OxfordAQA AS and A-level Economics: Index numbers and money to real terms (9640)

This guide teaches quantitative skills QS5 (calculate and interpret index numbers) and QS7 (make calculations to convert from money to real terms) from section 3.5 of the OxfordAQA International AS and A-level Economics (9640) specification, version 1.2. The specification says these skills could be assessed in any of the assessments, so no stage applies to them. For context, sections 3.1 and 3.2 are International AS content and sections 3.3 and 3.4 are the extra International A2 content. Every country, firm and number below is invented for practice. Track coverage with the OxfordAQA Economics hub and the printable checklist. For recall, use the revision notes. To test yourself, use the practice questions or the free diagnostics.

What this unit covers

Skill	What you must be able to do
QS5	Calculate an index number from raw data, change the base year, build a weighted index, and interpret what an index does and does not tell you
QS7	Convert a money (nominal) value into a real value using a price index, and work out real changes

The same ideas appear in section 3.2.1.2, which asks you to understand how index numbers are calculated, including the base year and weights, how they measure changes in the price level and other variables, and the difference between real and nominal data.

QS5: index numbers

An index number expresses a value as a percentage of its value in a chosen base year. The base year is set to 100. Every other year is measured against it.

index = (value in the year / value in the base year) x 100

The index shows change over time. It does not show the size of the original variable.

Worked example 1: a simple index

Country A records retail sales volume (million units, illustrative figures).

Year	2019	2020	2021	2022	2023
Sales volume	480	504	456	528	552

With 2019 as the base year:

• 2020: 504 / 480 x 100 = 105
• 2021: 456 / 480 x 100 = 95
• 2022: 528 / 480 x 100 = 110
• 2023: 552 / 480 x 100 = 115

Index series: 100, 105, 95, 110, 115.

Interpretation:

• 2021 is 5% below the base year, because 95 is 5 below 100.
• 2023 is 15% above the base year.
• Between 2022 and 2023 the index rose by 5 index points (115 - 110). The percentage change is 5 / 110 x 100 = 4.5%, not 5%. Points are measured against the base. A percentage change is measured against the earlier year.

Changing the base year

To rebase, divide every value in the old index by the old index value of the new base year, then multiply by 100. To make 2021 the base:

• 2019: 100 / 95 x 100 = 105.3
• 2020: 105 / 95 x 100 = 110.5
• 2021: 100
• 2022: 110 / 95 x 100 = 115.8
• 2023: 115 / 95 x 100 = 121.1

The shape of the series is unchanged. Only the reference point moves. Rebasing is useful when you want to compare two series from a common starting year.

Weighted index numbers

A price index for a whole economy covers many goods. Goods do not matter equally to households, so each category gets a weight: its share of typical spending. The weights add to 100 (or to 1).

weighted index = sum of (weight x category index) / sum of weights

Worked example 2: a weighted price index

Country B, year 5 compared with the base year (illustrative).

Category	Weight	Price index, year 5	Weight x index
Food	35	112	3,920
Housing	25	106	2,650
Transport	15	120	1,800
Leisure	10	99	990
Other	15	104	1,560
Total	100		10,920

Weighted index = 10,920 / 100 = 109.2.

An unweighted average of the five category indices is (112 + 106 + 120 + 99 + 104) / 5 = 108.2. The two differ because food has a weight of 35 and leisure only 10. Transport prices rose most (20%), but transport carries a modest weight, so it pulls the overall index up by less than food does.

Inflation from an index

The rate of change of a price index is the inflation rate. If the index was 105.5 in year 4 and is 109.2 in year 5:

(109.2 - 105.5) / 105.5 x 100 = 3.5%

Interpreting an index: what it can and cannot tell you

• Base year and weights matter. If the weights are out of date, the index may not match what households now buy. If the base year was unusual, later changes can look larger or smaller than they are.
• An index records change, not level. Two indices that are both 100 in the base year cannot show which variable is bigger. An export index of 126 and an import index of 138 (both with the same base year) show that imports grew faster. They do not show that imports are larger than exports in value.
• Averages hide differences. An index of 109.2 does not mean every household faced a 9.2% rise. A household that spends mostly on food and transport faces a different rate from the average.
• Other variables. Index numbers also track output, employment, export volumes and real incomes, not only prices.

