Actuarial Mathematics for Modelling · Allowing for inflation

Inflation and Price Indices: How CPI and WPI Measure Inflation

Updated 11 October 2026 · Fact-checked

Inflation is a sustained rise in the general price level. A price index measures it by tracking the cost of a fixed basket of goods over time. The inflation rate is the percentage change in the index between two dates: (I(t) ÷ I(t−1)) − 1. CPI and WPI use different baskets, so they give different rates.

Understand Inflation and Price Indices

Inflation is a sustained rise in the general level of prices, so each rupee buys less over time. Actuaries care because many cash flows (pensions, salaries, claims, index-linked bonds) move with prices. To model them, you need a number that measures price change.

A price index gives that number. You pick a basket of goods and services, fix the quantities, and record the cost of the basket each period. You then divide by the cost at a base date and multiply by 100 (or another base value). The index is 100 at the base date. If it reads 125 later, prices of the basket have risen 25%.

The most common form is a Laspeyres index, which uses base-period quantities as weights. Index = Σ(p₁ × q₀) ÷ Σ(p₀ × q₀) × 100. Equivalently, it is a weighted average of price relatives p₁ ÷ p₀, with weights equal to base-period expenditure shares. A Paasche index uses current-period quantities instead.

In India, the Consumer Price Index (CPI) tracks retail prices paid by households. The basket comes from household consumption surveys, and food has a large weight. The Wholesale Price Index (WPI) tracks prices of goods at the wholesale stage, covering primary articles, fuel and power, and manufactured products. WPI generally excludes services and is not what households directly pay. So the two can show different inflation rates. Check the exact current coverage and base year in the material you are given, as these are revised from time to time.

Price indices are imperfect measures of inflation. Fixed baskets go out of date, consumers switch to cheaper goods, quality changes, new products appear, and each person's spending pattern differs from the average. Indices are also published with a lag, which matters when cash flows are linked to them.

Key rules to remember

Inflation rate from an index: i(t) = I(t) ÷ I(t−1) − 1; Use the same base for both index values. Express as a percentage if asked.
Rebasing an index: New index at t = Old index at t ÷ Old index at new base date × 100; Needed when two series have different base dates.
Laspeyres price index: Σ(p₁ × q₀) ÷ Σ(p₀ × q₀) × 100; Base-period quantities as weights.
Paasche price index: Σ(p₁ × q₁) ÷ Σ(p₀ × q₁) × 100; Current-period quantities as weights.
Weighted average of price relatives: Index = Σ w × (p₁ ÷ p₀) × 100, where w = p₀q₀ ÷ Σ(p₀q₀); Same as Laspeyres when weights are base expenditure shares.
Inflation over several periods: Average annual rate j: (1 + j)ⁿ = I(n) ÷ I(0); Compound, not simple, averaging.

How to solve Inflation and Price Indices questions

Use this method for any question on inflation and price indices.

1Identify what is asked: an index value, an inflation rate, a rebased series, or a comment on limitations.
2Write down the index values or the prices and quantities, noting the base date and the dates involved.
3If two series have different bases, rebase one so both equal 100 at the same date.
4For a constructed index, check the weights: base quantities (Laspeyres) or current quantities (Paasche), or expenditure shares.
5Compute the index, then the inflation rate as I(t) ÷ I(t−1) − 1. For several years, use the compound formula.
6State the result with units and the period it covers.
7If asked to comment, link the weakness to the specific data given: substitution, quality change, outdated weights, lag or coverage.

Quickest way: Ratio of index values

When to use it: Use when you are given index values or a basket and need an inflation rate fast, especially in MCQs.

Pick out the two index values or the two basket costs.
Divide the later by the earlier.
Subtract 1 and convert to a percentage.
If the gap is more than one year and an annual rate is wanted, take the nth root before subtracting 1.
Sanity-check: a rising index must give positive inflation.

