before?
- Reset, then lower annual inflation to 2% while income growth remains 5%. Do prices fall? What happens to purchasing power?
Try a new case
Find a pair of nonzero rates that keeps real income unchanged. Explain why matching income and price growth works.
Exit ticket
What changed, what stayed fixed, and which term helps explain the result?
A 35 minute teaching plan
Use 5 minutes to introduce the question and vocabulary, 10 to predict and test inputs in pairs, 12 for the worksheet, 5 to compare explanations, and 3 for the exit ticket. Without devices, use the printed starting case and calculate changes by hand.
Look for a correct calculation, precise terminology, and an explanation that respects the model’s limits. For the open challenge, accept different cases when the arithmetic and reasoning support them.
Open teacher answer key
- Basket: $110 in Year 1 and $121 in Year 2. Income: $105 and $110.25. Each second-year calculation uses the first-year level.
- Real income = $110.25 ÷ 1.21 = $91.12 in Year 0 dollars, a purchasing-power decline of about 8.88%. Nominal income rose but prices rose faster.
- Prices still rise: $102 and $104.04. Year 2 real income = $110.25 ÷ 1.0404 = $105.97, about 5.97% above the starting level. This is a separate constant-rate scenario, not a falling rate within one timeline.
Teacher answer key: Inflation & purchasing power
- Basket: $110 in Year 1 and $121 in Year 2. Income: $105 and $110.25. Each second-year calculation uses the first-year level.
- Real income = $110.25 ÷ 1.21 = $91.12 in Year 0 dollars, a purchasing-power decline of about 8.88%. Nominal income rose but prices rose faster.
- Prices still rise: $102 and $104.04. Year 2 real income = $110.25 ÷ 1.0404 = $105.97, about 5.97% above the starting level. This is a separate constant-rate scenario, not a falling rate within one timeline.
For the challenge and exit ticket, credit correct calculations, a clearly stated assumption, and precise use of a relevant term. Different supported examples are acceptable.
Where the model stops
This tiny uniform-price basket is not an official CPI. Real households have different spending weights, substitution choices, taxes, and income paths.
Further reading: OpenStax: inflation concepts. These fictional activities are original to World Economy. Reference links do not imply endorsement.
World Economy · losttofound.org/classroom/labs/purchasing-power. An adult educator may print or privately share this free activity with their own learners. Keep the source attached. No resale or public rehosting.