A nominal change is a change in the value measured in money at the time. A real change removes the effect of price changes, so it shows what the money can actually buy.
This lesson belongs to economic indicators. It builds on interpreting inflation data, because the price index used here is how inflation is measured.
How do you turn a nominal value into a real one?
Choose a base year with a price index of 100. Then divide the nominal value by the index of the later year and multiply by 100. The result is the value in base-year prices.
Check which way to go. If prices rose, the index is above 100, so dividing makes the real value smaller than the nominal value.
Worked example: income in a fictional household
A fictional household earns RM3 000 a month in Year 1, when the price index is 100. In Year 2 the household earns RM3 300 and the price index is 108.
Nominal change. (3 300 − 3 000) ÷ 3 000 × 100 = 10%.
Real income in Year 2. 3 300 ÷ 108 × 100 = RM3 055.56, which is about RM3 056 in Year 1 prices.
Real change. (3 055.56 − 3 000) ÷ 3 000 × 100 = 1.85%, which is about 1.9%.
So income rose 10% in money terms, but the money buys only about 1.9% more. Most of the rise was used up by higher prices. A quick check: 10% minus 8% is 2%, close to 1.9%, so the answer is sensible.
The same rise in another year
Keep the nominal rise at 10% but change the index. The table shows what happens.
| Year 2 index 108 | Year 2 index 115 | |
|---|---|---|
| Nominal income | RM3 300 | RM3 300 |
| Real income | RM3 056 | RM2 870 |
| Real change | +1.9% | −4.3% |
The second column uses 3 300 ÷ 115 × 100 = RM2 869.57, which rounds to RM2 870. Against 3 000, the change is (2 869.57 − 3 000) ÷ 3 000 × 100 = −4.35%, written here as about −4.3%.
The nominal rise is identical in both columns. Only the price index changed, and it decided whether the household gained or lost.
The mistake that costs marks
A common answer is “income rose by 10%, so the household is 10% better off”. It reads the nominal figure as if it were the real one.
The fix is to ask two questions before any conclusion. What happened to the money value? What happened to prices over the same period? Without the second question, the first answer cannot say anything about what the money buys.
Another slip is to multiply by the index instead of dividing. A quick sanity check catches it: if prices rose, the real value must be smaller than the nominal value.
Check yourself
A fictional wage is RM2 500 in Year 1 (index 100) and RM2 650 in Year 2. Find the nominal change. Then find the real change if the Year 2 index is (a) 104 and (b) 110.
Answer
Nominal change: 150 ÷ 2 500 × 100 = 6%.
(a) Real wage = 2 650 ÷ 104 × 100 = RM2 548.08. Change = 48.08 ÷ 2 500 × 100 = about +1.9%.
(b) Real wage = 2 650 ÷ 110 × 100 = RM2 409.09. Change = −90.91 ÷ 2 500 × 100 = about −3.6%.
The same 6% nominal rise is a real gain in (a) and a real loss in (b), because prices rose by less than 6% in (a) and by more in (b).
What to study next
Go on to reading growth indicators if you have not done it, or read distinguishing nominal change from real change in a fictional index example for a second example. Test your index arithmetic with the percentage base and index comparison explorer, then use the indicators practice set.
If a teacher checking your conversions would help, see online one-to-one Economics tuition.