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Inflation and purchasing power
When prices rise, the same money buys less.
purchasing power = income / price levelProblem / motivation
Your salary hasn't moved this year, but your shopping trolley costs you more. What happened?
With the same €100 note, you fill a trolley today that is a little less full than a few years ago. The money has not disappeared: it is prices that have climbed — that is inflation, the overall rise in prices (the course “Inflation” tells you how it is measured). What your money can actually buy is called purchasing power — and inflation nibbles away at it, gently but surely.
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.
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0 idea(s) proposedFormalization
It all comes down to a division. An income of €1,500 facing a shopping basket at €50: you can afford 1,500 ÷ 50 = 30 baskets. That number of baskets is your purchasing power — what your money REALLY buys. (A measure, not an actual trolley: 21.4 baskets is a perfectly good answer.)
Economists have two words for this. The figure written on your payslip — €1,500 — is your NOMINAL income (“in name”: what is written). What it lets you buy — 30 baskets — is your REAL income. Inflation never touches the first; it eats away at the second. The whole of the rest of the course fits into that pair of words.
A tool for what follows: rising by 10% means multiplying by 1.10 (a €50 basket goes to €55); rising by 2%, multiplying by 1.02. Remember the bridge — +x% is ×(1 + x/100) — it comes from the course “Inflation” and it will do every computation from here to the end.
Hence the formula in the header: purchasing power = income ÷ price level. When the bottom (prices) rises and the top (income) does not follow, the result falls — mechanically. The “price level” is the average price of the basket: the one the consumer price index (CPI) of the course “Inflation” measures for real. Click each term:
Solving / calculation
Let's take the €50 basket and the €1,500 income again, and push prices up by 20% — the bridge from the formalisation does the work. Count the baskets, then the CHANGE in %; then have a go yourself.
- To start with: basket at €50
1500 / 50= 30 baskets - Prices rise by 20%: the basket goes to 50 × 1.20 = €60
1500 / 60= 25 baskets - Baskets lost
30 − 25= 5 fewer baskets - The change in purchasing power, in %: 5 baskets lost out of 30
−5 / 30 × 100≈ −16.7%
Look carefully at the two numbers: prices +20%, purchasing power −16.7% — NOT −20. The two percentages are never symmetric (dividing by 1.20 does not take off 20%): the Interpretation step turns this into a rule. And your income has not moved: the whole loss comes from prices.
purchasing power = income / price levelSet the income, the starting basket, and move prices AND income in %: baskets and the change in purchasing power recompute themselves EXACTLY, compared with the shortcut “income − prices”.
Economic interpretation
Purchasing power tells you what your money is REALLY worth, beyond the figure on display — and the same rule serves for your salary AND your savings.
Salary +2% while prices do +4%: you lose roughly the gap, 2 − 4 ≈ −2% (exactly, via the bridge: 1.02 ÷ 1.04 − 1 ≈ −1.9%). This “just subtract” shortcut holds for SMALL rises. When things climb steeply, divide the coefficients: prices ×2 → purchasing power ÷2, that is −50% — certainly not −100%. That was the 10%/9.1% discrepancy of the poll, and the simulator shows it to you live.
A savings account at 2% during inflation of 3.8% (the example from the course “Inflation”): 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. The same gap as for the salary. And the EXACT formula (the one promised in the course “Inflation”) fits on one line, still using the bridge: real rate = (1 + nominal rate) ÷ (1 + inflation) − 1. Here: 1.02 ÷ 1.038 − 1 ≈ −1.7% — subtracting remains a good approximation as long as inflation is moderate.
Inflation redistributes in silence: repaying a FIXED-rate loan with euros that buy less lightens the real debt — the borrower gains, the lender loses; incomes and savings that are not indexed take the hit. BUT if inflation is ANTICIPATED — expected by everyone — lenders add it to their rates in advance (lending at 2% while expecting 4% inflation would amount to paying for the privilege of lending): the advantage evaporates. Who wins and who loses therefore depends above all on who SAW IT COMING. Why prices rise is the business of the course “The causes of inflation”.
No line on your payslip goes down: each euro simply buys a little less than before, and each year applies to prices already raised. The widget below shows you what becomes of €100 over the years.
Limits / critiques
Exercises
Your income is €1,200 and the basket costs €40. How many baskets can you buy?
Your income stays at €1,500, but the price of the basket goes from €50 to €75. Your purchasing power…
Your salary rises by 2% while prices rise by 4%. Your purchasing power…
Your savings account pays 3% a year; inflation is 5%. What is your approximate REAL rate (in %)?
True or false: if your income and all prices rise by 5%, your purchasing power is unchanged.
Your income is €2,000; the basket goes from €50 to €80. How many baskets do you LOSE?
Prices DOUBLE (+100%) and your income does not move. Your purchasing power falls by…
Inflation takes everyone by surprise at 6% (nobody had anticipated it). Who GAINS?