Technical note: How do you see the contribution of any individual element to inflation?

Assume we have two items, A and B, which are priced at Rs. 100 each, which form an index I that has 40% weight to A and 60% of weight to B.

So I = (0.40 x A + 0.60 x B)

Initially, since A and B are Rs. 100, I = 100.

### Inflation Hits

Let’s say, after one year, A becomes 120 (20% inflation) and B becomes 105 (just 5% higher).

So I = (0.40 x 120 + 0.60 x 105) = 111

The Index has gone from 100 to 111, which is 11% inflation.

### How much of that is contributed by A and how much by B?

We need to find out how much of that 11% inflation was because of inflation in A, and correspondingly so for B. Obviously, both will add up to 11%.

The formula to find out is to take the index change (11 points) and find out how much of those points were because of the change in A and the change in B.

The change in A was Rs. 20 (from 100 to 120). The weight of A is 40%, so the effective index impact is: 20 x 0.40 = 8 points.

Therefore A was responsible for 8 points out of the total 11 point change.

So A’s contribution = 8/11 = 73% of the index change.

Put another way, out of 11% inflation, 8% was because of item A.

By elimination B was the remaining 3%. (But you could calculate it the same way too).

### The Formula

If you’re technically aligned, let’s do a formula.

Let’s call an Item’s index now as ItemIndexNow, and a year ago as ItemIndexLastYear. The item’s weight in the index is ItemWeight .

Let’s call the overall index (of which Item is a component) as OverallIndexNow, OverallIndexLastYear.

Assume all weights add up to 100. You can substitute 100 for whatever items add up to.

Item’s Contribution = (ItemWeight/100) * (ItemIndexNow – ItemIndexLastYear)/OverallIndexLastYear

All item contributions will add up to Inflation in the index itself. For example, An index that is up by 10% may have contributions from its four subitems, each of which contributes 4%, 3%, 2% and 1% respectively.

### Example: CPI Chart.

(You can check this out in a shared Google Spreadsheet I have published)