AQA A-Level Economics (7136)

## Learning Outcomes

- Understand what an index number shows and why the base year is set at 100
- Calculate simple index numbers, weighted index numbers, and inflation rates from index data
- Interpret index values correctly without confusing index levels with percentage changes
- Identify the differences between CPI, RPI, and the GDP deflator
- Explain why weights, rebasing, and chain-linking matter when comparing data over time
- Evaluate the strengths and limits of index numbers in macroeconomic analysis

## AQA A-Level Economics (7136) Syllabus

For the AQA A-Level Economics (7136), you are expected to understand how index numbers are calculated and interpreted as macroeconomic data, with a focus on the following syllabus points:

- Know that an **index number** measures change relative to a **base year** set equal to 100
- Calculate a simple index number using the formula $(\text{current value} \div \text{base year value}) \times 100$
- Interpret an index number correctly, including values above and below 100
- Calculate percentage changes and inflation rates from index data
- Understand why some indices are **weighted** and how a weighted index number is calculated
- Identify the main features of the **Consumer Prices Index (CPI)**, **Retail Prices Index (RPI)**, and **GDP deflator**
- Explain why different inflation measures can give different results
- Understand the meaning of **rebasing** and why it does not itself change the underlying trend

## Test Your Knowledge

_Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, look more closely at that area during your revision._

1. What does an index number of 108 mean if the base year is 100?
2. How do you calculate a simple index number from raw data?
3. Why are weights used in CPI?
4. What is the difference between CPI and the GDP deflator?
5. If an index rises from 120 to 126, what is the percentage increase?

## Introduction

Index numbers are a core data skill in A-Level Economics. They are widely used to show changes in macroeconomic variables such as real GDP, labour productivity, and the average price level. In Paper 3, they often appear in extracts, tables, and charts, so you must be able not just to define them, but also to calculate and interpret them accurately.

A common reason students lose marks is that they confuse an index level with a rate of change. An index tells you the value relative to a base year. It does not automatically tell you the percentage change from one later year to another. That distinction matters in inflation and growth questions.

> **Key Term: index number**
> A number showing how a variable has changed relative to a base year, which is usually given a value of 100.

### What index numbers show

An index number expresses a variable in relative terms rather than raw figures. The **base year** is assigned the value 100. Later values show how much the variable has risen or fallen compared with that base.

> **Key Term: base year**
> The reference year used for comparison in an index, given a value of 100.

If a real GDP index is:

- **100** in the base year, there has been no change from the base year
- **103**, real GDP is **3% higher** than in the base year
- **98**, real GDP is **2% lower** than in the base year

This is why index numbers are useful. They make it easier to compare changes over time and between data series of different sizes.

The basic formula is:

$$
\text{Index number} = \frac{\text{current value}}{\text{base year value}} \times 100
$$

Worked example:

Suppose average house prices were £200,000 in the base year and £230,000 in the current year.

Step 1: Write the formula

$$
\text{Index number} = \frac{\text{current value}}{\text{base year value}} \times 100
$$

Step 2: Substitute the figures

$$
\text{Index number} = \frac{230000}{200000} \times 100
$$

Step 3: Calculate

$$
= 1.15 \times 100 = 115
$$

So the index is **115**. This means house prices are **15% higher than in the base year**.

> **Test Tip:** If the index is 115, do not write "115% higher". The correct interpretation is "15% higher than the base year".

A very common trap appears when the starting point is not 100. For example, if an index rises from 120 to 126, the increase is 6 index points, but the percentage increase is not 6%.

$$
\frac{126 - 120}{120} \times 100 = 5\%
$$

So the percentage increase is **5%**.

Students often confuse **index points** with **percentage change**. They are only the same when the comparison starts from 100.

> **Key Term: index points**
> The arithmetic difference between two index values.

Common errors:

- forgetting to multiply by 100
- saying an index of 108 means inflation is 108%
- treating a rise of 6 index points as a 6% rise when the starting point is not 100

### Weighted index numbers and price relatives

Some indices are more useful if items are given different importance. In real life, households spend much more on rent, transport, and food than on minor items. A good price index must reflect that.

