Inflation and the Phillips curve · Lesson 1 of 12
Measuring inflation: price indices and the inflation rate
Every lesson after this one leans on a single number, the inflation rate. Before asking what causes it, what it costs, or how it trades off against unemployment, we need to know how a statistician turns millions of prices into one figure, and what that figure leaves out.
A question to hold on to
“Inflation increases the average level of prices.” Which of the following is (are) necessarily implied by this statement? (i) The prices of commodities exceed income. (ii) Money supply grows at a higher rate than the real GDP. (Only (i); only (ii); both; neither.)
GATE 2021Solved at the end ↓
The idea
From many prices to one number
Prices do not all move together. In a year when rice gets 5% dearer and phones get 10% cheaper, did the “price level” go up or down? To answer, a statistician fixes a basket of goods and services, prices it in a base year and prices it again now. The ratio, times 100, is a price index. The base year is 100 by construction.
A price index (Laspeyres form)
p is a price and q a quantity in the base year (0). The same basket, priced at today's prices (1), over what it cost then.
Inflation is the percentage change in a price index from one period to the next, so the earlier period is the denominator (Hyderabad 2021):
The inflation rate
The index itself is not the rate. An index that goes from 120 to 132 means inflation of 10%, not 132% or 32%.
Two points to hold on to. First, inflation is a change in the average level of prices, so it is about absolute prices, not relative ones (Hyderabad 2014): if every price but one stays put and that one rises, relative prices have changed and the index barely moves. Second, an index is only as good as its basket. Change the weights and you change the answer, which is the subject of the next two chapters.
Pause and predict
A price index was 120 last year and is 132 this year. Inflation is
The three you will meet
Three indices, three baskets
Exam papers use three price indices. They differ in what they price and in whose basket they use.
| Index | What it prices | Weights | Use |
|---|---|---|---|
| Consumer price index (CPI) | What households buy, at retail prices, including imported goods and services | A fixed basket from a base year (Laspeyres in form) | The usual headline measure of inflation for households |
| Wholesale price index (WPI) | Goods at the wholesale stage, before retail. Goods only: no services | A fixed basket from a base year | Price pressure earlier in the supply chain |
| GDP deflator | Everything produced in the country: consumer goods, investment goods, government services and exports. Imports are not in it | The current year’s output (Paasche in form): the basket changes every year | Turning nominal GDP into real GDP |
Two consequences follow. When an imported good such as oil gets dearer, the CPI rises but the GDP deflator does not (the good is not produced at home); and when the price of a machine rises, the deflator moves but the CPI does not (households do not buy it). The two are close but never equal.
The Laspeyres and Paasche forms differ only in which year’s quantities weight the prices. Laspeyres uses the base year’s quantities, Paasche the current year’s:
Paasche index
Today's basket, priced today and at base prices. The deflator is of this kind. Fisher's ideal index is the geometric mean of the two.
Interactive
Try it: a basket
A basket of four invented goods. Start with the food shock: rice and vegetables get dearer, nothing else changes. Move the switching slider and watch the two indices part. Then tick and untick the goods that count as “core”.
An invented basket (every figure is illustrative): rice, vegetables, cooking fuel and everything else, with the base-year prices and quantities in the table. Press a case, then move any price. The switching slider says how much households buy less of what got dearer.
| Good | Base price | Price now | Base qty | Qty now | Weight | Adds | Out of core |
|---|---|---|---|---|---|---|---|
| Rice | 40 | 52 | 10 | 8.77 | 33.9% | 10.17 points | |
| Vegetables | 30 | 42 | 6 | 5.07 | 15.3% | 6.1 points | |
| Cooking fuel | 100 | 100 | 2 | 2 | 16.9% | 0 points | |
| Other goods and services | 50 | 50 | 8 | 8 | 33.9% | 0 points |
Laspeyres (the CPI’s way)
Index 116.27. The base-year basket now costs 116.27% of what it did, so inflation is 16.27%. The four bars add up to exactly this.
Paasche (the deflator’s way)
Index 115.06, so 15.06%. Lower than Laspeyres: households moved toward what got cheaper, which the base-year basket ignores.
Fisher’s ideal index
Index 115.66, the geometric mean of the two, so 15.66%. It always lies between them.
