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Understand economics at your own pace: step-by-step guided courses, and exercises to practice.
Inflation
When money loses a little of its purchasing power every year.
π = (CPI_t − CPI_t−1) / CPI_t−1 × 100Problem / motivation
Why doesn't €100 today buy as much as €100 did ten years ago?
Because the general price level is rising. This silent erosion has a name: inflation — a lasting and GENERAL rise in prices, not to be confused with one product shooting up: if coffee doubles while nothing else moves, that is not inflation; if almost everything rises a little, it is.
In France, it is INSEE — the national statistics institute — that measures it, tracking prices everywhere people buy: about 140,000 in-store price readings every month, supplemented by supermarket checkout data and hundreds of thousands of prices collected online. The figure regularly makes the headlines, in two forms: each month, the rise in prices compared with the same month a year earlier (the “year-on-year” rate of the newspapers); and as a yearly summary, the average for the year — +5.2% in 2022, +4.9% in 2023, +2.0% in 2024, +0.9% in 2025. But you still need to know how that figure is built — which is what we are about to do.
Assumptions
In your view, which assumptions are needed for this model to hold? Jot down your ideas — no lead is wrong, this is your worksheet.
Your worksheet is still empty. Go for it: propose at least one idea.
0 idea(s) proposedFormalization
Start from a shopping trolley: the typical basket from the assumptions, weighted like an average household's budget. What interests us is its total COST — say €200 in the base year. (A round number to follow the thread; INSEE's real basket aggregates thousands of collected prices.)
Comparing euros from one year to the next is awkward; we prefer a scale on which the base year equals 100. That is exactly what the consumer price index does: CPI = cost of the basket this year ÷ cost in the base year × 100. A basket that went from €200 to €210 gives CPI = 105 — 105 against 100 is 5 more per 100: prices have risen by 5% since the base.
Inflation, however, is not the LEVEL of the index: it is its SPEED. How much has the index gained in a year, relative to what it was at the start? That is the formula of the course — π, the Greek letter “pi”, the Greek equivalent of our P: remember “π for Prices”. We take this year's index (CPI_t), remove the one from a year ago (CPI_t−1), and divide by that starting point.
Always divide by the STARTING index, not by 100 out of habit: from 110 to 114.4, inflation is (4.4 ÷ 110) × 100 = 4%, not 4.4%. (The shortcut “CPI − 100” gives the CUMULATIVE rise since the base year — it coincides with π only when the starting year is the base itself.) And the formula reads both ways: adding 4% means multiplying by 1.04; adding 10%, multiplying by 1.10; adding 2.5%, multiplying by 1.025. Remember this bridge — adding x% means multiplying by (1 + x/100) — it will serve again. Click each term:
Solving / calculation
Let's take the €200 basket of the base year again and run through three years — then handle the prices yourself. (To connect with the notation of the formula: “this year” is year 2, so t = 2, and “last year” is year 1.)
- Base year (convention): the basket costs €200
CPI₀ = 200 / 200 × 100CPI₀ = 100 - Year 1: the basket costs €210 — and here is the first inflation rate (π₁: here t = 1, the starting point is year 0, the base). Starting point = 100: the shortcut “index − 100” happens to be right
CPI₁ = 210 / 200 × 100 = 105; π₁ = (105 − 100) / 100 × 100π₁ = 5% - Year 2: the basket costs €218
CPI₂ = 218 / 200 × 100CPI₂ = 109 - Inflation in year 2: the starting point is now 105, so 105 is what we divide by — certainly not (109 − 100), which would be the cumulative rise since the base (+9%)
π₂ = (109 − 105) / 105 × 100π₂ ≈ 3.8% - Reading it: prices are STILL rising (105 → 109), but more slowly than before (5% → 3.8%). This slowdown in inflation has a name: DISINFLATION5% → 3.8% = disinflation
In passing, your savings: during year 2, a savings account paying 2% earns less than the rise in prices (3.8%). Your NOMINAL rate — the advertised one — is 2%, but your REAL rate — what your purchasing power actually gains — is about 2 − 3.8 ≈ −1.8%: you lose. (An approximation valid as long as inflation stays moderate; the exact formula and all the details live in the course “Inflation and purchasing power”.)
π₂ = (CPI₂ − CPI₁) / CPI₁ × 100Set the three costs of the basket: indices and inflation rates follow. Do compare π₂ — inflation in year 2 — with the cumulative rise since the base: they are two different questions.
Economic interpretation
Positive inflation is not necessarily bad — it is all a question of pace, of duration, and of whom it suits:
On a fixed income, every rise in prices reduces what you can buy — and the effect COMPOUNDS: each rise applies to prices already raised (+10% two years running gives ×1.10 × 1.10 = +21%, not +20%). The widget below shows the mirror image of that mechanism: your €100 must now pay for a basket that has gone to 121, so it is worth only 100 ÷ 1.21 ≈ €82.64 of purchasing power. (We DIVIDE by the coefficient — taking off 21% would give €79, which would be too much.)
Repaying a FIXED-rate loan with euros that buy less lightens the debt in real terms; conversely, savers and incomes that are not INDEXED — those not automatically revalued with prices, unlike the French minimum wage — take the hit. (If inflation is anticipated, lenders raise their rates to compensate, and the advantage evaporates — details in “Inflation and purchasing power”.)
INFLATION: prices rise (π > 0). DISINFLATION: they rise more slowly (π falls but stays positive) — France thus went from +5.2% (2022) to +0.9% (2025) without average prices ever falling. DEFLATION: they fall (π < 0) — the course “What is deflation?” is devoted to it.
The ECB aims for 2% a year (on the euro area's HICP): a margin above zero so as not to brush against deflation, and enough to absorb the index's slight overstatement — the first of the limits below. Measured against the target, France's +0.9% in 2025 reads as “BELOW target”: being under it is not good news in itself. Why prices rise is dealt with in “The causes of inflation”, and their link with unemployment in “The Phillips curve”.
Limits / critiques
Exercises
A basket costs €250 in the base year and €265 a year later. What is the inflation rate (in %)?
The CPI goes from 120 to 118 from one year to the next. What is this phenomenon called?
Beef soars and households switch to chicken. What does the fixed-basket CPI do, compared with the inflation those households actually experience?
True or false: between 2022 and 2025, French inflation went from +5.2% to +0.9% a year — so prices fell over the period.
A savings account at 3% a year, inflation at 5%. Your savings…
The CPI goes from 110 to 114.4 from one year to the next. What is the inflation rate (in %)?
Two years running of inflation at +10%. By how much have prices risen in total (in %)?
The CPI was 104 last year and inflation for the year is 2.5%. What is this year's CPI? (The bridge from the formalisation — adding x% means multiplying — does all the work.)