> **Key Term: weighted index number**
> An index in which different items are given different weights according to their relative importance.

A **price relative** shows the current price of one item compared with its base-year price.

> **Key Term: price relative**
> The price of an item in the current period compared with its price in the base year, expressed as an index number.

Formula:

$$
\text{Price relative} = \frac{\text{current price}}{\text{base price}} \times 100
$$

Weighted index formula:

$$
\text{Weighted index number} = \frac{\Sigma(\text{weight} \times \text{price relative})}{\Sigma(\text{weights})}
$$

Worked example:

| Product | Base-year price (£) | Current price (£) | Weight |
| ------- | ------------------: | ----------------: | -----: |
| X       |                   6 |                 9 |      1 |
| Y       |                  12 |                18 |      3 |
| Z       |                  20 |                15 |      2 |

Step 1: Calculate each price relative

For X:

$$
\frac{9}{6} \times 100 = 150
$$

For Y:

$$
\frac{18}{12} \times 100 = 150
$$

For Z:

$$
\frac{15}{20} \times 100 = 75
$$

Step 2: Multiply each price relative by its weight

- X: $150 \times 1 = 150$
- Y: $150 \times 3 = 450$
- Z: $75 \times 2 = 150$

Step 3: Add the weighted values

$$
150 + 450 + 150 = 750
$$

Step 4: Add the weights

$$
1 + 3 + 2 = 6
$$

Step 5: Divide weighted total by total weight

$$
\frac{750}{6} = 125
$$

So the weighted index number is **125**. This means the overall price level is **25% higher than in the base year**.

If this was a price index moving from 100 in the base year to 125 in the current year, the inflation rate over the whole period would be **25%**.

Why weights matter:

- large spending categories should affect the index more
- a big rise in the price of a rarely bought item should not distort the whole measure
- weights make the index more realistic
  > **Test Tip:** In weighted index questions, divide by the **total of the weights**, not the number of items.

Common student errors:

- using cash price changes instead of price relatives
- ignoring weights
- dividing by 3 items instead of total weight 6

### CPI, RPI and the GDP deflator

Index numbers matter because major macroeconomic indicators are often presented in index form. The best-known examples are price indices.

> **Key Term: Consumer Prices Index (CPI)**
> The UK's main official measure of consumer price inflation, based on a weighted basket of goods and services.

The CPI measures average price changes for a representative basket of goods and services bought by households. It is a **weighted** index, so products with a bigger share of spending have a bigger impact.

> **Key Term: basket of goods and services**
> The representative collection of goods and services used to measure changes in consumer prices.
>
> **Key Term: weights**
> Numerical values showing the relative importance of items within a weighted index.

The basket and weights are updated regularly because spending habits change over time. New products appear, some older products matter less, and household budgets shift between categories.

The **inflation rate** is calculated from the percentage change in the price index between two periods, usually the same month in different years or one year to the next.

> **Key Term: inflation rate**
> The percentage change in a price index over a period of time.

Formula:

$$
\text{Inflation rate} = \frac{\text{index this year} - \text{index last year}}{\text{index last year}} \times 100
$$

Worked example:

Suppose CPI is 120 this year and 114 last year.

Step 1:

$$
120 - 114 = 6
$$

Step 2:

$$
\frac{6}{114} \times 100
$$

Step 3:

$$
= 5.26\%
$$

So the inflation rate is about **5.3%**.

This is different from saying prices are 20% above the base year. That statement comes from the index level of 120, not from the annual inflation rate.

> **Key Term: Retail Prices Index (RPI)**
> An older measure of consumer price inflation in the UK, with different coverage and methodology from CPI.

RPI differs from CPI in several ways:

- it includes some housing-related costs such as mortgage interest payments
- it has different coverage and weights
- it uses a different formula in parts of its construction

As a result, RPI and CPI often give different inflation figures. In many periods, RPI has been higher than CPI.

