A nominal rise in sales can come entirely from higher prices, so the quantity sold may not have changed at all. A real figure removes the price effect and shows the quantity change.
This lesson is part of reading national economic indicators carefully. The method of conversion is taught with income in comparing nominal and real changes. Here the same idea is tested with sales.
Why check the quantity as well as the value?
A value is price multiplied by quantity. If the value rises, either price, quantity or both rose. The index tells you how much of the rise came from price.
When you can, check in units. Units are real, so they show the quantity change without any index.
Worked example: restaurant sales
A fictional restaurant chain reports meal sales of RM2.0 million in Year 1 and RM2.2 million in Year 2. The meal price index is 100 in Year 1 and 110 in Year 2.
Nominal change. (2.2 − 2.0) ÷ 2.0 × 100 = 10%.
Real sales in Year 2. 2.2 ÷ 110 × 100 = RM2.0 million in Year 1 prices.
Real change. (2.0 − 2.0) ÷ 2.0 × 100 = 0%.
Check in units. Suppose an average meal cost RM20 in Year 1 and RM22 in Year 2, because the index rose by 10%. Year 1: RM2 000 000 ÷ RM20 = 100 000 meals. Year 2: RM2 200 000 ÷ RM22 = 100 000 meals.
The same number of meals was sold. The 10% rise in sales is entirely a rise in price.
The mistake that costs marks
The common answer is “sales rose by 10%, so the chain sold 10% more meals”. It is tempting because the table’s headline figure is 10% and it sounds like good news.
The error is to treat a value as a quantity. The contrast below shows where the conclusion goes wrong.
| Step | Wrong | Right |
|---|---|---|
| What the 10% measures | Meals sold | Money value of sales |
| Price effect | Ignored | Index rose by 10% |
| Meals sold | 110 000 | 100 000 |
| Conclusion | More meals sold | Quantity unchanged |
The fix is to write one line before concluding: “This figure is in money terms, so it includes the effect of prices.”
Check yourself
A fictional chain’s sales are RM3.0 million in Year 1 (index 100) and RM3.3 million in Year 2. Find the nominal change. Then find the real change if the Year 2 index is (a) 120 and (b) 105.
Answer
Nominal change: 0.3 ÷ 3.0 × 100 = 10%.
(a) Real sales = 3.3 ÷ 120 × 100 = RM2.75 million. Change = −0.25 ÷ 3.0 × 100 = about −8.3%. Prices rose faster than sales, so the quantity fell.
(b) Real sales = 3.3 ÷ 105 × 100 = RM3.1429 million. Change = 0.1429 ÷ 3.0 × 100 = about +4.8%. Prices rose by less than sales, so the quantity rose.
What to study next
Move to explaining why a rate can fall while the underlying level still rises, then the cluster practice set. The percentage base and index comparison explorer lets you change the index and watch the real figure move.
If you would like a teacher to check your reading of index tables, see online one-to-one Economics tuition.