An Index Number Rebases a Value Against a Base Year of 100, so Changes Are Easy to Read.
Definition
Index number: a figure that expresses the value of a variable relative to a base year, which is set equal to 100, so that changes over time can be read off easily.
- An index number equals the value in the year divided by the value in the base year, multiplied by 100: index=value in yearvalue in base year×100\text{index}=\dfrac{\text{value in year}}{\text{value in base year}}\times 100index=value in base yearvalue in year×100.
- This sets the base year to 100 by construction, and later years are measured against it.
- Weights reflect each item's share of spending, so the items people spend most on move the index most.
Note
- An index number shows a value relative to the base year, not an amount in pounds.
- The percentage change in the index measures the change since the base year.
A Price Index Applies This Method to a Basket of Goods to Track the Price Level.
- The CPI tracks the price of a weighted basket of goods and services to measure the price level.
- The inflation rate is the percentage change in that price index over a year.
Example
- An index of 105 means prices are 5%5\%5% above the base year; it does not mean the basket costs £105.
- To find inflation between two years, take the change in the index: if the CPI rises from 108.0 to 111.5, inflation is 111.5−108.0108.0×100≈3.2%\dfrac{111.5-108.0}{108.0}\times 100\approx 3.2\%108.0111.5−108.0×100≈3.2%.
Case study
- In the UK the ONS collects prices for a basket of around 700 goods and services and reweights it every year to reflect changing spending.
- The basket is built to represent the spending of a typical or 'average' family, so the CPI reflects the cost of living of the average household rather than any one person's.
- The Bank of England is set a target of 2 per cent CPI inflation, so the index is the anchor for monetary policy.
Worked Example: Building a Weighted Price Index
- Take a simplified basket with three categories whose weights sum to 100: food (weight 40), transport (30) and housing (30).
- Suppose that since the base year the price index has risen to 110 for food, 105 for transport and 120 for housing.
- Multiply each price index by its weight, add the results, then divide by the total weight of 100: (40×110)+(30×105)+(30×120)100\dfrac{(40\times 110)+(30\times 105)+(30\times 120)}{100}100(40×110)+(30×105)+(30×120).
- This gives 4,400+3,150+3,600100=11,150100=111.5\dfrac{4{,}400+3{,}150+3{,}600}{100}=\dfrac{11{,}150}{100}=111.51004,400+3,150+3,600=10011,150=111.5.
- The overall index is 111.5, so the basket costs 11.5%11.5\%11.5% more than in the base year, and food lifts the index most because it carries the largest weight.
Index Numbers Can Also Track Other Variables, Such as Wages, Output and Share Prices.
- The same method rebases any series, so wages, real output or share prices can each be shown as an index.
- The producer price index tracks factory-gate prices and acts as a leading indicator for consumer prices.
- Rebasing each series to 100 makes it easy to compare changes across very different variables.
An Index Can Mislead if Its Basket or Weights Fall out of Date.
- The basket and its weights can become outdated as spending habits change.
- Quality changes and unrepresentative weights can distort the figure.
- A single national index also cannot fit every household exactly, because spending patterns differ.
Common Mistake
- Do not read an index number as a price.
- It is a value relative to the base year of 100.
Self review
- How is an index number calculated?
- Why is a basket weighted?
- What does an index of 110 mean?
- Using weights of 50 and 50, work out the overall index if one item is at 120 and the other at 108.
- Name one other economic variable an index number could track.