Headline against core
Headline (all four goods) 16.27%. Core, leaving out the goods you ticked, 0%. Rice up 30% and vegetables up 40%, everything else flat. Headline inflation jumps; core, which leaves food and fuel out, does not move.
Why the two differ. When a price rises, households buy less of that good and more of its cheaper rivals. The Laspeyres basket ignores the shift and keeps pricing the old quantities of the dear good, so it overstates the rise in the cost of living; the Paasche basket prices the new quantities and understates it. With no switching (slider at 0) the two agree. When every price rises by the same percentage they agree whatever households do. The gap between a fixed-basket CPI and the true cost of living is called substitution bias.
Pause and predict
Households respond to a price rise by buying less of the dearer good. Compared with the Paasche index, the Laspeyres index shows
Signal and noise
Headline and core
Headline inflation is the rate for the whole basket. Core inflation takes out the items whose prices swing most, notably food and energy (CUET 2020, 2025), to show the slower underlying pressure on prices. A bad monsoon can lift vegetable prices for a few months and then reverse; nobody’s wages or rents move with it. Core tells you whether a jump in headline is a spike or a trend.
The lab shows it: leave the food shock on and core stays put while headline jumps; switch to broad pressure and core runs ahead of headline. Core is not “food and energy prices only”, which is a wrong option in the exam: it is the inflation rate with those items removed. Be careful too that different published series remove different things (some leave out food only, others food and fuel), so the exam’s answer is the idea, not a fixed list.
A real basket
India's basket: where inflation comes from
A basket’s weights decide how much each price matters. Here are the twelve divisions of India’s consumer price index with their 2024-base weights, as stored in our India Atlas (the weights are the share of household spending at the base and add to 100.01 only because of rounding).
Food and beverages36.8%
Housing and fuel17.7%
Transport8.8%
Clothing6.4%
Health6.1%
Personal care and jewellery5.0%
Household goods4.5%
Communication3.6%
Restaurants and hotels3.4%
Education3.3%
Tobacco and paan3.0%
Recreation1.5%
Food and beverages carry 36.75% of the weight, housing and fuel 17.67% and transport 8.8%. Each division’s contribution to headline inflation is, to a good approximation, its weight times its own price change. So if food prices alone rose by 10% and nothing else moved, headline inflation would be about 36.75% × 10% = 3.67 percentage points. This is why India’s inflation swings with vegetables and pulses, and why the central bank pays close attention to core.
The exact month-by-month split, with each division’s contribution adding up to the headline rate, is in the Atlas: the inflation waterfall, with the series behind it on the CPI inflation page and the core inflation page. Those pages carry the latest month and their sources; this lesson quotes no current rate because it would go out of date.
Using an index
Deflating: from nominal to real
A price index is also how we compare money amounts across years. Divide a nominal amount by the index (as a fraction of 100) to express it at base-year prices. For GDP the index is the deflator:
Nominal to real
Nominal GDP of 1,500 with a deflator of 125 is real GDP of 1,200 at base-year prices. The deflator is nominal over real, times 100.
The same step turns a wage, a pension or a price into “constant rupees”. It also gives the rule for real interest rates, which Lesson 4 takes up, and it is the reason that GDP growth and inflation in the national accounts are two halves of one calculation: nominal growth is, roughly, real growth plus inflation.
The three things to carry on
An index is a basket’s cost against a base year; inflation is its percentage change over the earlier year; and the answer depends on whose basket it is, which is why the CPI, the WPI and the deflator never agree exactly.
Traps
What examiners are fishing for
Watch out for
The mistakes examiners are fishing for
- The denominator. Inflation divides by the earlier price level. One of the wrong options in the exam divides by the later level (Hyderabad 2021).
- Index against rate. An index of 110 means prices are 10% above the base year, not that inflation is 110%.
- Percentage points against percent. Inflation rising from 4% to 6% is a rise of 2 percentage points, and a 50% rise in the rate.
- Absolute against relative prices. Inflation is the average level rising. A change in one price relative to the others is not inflation (Hyderabad 2014).
- Core is not food and energy. It is inflation without them (CUET 2020).
- Falling inflation is not falling prices. Inflation going from 8% to 5% means prices are still rising, more slowly. Lesson 4 gives the names: disinflation and deflation.
Worked questions
Worked questions
GATE 2021 · advanced (the opening question)
“Inflation increases the average level of prices.” Which is necessarily implied: (i) prices of commodities exceed income; (ii) money supply grows faster than real GDP?
