Splitting a change in revenue into the price effect and the volume effect: the index method on the example of one shop
A shop's revenue rose by 2 million soum in a month. Is that because it sold more, or because prices went up? Value, price and volume indices on the example of three goods, how they are linked, and why two ways of calculating give two different answers.
Malika, the owner of the «Doston» grocery shop, compared her September and October revenue and was pleased: it rose from 22.6 million to 24.63 million soum. But in October flour and sugar became more expensive. Indices will show how much of the growth came from prices and how much from sales volume.
Key rules
- Notation: p0, q0 are the price and quantity in the base period (September); p1, q1 are the price and quantity in the current period (October)
- Value (revenue) index = Σp1q1 : Σp0q0. It shows the overall change, not its cause
- Paasche price index = Σp1q1 : Σp0q1: it keeps the current-period quantities as they are and changes only the price
- Laspeyres volume index = Σp0q1 : Σp0q0: calculated at base prices, it shows only the change in quantity
- Their product is exactly equal to the value index. The absolute increase also splits in two: the price effect Σp1q1 − Σp0q1 and the volume effect Σp0q1 − Σp0q0
- If you swap the order (Laspeyres price index × Paasche volume index), the product again gives the value index, but the factors' shares change. Write down which method you chose and apply the same method every month
- An individual index for a single product (p1 : p0) does not give the overall picture: products are combined with a "weight" according to their share in revenue
Example: the «Doston» shop, three goods
Prices in soum; amounts are hypothetical and compiled by the author.
| Product | p0 | p1 | q0 | q1 | p0q0 | p1q1 | p0q1 |
|---|---|---|---|---|---|---|---|
| Flour, kg | 8 000 | 9 000 | 1 200 | 1 100 | 9 600 000 | 9 900 000 | 8 800 000 |
| Sugar, kg | 14 000 | 15 400 | 500 | 450 | 7 000 000 | 6 930 000 | 6 300 000 |
| Tea, pack | 20 000 | 20 000 | 300 | 390 | 6 000 000 | 7 800 000 | 7 800 000 |
| Total | 22 600 000 | 24 630 000 | 22 900 000 |
Calculation: - revenue index: 24 630 000 : 22 600 000 = 1.0898, that is +8.98% (absolute increase of 2 030 000 soum); - Paasche price index: 24 630 000 : 22 900 000 = 1.0755, that is +7.55% due to prices; - Laspeyres volume index: 22 900 000 : 22 600 000 = 1.0133, that is +1.33% due to volume; - check: 1.0755 × 1.0133 ≈ 1.0898.
| Factor | Absolute effect, soum |
|---|---|
| Change in prices: 24 630 000 − 22 900 000 | +1 730 000 |
| Change in volume and product mix: 22 900 000 − 22 600 000 | +300 000 |
| Total | +2 030 000 |
In the second method we value the September quantities at October prices: Σp1q0 = 1 200 × 9 000 + 500 × 15 400 + 300 × 20 000 = 24 500 000. Then the price effect is 24 500 000 − 22 600 000 = 1 900 000 and the volume effect is 24 630 000 − 24 500 000 = 130 000 soum. The total is again 2 030 000, but the split is different.
The takeaway for Malika: most of the growth came from prices. Less flour and sugar was sold (1 200 → 1 100 kg and 500 → 450 kg); sales were lifted only by tea, whose price did not change. If prices rise again, there is a risk that customers will leave.
Test yourself
5 questions on this topic: pick an option or reveal the answer.
For a confectionery workshop's sales: the price index is 108% and the physical volume (quantity) index of products sold is 125%. What is the sales value (revenue) index?
A shop's revenue was 80 mln soum last year and 100 mln soum this year. What is the growth rate (dynamics index)?
A tea shop calculated the linear correlation coefficient between advertising spending and weekly sales: r = 0.9. What share of the variation in sales does the coefficient of determination (r²) explain as linked to advertising?
In the current month a canteen bought 30 kg of meat (the price rose from 80 000 to 88 000 soum) and 100 kg of carrots (the price rose from 5 000 to 6 000 soum). What is the aggregate price index weighted by current-period quantities (Paasche formula: Σp1q1 / Σp0q1)?
A teahouse's revenue in 2025 was 120% of 2024, and in 2026 it was 110% of 2025. What percentage of 2024 is the 2026 revenue (base index)?
Answered: 0 / 50 of 5 correct
All tests →See also
Sources
- Fundamentals of statistics (general concepts) · individual and aggregate indices; Laspeyres and Paasche indices; the value index equals the product of the price and volume indices; splitting the absolute increase by factor
- Example, shop name, prices, quantities and calculations · compiled by the author, hypothetical