How Is the CPI Calculated? A Worked Example
Learn how the CPI is calculated from a weighted basket of goods and services, with a worked example, the inflation rate formula and a common exam mistake.
The consumer price index (CPI) is calculated by tracking the cost of a representative basket of goods and services over time. The basket reflects what households buy, and its cost in a chosen base period is set to an index of 100100100.
This is part of Cambridge International AS Level Economics, 4.6 Price stability, specifically 4.6.2: measurement of changes in the price level using the CPI, including possible difficulties in measurement.
How the calculation works
Prices are collected for items in the basket. Items receive different weights according to their share of household spending: a large expense has more influence on the CPI than a small one. For example, a change in housing costs usually affects the index more than the same percentage change in a minor household purchase. The cost of the basket at current prices is then compared with its cost at base-period prices:
CPI=Cost of the basket at current pricesCost of the basket at base-period prices×100\text{CPI}=\frac{\text{Cost of the basket at current prices}}{\text{Cost of the basket at base-period prices}}\times 100CPI=Cost of the basket at base-period pricesCost of the basket at current prices×100Suppose a simplified basket contains 222 food items costing 101010 each and 111 transport item costing 202020. Its base-period cost is 404040. A year later, the food items cost 111111 each and transport costs 222222, so the same basket costs 444444. The CPI is 4440×100=110\frac{44}{40}\times100=1104044×100=110. Because the index was 100100100 a year earlier, the basket’s measured cost has risen by 10%10\%10%.
What to watch for
To calculate the inflation rate between any two periods, compare their CPI figures: new CPI−old CPIold CPI×100\frac{\text{new CPI}-\text{old CPI}}{\text{old CPI}}\times100old CPInew CPI−old CPI×100. Do not assume an index of 110110110 always means inflation was 10%10\%10% this year; that is true only if the previous year’s index was 100100100.
CPI is an estimate. Spending patterns change, and it can be difficult to account for new products or changes in quality. For instance, a product may become more expensive because its quality improved, rather than because prices rose for an identical product. The basket may therefore not perfectly reflect every household’s experience.
