Economics
Inflation: Formula, Causes and Effects + 7 Exercises
Inflation = (final index − initial index) / initial index × 100. Learn the causes, types and effects on wages and savings, with tables and 7 solved exercises.
Recommended for: Grade 11 · Grade 12
Inflation is a general and sustained rise in the price level that reduces the purchasing power of money. It is measured as the percentage change in a price index: inflation = (final index − initial index) / initial index × 100. If the price index goes from 200 to 210, inflation is 5%. This guide covers the formula, causes, types, effects and the mistakes students make most often in economics exams.
What inflation is (and what it is not)
Inflation is not the rise in the price of a single good: if oil gets more expensive while everything else stays put, a relative price has changed. We speak of inflation when the general price level rises and the rise lasts over time. A one-off seasonal increase, like tomatoes in winter, is not inflation.
The key consequence is that the same amount of money buys fewer goods. That is why economists always distinguish nominal values (in current dollars) from real values (adjusted for inflation, i.e. expressed in purchasing power).
How it is measured: price indices
In the United States the Bureau of Labor Statistics publishes the Consumer Price Index (CPI) every month. It tracks the cost of a basket of goods and services bought by households, with each item weighted by how much people spend on it. The Federal Reserve’s 2% inflation target is formally set in terms of a related index, the PCE price index.
| Tool | What it measures | What it is for |
|---|---|---|
| Consumer price index (CPI) | cost of an average basket of goods and services | calculating the inflation rate |
| Basket | goods and services with spending weights | representing typical household consumption |
| Year-over-year rate | change compared with the same month a year earlier | annual comparison without seasonal effects |
| Month-over-month rate | change compared with the previous month | spotting short-term trends |
| GDP deflator | prices of everything produced in the country | comparing real and nominal GDP |
The formulas you need
| What you want | Formula | Example |
|---|---|---|
| Inflation rate | (final index − initial index) / initial index × 100 | (210 − 200) / 200 × 100 = 5% |
| Price after inflation | initial price × (1 + π) | 100 × 1.05 = 105 |
| Price before inflation | final price / (1 + π) | 105 / 1.05 = 100 |
| Real value | nominal value / (1 + π) | 1,050 / 1.05 = 1,000 |
| Inflation over several years | (1 + π)^n − 1 | 1.03^5 − 1 ≈ 15.93% |
| Real interest rate (approximate) | nominal rate − inflation | 5% − 3.2% = 1.8% |
| Real interest rate (exact) | (1 + i) / (1 + π) − 1 | 1.05 / 1.032 − 1 ≈ 1.74% |
To estimate how long it takes prices to double, use the rule of 70: years ≈ 70 / percentage rate. At 2% inflation prices double in about 35 years, at 7% in about 10.
Causes: demand-pull, cost-push, expectations
| Type | Mechanism | Example |
|---|---|---|
| Demand-pull inflation | aggregate demand exceeds what the economy can produce, so prices rise | a strong rebound in spending after a recession, with firms unable to keep up |
| Cost-push inflation | the cost of energy, raw materials or labor rises and firms pass it on in prices | a jump in natural gas prices raising utility bills and factory prices |
| Expected inflation | if everyone expects higher prices, workers ask for higher wages and firms raise prices, making the expectation come true | wage bargaining tied to expected inflation |
| Monetary inflation | the money supply grows much faster than the goods available | printing money to finance government spending |
The supply and demand model helps you picture the first two: in demand-pull inflation the demand curve shifts right, in cost-push inflation the supply curve shifts left.
Effects of inflation
| Who | Effect | Why |
|---|---|---|
| Workers on fixed pay | lose purchasing power | nominal wages do not adjust right away |
| People holding idle cash | lose value | cash earns nothing while prices rise |
| Fixed-rate borrowers | gain | they repay money worth less than when they borrowed it |
| Lenders | lose if the rate does not cover inflation | they earn low or negative real interest |
| Firms | uncertainty | planning investment and prices gets harder |
| Exports | may suffer | if domestic prices rise faster than foreign ones, products become less competitive |
There are also the costs of repricing (often called menu costs) and the risk that very high inflation weakens money as a unit of account.
