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

These notes condense 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. Sections 3.1 and 3.2 are International AS content and sections 3.3 and 3.4 are the extra International A2 content, but the two skills here carry no stage label. For full explanations and longer worked examples, read the study guide. Check coverage on the OxfordAQA Economics hub and the printable checklist. All data here are invented. When you finish, test yourself with the practice questions and the free diagnostics.

Definitions

Term	Meaning
Index number	A value expressed as a percentage of its value in a base year
Base year	The reference year, set to 100
Weight	The share of spending (or importance) given to a category in a combined index
Index point	One unit on the index scale
Nominal (money) value	Measured at the prices of the year recorded
Real value	Nominal value adjusted for price changes, so it shows purchasing power
Price index	An index that tracks the general level of prices, such as a consumer price index

Formulas

Task	Formula
Simple index	value in year / value in base year x 100
Percentage change from an index	(new index - old index) / old index x 100
Change in points	new index - old index
Rebase to a new year	old index / old index of new base year x 100
Weighted index	sum of (weight x category index) / sum of weights
Real value (base-year prices)	nominal value / price index x 100
Real growth (exact)	(1 + nominal growth) / (1 + inflation) - 1
Real growth (approximate)	nominal growth - inflation

Method in steps: building an index

1. Pick the base year and set it to 100.
2. Divide each year’s value by the base-year value.
3. Multiply by 100.
4. Check: the base year must show exactly 100.
5. Describe the result as a percentage change from the base, or compare two years by dividing, not subtracting.

Reminder: a bakery’s output is 250 units in the base year and 275 units later. The index is 275 / 250 x 100 = 110, so output is 10% above the base year.

Method in steps: weighted index

1. Multiply each category index by its weight.
2. Add the products.
3. Divide by the total of the weights.

Reminder: weights 60 and 40 with category indices 110 and 95 give (60 x 110 + 40 x 95) / 100 = (6,600 + 3,800) / 100 = 104.0.

A larger weight means a given price change moves the overall index more.

Method in steps: money to real terms

1. Identify the price index and its base year.
2. Divide the nominal value by the index.
3. Multiply by 100.
4. State the price year, for example “in base-year prices”.
5. Compare real values, or work out real growth, to say what happened to purchasing power.

Reminder: nominal income 5,250 with a price index of 105 gives 5,250 / 105 x 100 = 5,000 in base-year prices.

Must-know distinctions

Pair	The difference
Points and percent	A rise from 120 to 138 is 18 points but 15%. Points are measured against 100, percent against the earlier value
Nominal and real	Nominal can rise with prices alone. Real shows what the money can buy
Index and level	An index records change since the base year. It does not show which variable is larger
Weighted and unweighted	Weighted indices reflect how much each category matters
Real growth and nominal growth	Real growth is smaller when inflation is positive
Price level and inflation	The index is the price level. Inflation is its rate of change

More worked reminders

Inflation from an index. A price index rises from 96.0 to 100.8. Inflation = (100.8 - 96.0) / 96.0 x 100 = 5.0%.

Real national income. Nominal national income is 1,200 and the price index is 120 (base year 100). Real national income = 1,200 / 120 x 100 = 1,000 in base-year prices. Nominal figures overstate any rise in output when prices are rising.

Changing the price year. To restate a base-year nominal value of 900 in the prices of a year with index 120, multiply by 120 / 100: 900 x 1.2 = 1,080. To go the other way, divide.

A real price. A product costs 6.00 in the base year and 7.50 when the price index is 125. The nominal price rose 25%. The real price is 7.50 / 125 x 100 = 6.00, so it is unchanged in real terms: it kept pace with prices in general.

Two series, one base. If two indices share a base year, compare their growth by comparing their values in a later year, for example 126 and 138 mean 26% and 38% growth. If the base years differ, rebase one of them first.

Linking to other topics

• Inflation and the price level. An index measures the price level. Its percentage change is inflation. Deflation is a fall in the price level, which shows as a falling index.
• Real and nominal income. Real national income is the better indicator of changes in output. Nominal figures mix output and price changes.
• Living standards. Rising real income suggests higher purchasing power, but it says little about distribution or non-income factors.
• Comparing over time. Rebase series to a common year before comparing growth in different variables.

Interpreting and evaluating

• Base year. An unusual base year (for example a recession) can make later changes look bigger.
• Weights. Out-of-date weights may miss changes in spending patterns.
• Different households. An average index may not fit a household with unusual spending. A household that spends more on a fast-rising category faces a higher personal rate than the average.
• Real is not everything. Real national income is an important indicator, but well-being also depends on factors such as hours worked, inequality and the environment, as the specification points out.
• Chain of reasoning. Nominal change, then price change, then real change, then who is affected, then a judgement about how far the claim holds.

Quick self-test

1. Output is 250 in the base year and 275 later. What is the index?
2. An index falls to 88 from a base of 100. State the change in words.
3. An index rises from 120 to 138. Give the change in points and in percent.
4. Weights 60 and 40, category indices 110 and 95. Find the weighted index.
5. A price index rises from 102 to 107.1. What is the inflation rate?
6. Nominal income is 5,250 and the price index is 105 (base 100). Find the real income.
7. Nominal spending is 4,400 and the price index is 110. Find the real value in base-year prices.
8. Nominal income grows by 5% and prices by 3%. Find real growth (exact, to 1 decimal place).
9. A series has 2010 = 100, 2015 = 125 and 2020 = 150. Rebase it so 2015 = 100.
10. Nominal wages rise 4% while prices rise 7%. What happens to real wages (to 1 decimal place)?
11. A price index for good X is 90 and for good Y is 120, both with the same base year. Is good Y more expensive than good X?

Answers

1. 275 / 250 x 100 = 110.
2. Output (or the variable) is 12% below the base year.
3. 18 points; (138 - 120) / 120 x 100 = 15%.
4. (60 x 110 + 40 x 95) / 100 = 104.0, so 104.
5. (107.1 - 102) / 102 x 100 = 5.0%.
6. 5,250 / 105 x 100 = 5,000.
7. 4,400 / 110 x 100 = 4,000.
8. 1.05 / 1.03 = 1.0194, so real growth is 1.9%.
9. 2010 = 80.0, 2015 = 100, 2020 = 120.0.
10. 1.04 / 1.07 = 0.9720, so real wages fall by 2.8%.
11. Not necessarily. The indices show how much each price has changed since the base year, so Y’s price rose by more. They do not give the actual prices.

Where marks are usually lost

• Showing only a final figure with no formula or working, so a slip leaves your method unclear.
• Dividing by the previous year instead of the base year when building an index.
• Giving index points when the question asks for a percentage change.
• Multiplying by the price index instead of dividing when deflating.
• Not stating the price year for a real value.
• Using the approximation for real growth when the question asks for an exact result.
• Reading an index of 120 and an index of 90 as actual price levels.
• Dropping the division by total weights in a weighted index.
• Concluding that living standards rose from nominal data alone.

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.