Common mistakes in Inflation and Price Indices

Taking the difference in index points as the inflation rate.
Index values like 120 and 126 look like percentages.
Fix: Divide the change by the earlier value: (126 − 120) ÷ 120 = 5%, not 6%.
Comparing index values with different base dates.
Two published series look comparable but are not.
Fix: Rebase one series so both equal 100 at the same date before comparing.
Using current quantities in a Laspeyres index.
Confusing Laspeyres with Paasche.
Fix: Laspeyres weights with base quantities (q₀). Write the formula first.
Averaging annual inflation rates with a simple mean.
It is quicker and looks reasonable.
Fix: Use the compound relation (1 + j)ⁿ = I(n) ÷ I(0), or a geometric mean of (1 + i).
Treating CPI and WPI as interchangeable.
Both are called inflation measures.
Fix: State what each covers: CPI is consumer retail prices; WPI is wholesale goods prices, largely excluding services.
Giving generic limitations without linking them to the question.
Students memorise a list.
Fix: Pick two or three limitations that fit the scenario, such as a pensioner whose spending differs from the basket, and explain the effect.

Worked examples

Example 1

A price index was 150.0 at 1 January 2023 and 162.0 at 1 January 2024. (a) Find the inflation rate over 2023. (b) The index was 135.0 at 1 January 2021. Find the average annual inflation rate over the three years to 1 January 2024.

Show the solution

(a) Inflation = 162.0 ÷ 150.0 − 1 = 1.08 − 1 = 0.08.
(b) Total growth over three years = 162.0 ÷ 135.0 = 1.2.
Solve (1 + j)³ = 1.2, so 1 + j = 1.2^(1/3).
1.2^(1/3) ≈ 1.0627, so j ≈ 0.0627.

Answer: (a) 8% for 2023. (b) About 6.27% a year.

Example 2

A basket has two items. Base-year prices and quantities: item A price ₹40, quantity 10; item B price ₹100, quantity 5. Current prices: A ₹46, B ₹110. Find the Laspeyres price index (base = 100) and comment on one limitation.

Show the solution

Base cost = Σ p₀q₀ = 40 × 10 + 100 × 5 = 400 + 500 = ₹900.
Current cost at base quantities = Σ p₁q₀ = 46 × 10 + 110 × 5 = 460 + 550 = ₹1,010.
Index = 1,010 ÷ 900 × 100 = 112.22.
Limitation: base quantities are fixed. If consumers switch from the dearer item to the cheaper one, the index overstates the rise in their cost of living.

Answer: Laspeyres index ≈ 112.2, implying about 12.2% price rise on the base basket. It ignores substitution, so it tends to overstate inflation.

Exam tips

Write the formula before substituting. Examiners give method marks for it.
In CM1 questions, state whether inflation is annual effective and which dates the index values refer to.
For limitation questions, give specific points tied to the scenario rather than a bare list.
Check the base date of every index value given. A rebasing step is a common hidden trap.
Round only at the end. Index ratios are sensitive to early rounding.

Practice questions from Allowing for inflation

Inflation and Price Indices: frequently asked questions

How is the consumer price index calculated in India?

It is built as a weighted average of price changes across a basket of goods and services. The weights come from household consumption surveys, and prices are collected regularly. The index is compared with a base date to give inflation. For exact current weights and base year, use the official source or your study material.

What is the difference between CPI and WPI inflation?

CPI measures retail prices faced by consumers, including food and services. WPI measures wholesale prices of goods and mostly excludes services. So CPI reflects household cost of living, while WPI reflects price pressure earlier in the supply chain.

What are the limitations of a price index as a measure of inflation?

The basket is fixed and ages, consumers substitute, quality changes and new goods are hard to capture, and individual spending differs from the average. Indices are also published with a delay. Mention the ones relevant to the question.

Why do actuaries need price indices?

Many liabilities and assets are linked to inflation, such as pensions in payment, salaries and index-linked bonds. Price indices give the measure used to project and value these cash flows.