Inflation, deflation, disinflation and related terms
| Term | Meaning | What happens to prices |
|---|---|---|
| Inflation | general rise in prices | rise |
| Disinflation | inflation slows (for example from 8% to 5%) | still rise, but more slowly |
| Deflation | general fall in prices, negative rate | fall |
| Stagflation | high inflation together with weak growth and high unemployment | rise while the economy stagnates |
| Hyperinflation | inflation out of control, usually above 50% a month | soar |
Hyperinflation destroys trust in money. The classic case is Germany in 1923, when prices multiplied within days.
Who keeps inflation in check
In the United States this is the job of the Federal Reserve, which aims for stable prices and maximum employment, with a long-run inflation target of 2%. The main tool is the interest rate: if inflation is too high, the central bank raises rates, borrowing becomes more expensive, spending and investment slow down and prices rise more slowly; if inflation is too low, it lowers them. Moderate inflation is considered normal because it leaves room for monetary policy and avoids the risk of deflation.
Most common mistakes
- Adding rates from different years. 3% for 5 years is not 15% but about 15.93%, because increases compound.
- Subtracting instead of dividing. To find last year’s price you do not take 4% off today’s price: you divide by 1.04.
- Confusing the loss of purchasing power with inflation. With 4% inflation, purchasing power falls 3.85%, not 4%.
- Mixing up disinflation and deflation. If inflation drops from 8% to 5%, prices are still rising.
- Forgetting to go from nominal to real. A 5% interest rate with 5% inflation leaves purchasing power unchanged.
- Believing +10% and −10% cancel out. Starting from 100 you end at 99.
- Using a simple average of price changes. The index uses spending weights: a rise in bread prices matters more than a rise in jewelry prices.
Quick summary
| Concept | Key idea |
|---|---|
| Inflation | general, sustained rise in prices |
| Formula | (final index − initial index) / initial index × 100 |
| Real value | nominal value / (1 + inflation) |
| Real rate | about nominal rate − inflation; exact with Fisher |
| Causes | demand, costs, expectations, money |
| Disinflation | prices rising more slowly |
| Deflation | prices falling |
| Typical remedy | the central bank raises interest rates |
To practice the arithmetic, review the solved exercises on percentages: almost everything needed for inflation is there.
Solved exercises
1. The consumer price index rises from 200 last year to 210 this year. Calculate the inflation rate. base
Show solution
- Use the formula: inflation = (final index − initial index) / initial index × 100.
- Change in the index: 210 − 200 = 10.
- Divide by the starting value: 10 / 200 = 0.05.
- Multiply by 100 to get a percentage: 0.05 × 100 = 5%.
Answer: The inflation rate is 5%.
2. A salary of $1,500 a month stays the same while annual inflation is 4%. What is it worth in last year's dollars, and by what percentage has purchasing power fallen? base
Show solution
- Prices have risen by 4%, so the growth factor is 1.04.
- Real value = nominal value / growth factor = 1,500 / 1.04 = $1,442.31.
- Loss in last year's dollars: 1,500 − 1,442.31 = $57.69.
- Percentage loss: 57.69 / 1,500 = 0.0385, or 3.85%. It is not 4%: the real value comes from dividing by 1.04, not from subtracting 4%.
Answer: It is worth about $1,442.31 in last year's dollars; purchasing power fell by 3.85%, not 4%.
3. A coffee costs $3.90 today. Prices in the sector rose 4% over the past year. What did it cost a year ago? base
Show solution
- Today's price is last year's price times 1.04: old price × 1.04 = 3.90.
- To go back you divide; you do not subtract 4%: old price = 3.90 / 1.04 = $3.75.
- Check: 3.75 × 1.04 = 3.90. Subtracting 4% of 3.90 (0.156) would give 3.744, which is wrong.
Answer: A year ago the coffee cost $3.75.
4. Inflation stays at 3% a year for 5 years. By how much do prices rise in total? What would a rent of $800 a month cost after 5 years, all else equal? intermedio
Show solution
- Increases compound: each year 3% is applied to the already-increased price. Total factor = 1.03^5.
- Calculation: 1.03^5 = 1.159274 (approximately).