> **Key Term: GDP deflator**
> A broad price index measuring the price of all domestically produced final goods and services in the economy.

The GDP deflator is calculated as:

$$
\text{GDP deflator} = \frac{\text{nominal GDP}}{\text{real GDP}} \times 100
$$

Worked example:

If nominal GDP is 220 and real GDP is 200:

$$
\frac{220}{200} \times 100 = 110
$$

So the GDP deflator is **110**, meaning the overall price level of domestically produced output is **10% above the base-year level**.

CPI vs RPI vs GDP deflator:

- **CPI**: consumer prices only, weighted basket, main UK inflation target measure
- **RPI**: older consumer price measure, includes some housing costs, different method
- **GDP deflator**: economy-wide domestic output prices, not just consumer purchases

This distinction is useful in essays. If the question is about the cost of living, CPI is usually more relevant than the GDP deflator. If the question is about overall domestic inflation in output, the GDP deflator is broader.

### Rebasing, chain-linking, and evaluation

Sometimes two index series use different base years. This makes direct comparison harder, so economists may **rebase** an index.

> **Key Term: rebasing**
> Changing the base year of an index so that a different year is set equal to 100.

Rebasing formula:

$$
\text{New index} = \frac{\text{old index in given year}}{\text{old index in new base year}} \times 100
$$

Worked example:

Suppose an old series has:

- 2020 = 125
- 2022 = 150

If 2022 becomes the new base year:

For 2020:

$$
\frac{125}{150} \times 100 = 83.3
$$

For 2022:

$$
\frac{150}{150} \times 100 = 100
$$

Rebasing changes the scale, not the real pattern of change. It does not alter actual inflation or growth.

> **Key Term: chain-linking**
> A method of constructing an index by updating weights and linking short-period changes together over time.

Chain-linking helps keep an index more representative because household spending patterns change. This is useful for measures like CPI and real GDP where fixed weights can become out of date.

Strengths of index numbers:

- simple way to compare changes over time
- useful for large macroeconomic series
- helps convert raw data into a standard form
- weighted indices can better reflect actual spending patterns

Limitations of index numbers:

- no average basket matches every household
- quality changes are difficult to measure
- new products can be hard to include quickly
- different methods and weights can give different answers
- rebased series can confuse students if they compare raw index levels without checking the base year

For evaluation questions, use the "it depends on" approach. On one hand, index numbers are very useful for comparing changes over time and spotting trends in inflation or output. On the other hand, their accuracy depends on representative weights, appropriate coverage, and careful interpretation. It depends on what you are trying to measure: cost of living, consumer inflation, or economy-wide price change.

> **Test Tip:** If two data series have different base years, check whether rebasing is needed before making direct comparisons.

## Key Point Checklist

_This article has covered the following key knowledge points:_

- An index number shows change relative to a base year, which is usually set at 100
- An index of 108 means the variable is 8% higher than in the base year
- The simple index formula is $(\text{current value} \div \text{base year value}) \times 100$
- A change in index points is not always the same as a percentage change
- Percentage change between two index values is calculated using the standard percentage change formula
- Weighted index numbers give more importance to items with larger spending shares
- CPI is the UK's main official consumer inflation measure and uses a weighted basket of goods and services
- RPI is an older inflation measure with different coverage and methodology, including some housing-related costs
- The GDP deflator measures price changes for all domestically produced final goods and services
- The inflation rate is the percentage change in a price index over time, not the index level itself
- Rebasing changes the base year to 100 but does not change the underlying trend
- Chain-linking updates weights over time to make an index more representative

## Key Terms and Concepts

- index number
- base year
- index points
- weighted index number
- price relative
- Consumer Prices Index (CPI)
- basket of goods and services
- weights
- inflation rate
- Retail Prices Index (RPI)
- GDP deflator
- rebasing
- chain-linking


Measuring Macroeconomic Performance - Index numbers