# How a consumer prices index/retail prices index is calculated

Retail Price Index(RPI) and Consumer Price index(CPI) are both used to measure inflation. These indices measure changes in average prices over a year. Measurements are made by recording prices of goods and services that most people will be expected to buy, or put in an imaginary shopping basket. Government statisticians decide what goods to include in this basket. This list should be updated to take account of changing spending patterns. Most governments measure prices in similar ways.

The imaginary shopping basket for a typical family contains, for example, milk, bottled water, sugar, tea, meat, cooking fuel, school books and mobile phone charges. The contents included in the basket are fixed in the short term, but the prices of individual goods change.

A price index uses a single number to indicate changes in prices of a number of different goods. This is calculated by comparing the price of buying the basket of goods with a starting period, called the base year. The base year is given a figure of 100. So if the average price of goods in the basket today is 10 per cent higher than the base year, the price index will be 110. Changes in average prices (the cost of the basket of goods) can be measured on a monthly, quarterly or annual basis.

## Inflation

Inflation is a persistent or sustained rise in the general level of prices over a period of time. So not every price will rise, but average prices will. The effect of this rise on ordinary people will vary, depending on what they buy.

## Weighting

The weighting is a figure given to a category of goods according to the percentage of a typical household’s income that is spent on it.

## Calculating average price changes

Calculating average price changes will give the rate of inflation. The calculation involves two sets of data:
• The price data (collected each month).
• The weights (representing patterns of spending, updated each year).

With this data it is possible to construct a weighted price index.
A consumer spending survey has been carried out that shows the
percentage spend of typical households in an imaginary country. The
table below shows how the percentage spend forms the basis of
the weighting given to the categories.

Category Percentage spend Weight
Food 40 4
Clothing 20 2
Transport 10 1
Other household goods 30 3
Total 100 10

The next stage is to identify price changes in each of these product categories. Let us suppose that surveys carried out in supermarkets, shops and other retail outlets across the country show the following changes since the base year:
• Food prices have increased by 20 per cent.
• Clothing has increased by 10 per cent.
• Transport has fallen by 10 per cent.
• Other household goods have increased by 30 per cent.

To find out the average change in price we need to take account of each of these price changes in terms of how much consumers spend on that item (the weight). For example, the increase in food prices of 20 per cent will have a major impact on average prices because 40 per cent of household income is spent on food. In contrast, even though transport prices have fallen by 10 per cent, this will have a smaller impact on average prices because consumers only spend a tenth of their income on transport.
To create a weighted price index we need to multiply the weight for each item by the price index for that item. This is shown in the table below.

Product Category Weight Price Index Weighted Price Index
Food 4 x 120 480
Clothing 2 x 110 220
Transport 1 x 90 90
Other Goods 3 x 130 390
Total 1180

Finally, divide the weighted price index by the total number of weights:
1180/10
= 118
This shows that prices have risen on average by 18 per cent (i.e. from the base year figure of 100 to 118 in the new year).

Next topic: Inflation