- Test (i).Prices and income are different kinds of quantity, and nothing in a rising average price level says one exceeds the other. Not implied.
- Test (ii).In the quantity theory, MV = PY. With velocity V constant, the growth rate of prices is the growth of money less the growth of real output, so a rising price level goes with money outgrowing real GDP.
- Read the key.The official key is B, only (ii).
Answer
B, only (ii). The keyed answer follows the quantity theory and so needs velocity to be constant. If velocity rose, or a supply shock lifted costs, prices could rise without money outgrowing output, which is why the word “necessarily” is strong. Lesson 3 returns to this.
Hyderabad 2021 · foundation
The aggregate price level at time t is CPIt. The inflation rate from t − 1 to t is defined as?
- Change over the earlier level.πt = (CPIt − CPIt−1) / CPIt−1.
- Reject the others.Dividing by CPIt uses the later level; the options with CPIt+1 look a period ahead.
Answer
The first option: the change divided by last period’s level.
CUET 2025 · foundation
Which of the following is excluded from headline inflation to arrive at core inflation: energy prices, gold prices, automobile prices or share prices?
- Recall what core drops.The volatile items, notably food and energy.
- Match to the options.Only energy prices appear among them.
Answer
Energy prices.
Revise
The lesson on one screen
The lesson on one screen
- Price index
- The cost of a fixed basket against a base year, base = 100.
- Inflation rate
- (P_t − P_{t−1}) / P_{t−1}: the change in the index over the earlier level.
- CPI, WPI, deflator
- Households' basket; wholesale goods only; everything produced at home, with current weights.
- Laspeyres, Paasche
- Base-year quantities, current quantities. Laspeyres overstates when households switch; Fisher is the geometric mean.
- Core
- Inflation without the volatile items, notably food and energy: the trend, not the spike.
- A division's contribution
- About its weight times its own price change; the pieces add to headline.
- Nominal to real
- Divide by the index over 100. Deflator = nominal over real, times 100.
Practice
Check yourself
Quick questions
1The CPI was 150 last year and 159 this year. Inflation is
2The index that weights prices by the current year's quantities is
3Households switch toward goods that have become cheaper. The Laspeyres index, compared with the true rise in the cost of living, tends to
4Inflation falls from 8% to 5%. The price level is
5Core inflation is the inflation rate
Numerical problems
Inflation from an index
A price index rises from 200 to 214. What is the inflation rate, in percent?
Real GDP from the deflator
Nominal GDP is 1,500 and the GDP deflator is 125. What is real GDP, at base-year prices?
A division's contribution
Food and beverages carry 36.75% of the CPI weight. If food prices rise by 10% and every other price is unchanged, by about how many percentage points does headline inflation rise?
A Laspeyres index
Base year: good A costs Rs 2 and she buys 10; good B costs Rs 5 and she buys 4. Now A costs Rs 3 and B is still Rs 5. What is the Laspeyres inflation rate, in percent?
Real questions
Past papers, by level
Foundation
Definitions, formulas and one-step problems. Most CUET, UGC NET and Hyderabad questions on this topic sit here.
3 questionsPractise →
Standard
Statements to judge, matching lists and calculations with several steps, up to the hardest JNU, JAM and GATE questions.
2 questionsPractise →
All 5 past-paper questions for this lesson, easiest first: practise the full set →
These are questions from the TestStop bank. A free account answers 10 a day, each with its worked solution; All-Access opens every set with no daily limit.
Read next
All resources →MacroeconomicsMeasuring unemployment: labour force, participation rate and the types of unemploymentEmployed, unemployed and outside the labour force, the unemployment rate and its denominator, participation and worker ratios, frictional, structural and cyclical unemployment, and the steady state of job flows.MacroeconomicsMacroeconomics 2: real and nominal GDP and the deflatorBase years, real growth, the GDP deflator against the CPI, stocks and flows, comparing countries, and how to read the national accounts tables JNU sets.MacroeconomicsInflation, unemployment and the Phillips curve: a module from price indices to the natural rateA module in twelve lessons: measuring inflation and unemployment, the causes and costs of inflation, the original and expectations-augmented Phillips curves, Okun's law, wage-setting and price-setting, supply shocks, disinflation, the curve in real data, and a lesson of Delhi School problems. With labs, worked questions and graded past papers.