Measurement of inflation using the Consumer Prices Index (CPI)

Measurement of Inflation using the Consumer Prices Index (CPI)

What is the CPI? 🔍

The Consumer Prices Index (CPI) is a statistical measure that shows how the price of a fixed basket of goods and services changes over time. Think of it as a “price tag” on a favourite snack that keeps rising as the cost of ingredients goes up.

CPI Formula

The CPI for a given year is calculated as:

$$\text{CPI} = \frac{\text{Cost of basket in current year}}{\text{Cost of basket in base year}} \times 100$$

• Base year is the year chosen as the reference (usually 100). • Current year is the year you are measuring.

Calculating the Inflation Rate

The inflation rate between two consecutive years is:

$$\text{Inflation Rate (\%)} = \frac{\text{CPI}_{\text{current}} - \text{CPI}_{\text{previous}}}{\text{CPI}_{\text{previous}}} \times 100$$

It tells you how much prices have increased (or decreased) in percentage terms.

Example: A Simple Basket

Suppose the government uses a basket of 5 items. Prices in the base year (2015) and current year (2020) are:

Total cost in 2015: £4.30 Total cost in 2020: £5.45

Now calculate CPI for 2020 (base year 2015 = 100):

$$\text{CPI}_{2020} = \frac{5.45}{4.30} \times 100 \approx 126.74$$

Inflation rate from 2015 to 2020:

$$\text{Inflation} = \frac{126.74 - 100}{100} \times 100 \approx 26.74\%$$

So, on average, prices rose by about 27% over those five years.

Exam Tips & Tricks 📝

Quick Check ??

If the CPI in 2021 is 130, what is the inflation rate from 2020 (126.74) to 2021?

Answer: $$\frac{130 - 126.74}{126.74} \times 100 \approx 2.57\%$$