QS7: converting money to real terms

A nominal (money) value is measured at the prices of the year it was recorded. It can rise just because prices rose. A real value removes the effect of price changes, so that you compare purchasing power. To deflate, use a price index.

real value (in base-year prices) = nominal value / price index x 100

Worked example 3: a real wage

A worker in Country B earns 2,000 a month in the base year (price index 100) and 2,300 in year 5 (price index 109.2).

• Nominal rise: (2,300 - 2,000) / 2,000 = 15.0%
• Real wage in year 5: 2,300 / 109.2 x 100 = 2,106.2 in base-year prices
• Real rise: (2,106.2 - 2,000) / 2,000 = 5.3%

The wage grew by 15% in money terms, but only 5.3% in purchasing-power terms, because prices rose too.

Worked example 4: real GDP growth

Country C has nominal GDP and a price index (base year 1 = 100). All figures are illustrative.

Year	Nominal GDP	Price index	Real GDP (year 1 prices)
1	800	100	800.0
2	860	104	826.9
3	930	110	845.5

• Real GDP year 2 = 860 / 104 x 100 = 826.9
• Real GDP year 3 = 930 / 110 x 100 = 845.5
• Nominal growth: year 2 = 7.5%, year 3 = 8.1%
• Real growth: year 2 = 3.4%, year 3 = 2.2%

Nominal growth overstates the rise in output, because part of it is price inflation. This is why real national income is the better indicator of changes in output.

Choosing which year’s prices

You can express real values in the prices of any year. To state year 3 figures as real values in year 3 prices, multiply each nominal value by 110 and divide by its own index: 880.0, 909.6, 930.0. The growth rates are identical. Only the units change. Always say which year’s prices you use.

A quick rule for real growth

Real growth is approximately nominal growth minus inflation. For exact work, divide the growth factors: 1.09 / 1.06 = 1.0283, so 9% nominal growth with 6% inflation gives 2.8% real growth, not 3%. The approximation is fine for small rates, but exact division is safer when the question wants a specific figure.

Worked example 5: a real price

A small bakery sold a loaf for 2.00 in the base year (index 100) and sells it for 2.40 when the index is 115.

• Nominal price rise: 20%
• Real price: 2.40 / 115 x 100 = 2.09 in base-year prices
• Real price rise: (2.087 - 2.00) / 2.00 = 4.3%

The bakery’s loaf became only a little dearer relative to prices in general.

Linking to evaluation

When a question asks you to assess a claim such as “living standards rose”, build a chain:

1. State the nominal change.
2. Deflate it with the price index to get the real change.
3. Check whether the index suits the people concerned (weights, base year).
4. Note other influences on well-being that real income misses, such as hours worked, inequality or the environment, which the specification stresses for national income.

A short, qualified judgement beats a long list.

Common errors

• Dividing by the wrong year. In an index, the base year value is the denominator, not the previous year.
• Calling a 5-point rise a 5% rise when the starting index is not 100.
• Deflating with the price index of the wrong year, or multiplying instead of dividing.
• Saying a real value “fell” when only the nominal value was checked.
• Treating an index of 120 for one good and 90 for another as meaning the first is dearer. It means its price rose more since the base year.
• Forgetting to state units or the price year for a real value.
• Using weights that do not sum to 100 without dividing by their total.

Official syllabus

OxfordAQA International AS and A-level Economics (9640), specification version 1.2, section 3.5 Quantitative skills (QS5 and QS7), with related content in 3.2.1.2 and 3.2.2.1. First teaching September 2020; first International AS exams May/June 2021; first International A-level exams May/June 2022. Published by OxfordAQA.