- Total increase: 1.159274 − 1 = 0.159274, about 15.93%. The typical mistake is 3% × 5 = 15%.
- Rent after 5 years: 800 × 1.159274 = $927.42.
Answer: Prices rise by about 15.93%; the rent would go from $800 to about $927.42 a month.
5. You put $10,000 in an account paying 5% nominal interest a year while inflation is 3.2%. Find the real interest rate (approximate and exact) and the real value of your balance after one year. intermedio
Show solution
- Approximate formula: real rate ≈ nominal rate − inflation = 5% − 3.2% = 1.8%.
- Exact formula (Fisher equation): (1 + i) / (1 + π) − 1 = 1.05 / 1.032 − 1 = 0.017442, about 1.74%.
- Nominal balance after one year: 10,000 × 1.05 = $10,500.
- Real value (in the purchasing power of a year ago): 10,500 / 1.032 = $10,174.42. The gain in purchasing power is $174.42, not $500.
Answer: Approximate real rate 1.8%, exact about 1.74%; the balance is worth about $10,174.42 in real terms.
6. A household CPI basket has these weights and price changes: food 30% (+6%), housing and energy 40% (+3%), transportation 20% (+10%), other goods and services 10% (+2%). Find the overall inflation rate and the new cost of a basket that used to cost $400. avanzato
Show solution
- Overall inflation is the weighted average of the price changes, using spending weights.
- Food: 0.30 × 6 = 1.8. Housing and energy: 0.40 × 3 = 1.2.
- Transportation: 0.20 × 10 = 2.0. Other: 0.10 × 2 = 0.2.
- Sum: 1.8 + 1.2 + 2.0 + 0.2 = 5.2%. This is not the simple average (6 + 3 + 10 + 2) / 4 = 5.25%, which ignores the weights.
- New basket cost: 400 × 1.052 = $420.80.
Answer: Overall inflation is 5.2%; the basket goes from $400 to $420.80.
7. Edge case 1: a price rises 10% and the next month falls 10%. Does it return to the starting value? By how much would it need to fall? Edge case 2: inflation slows from 8% to 5%. Are prices falling? Starting from an index of 100, find the index after both years. avanzato
Show solution
- Case 1: from 100, +10% gives 110. Then −10% of 110 is 11, so the price is 99. That is −1% compared with 100: the percentages do not cancel because they apply to different bases.
- To get from 110 back to 100 it must fall by 10 / 110 = 0.0909, i.e. 9.09%.
- Case 2: 5% inflation is still inflation, only slower. This is called disinflation. Prices keep rising. Deflation needs a negative rate.
- Index: after year one 100 × 1.08 = 108; after year two 108 × 1.05 = 113.4. The cumulative increase is 13.4%, not 8% + 5% = 13%.
Answer: Case 1: the price ends at 99 (−1%); a 9.09% drop would be needed. Case 2: disinflation, prices still rise; final index 113.4 (+13.4%).
FAQ
How do you calculate the inflation rate?
Compare the consumer price index in two periods: (final index − initial index) / initial index × 100. If the index goes from 200 to 210, inflation is (210 − 200) / 200 × 100 = 5%. Over several years, annual rates are compounded, not added.
What is the difference between inflation and deflation?
With inflation the general price level rises and money buys less; with deflation it falls and money buys more. Disinflation sits in between: prices still rise, but more slowly than before.
Why is inflation bad for savings?
Because the nominal amount of idle money stays the same while its purchasing power falls. At 3% inflation, $10,000 kept in a drawer buys after a year what about $9,709 bought before. What matters is the real interest rate: nominal interest minus inflation.
What causes inflation?
There are three main causes: demand exceeding the economy's productive capacity (demand-pull inflation), higher production costs such as energy and raw materials (cost-push inflation), and expectations, when households and firms expect higher prices and push them up through wages and price lists. Excessive growth in the money supply can also contribute.
Who gains and who loses from inflation?
People on fixed incomes and those holding idle cash lose. Borrowers with fixed-rate debt gain because they repay money that is worth less, and so do owners of assets whose prices rise with inflation. The net effect depends on expected inflation and how quickly incomes adjust.