Measurement of inflation using the Consumer Prices Index (CPI)

Published by Patrick Mutisya · 14 days ago

IGCSE Economics 0455 – Government and the Macro‑economy: Inflation – Measuring Inflation with the CPI

Government and the Macro‑economy – Inflation

Objective

To understand how inflation is measured using the Consumer Prices Index (CPI) and to be able to calculate the inflation rate.

1. What is the Consumer Prices Index (CPI)?

The CPI is a statistical measure that reflects the average change over time in the prices paid by households for a fixed basket of goods and services.

  • It represents the cost of a “typical” consumption basket.

  • The basket is based on household expenditure surveys.

  • It is expressed as an index number, with a base year set to 100.

2. How is the CPI calculated?

The CPI for a given year t is calculated by comparing the total cost of the basket in year t with the total cost of the same basket in the base year.

Mathematically:

\$CPI{t}= \frac{\displaystyle\sum{i=1}^{n} P{i,t}\,Q{i,base}}{\displaystyle\sum{i=1}^{n} P{i,base}\,Q_{i,base}}\times 100\$

where:

  • \$P_{i,t}\$ = price of item i in year t

  • \$P_{i,base}\$ = price of item i in the base year

  • \$Q_{i,base}\$ = quantity of item i in the base‑year basket (fixed)

  • \$n\$ = number of items in the basket

3. Calculating the Inflation Rate from the CPI

The inflation rate between two consecutive periods is the percentage change in the CPI.

\$\text{Inflation Rate}{t}= \frac{CPI{t}-CPI{t-1}}{CPI{t-1}}\times 100\%\$

4. Example Calculation

Assume a simple basket containing three items: bread, milk, and cinema tickets. The quantities in the base year (2020) are fixed.

ItemQuantity (base year)Price in 2020 (base year)Price in 2021Price in 2022
Bread (loaf)100£0.80£0.85£0.90
Milk (litre)80£0.50£0.55£0.60
Cinema ticket20£5.00£5.20£5.50

Step 1 – Calculate total cost of the basket in each year:

  • 2020 (base year): \$100(0.80)+80(0.50)+20(5.00)=£80+£40+£100=£220\$

  • 2021: \$100(0.85)+80(0.55)+20(5.20)=£85+£44+£104=£233\$

  • 2022: \$100(0.90)+80(0.60)+20(5.50)=£90+£48+£110=£248\$

Step 2 – Compute CPI (base year = 2020, CPI = 100):

  • CPI2020 = \$ \frac{£220}{£220}\times100 = 100\$

  • CPI2021 = \$ \frac{£233}{£220}\times100 \approx 106.0\$

  • CPI2022 = \$ \frac{£248}{£220}\times100 \approx 112.7\$

Step 3 – Calculate annual inflation rates:

  • 2021 inflation = \$\frac{106.0-100}{100}\times100\% = 6.0\%\$

  • 2022 inflation = \$\frac{112.7-106.0}{106.0}\times100\% \approx 6.3\%\$

5. Interpretation of CPI and Inflation Rate

  1. Rising CPI: Indicates that, on average, the price of the consumption basket is increasing – i.e., inflation.

  2. Stable CPI: Suggests price stability (zero inflation).

  3. Falling CPI: Implies deflation – a general decline in prices.

  4. The magnitude of the inflation rate helps policymakers decide whether to tighten or ease monetary policy.

6. Limitations of the CPI

  • Fixed basket bias: The basket does not reflect changes in consumer preferences or the introduction of new goods.

  • Substitution bias: Consumers may switch to cheaper alternatives when prices rise, which the CPI does not fully capture.

  • Quality changes: Improvements in product quality can raise prices without reflecting pure inflation.

  • Coverage: The CPI typically excludes owner‑occupied housing costs, which can be a large part of household expenditure.

  • Regional differences: A single national CPI may mask variations in inflation across different regions.

Suggested diagram: A line graph showing CPI values for 2020‑2022 with the corresponding inflation rates annotated.

7. Quick Revision Checklist

  • Know the definition of CPI and why a base year is used.

  • Be able to write and explain the CPI formula.

  • Calculate the inflation rate from two CPI figures.

  • Interpret what a rise, fall, or stability in CPI means for the economy.

  • Recall at least three limitations of the CPI as a measure of inflation.