Consumer Price Index (CPI)
A measure of the cost of living carried out by comparing the value of a basket of goods and services in a given year to a base year.
HL students must be able to construct weighted price indices from raw data. The example below shows how it can be done, step by step:
| Good/Service | Weight (%) | Price Year 1 ($) | Price Year 2 ($) |
|---|---|---|---|
| Food | 35 | 100 | 120 |
| Housing | 40 | 200 | 230 |
| Transport | 15 | 150 | 170 |
| Clothing | 10 | 80 | 85 |
The percentage change in price for each category is calculated using the formula:
$$Price Change=\frac{\text{New Price}}{\text{Old Price}} \times 100$$
Applying this formula to different goods:
$$\text{Food} = \left( \frac{120}{100} \right) \times 100$$
$$\text{Housing} = \left( \frac{230}{200} \right) \times 100$$
$$\text{Transport} = \left( \frac{170}{150} \right) \times 100$$
$$\text{Clothing} = \left( \frac{85}{80} \right) \times 100$$
Each category is weighted by its relative importance in consumer spending, so goods people buy more of count more. The formula for applying weights is:
$$\text{Weighted Value} = \text{Price Index} \times \text{Weight}$$
Therefore:
$$\text{Food} = 120 \times 0.35 = 42.0$$
$$\text{Housing} = 115 \times 0.40 = 46.0$$
$$\text{Transport} = 113.3 \times 0.15 = 17.0$$
$$\text{Clothing} = 106.3 \times 0.10 = 10.6$$
To obtain the overall weighted price index, sum all the weighted values:
$$\text{Weighted Price Index} = 42.0 + 46.0 + 17.0 + 10.6 = 115.6$$
With the CPI known, the inflation rate is found as the percentage change in CPI from one period to the next, using this formula:
$$\text{Inflation Rate}=\frac{(100\text{Weighted Price Index}−100)} \times 100$$
| Year | Consumer Price Index (CPI) | Inflation Rate (%) |
|---|---|---|
| 2020 (Base Year) | 100 | - |
| 2021 | 105 | 5.00% |
| 2022 | 110 | 4.76% |
| 2023 | 120 | 9.09% |
| 2024 | 125 | 4.17% |
The base year's CPI is always 100.0, because CPI is an index that measures every later year relative to that starting point.
Table 1 above shows the CPI data for an imaginary economy, Econland. The inflation rate for each year is found by applying the formula above.
Don't forget to convert your weights to decimals when calculating, because using the raw percentage inflates every value: 40% should be written as 0.40, not 40.
In IB exams you may need to calculate CPI and inflation rates, so show clear steps in your working: it earns method marks even if a small arithmetic slip costs the final answer.
An economy's CPI rises from 120 in Year 1 to 126 in Year 2. What is the inflation rate over that year?
Markscheme
Several limitations reduce the CPI's accuracy as a measure of inflation, because a fixed basket cannot fully track how people really shop. These include:
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