- Measuring inflation
- Real and nominal GDP
- Percentage problems: interest · coming soon
Two neighbours, one inflation
Rosa and Tendai (invented) live on the same street. At the start of a year, Rosa puts $50 000 of savings in a bank account that pays 1% interest. On the same day, Tendai borrows $50 000 to buy a small flat. He agrees to repay it, with 3% interest, at the end of the year.
During the year, prices rise by 10%. Nobody expected it.
At the end of the year, Rosa has $50 500. But prices are 10% higher, so her money buys only what dollars bought at the start. She has lost about $4 091 of buying power, and she did nothing wrong. Tendai repays $51 500. In start-of-year prices, that is worth only about $46 818. He borrowed $50 000 of buying power and paid back less than that.
Many people say that inflation makes everyone poorer. This example shows something different: inflation quietly moves buying power from some people to others. The last lecture promised to ask who gains and who loses. This lecture answers it, and explains why.
Money amounts and buying power
The lecture on real and nominal GDP separated an amount of money from what it can buy. The same idea works for savings, a debt, a wage or a pension. With a price index whose base period is 100:
Suppose the price index rises from 100 to 125. Then $10 000 buys what dollars bought in the base period. Its buying power has fallen by a fifth.
Now apply this to interest. The interest rate written on a savings account or a loan is the nominal interest rate. What matters to a saver is the real interest rate: how much more the money can buy after a year. As in the GDP lecture, you divide growth factors.
Rosa's account: . So her real interest rate was about . The shortcut "nominal rate minus inflation" gives . The shortcut is close when the rates are small, and it gets worse as they grow.
The real interest rate measures the change in buying power: , where is the nominal interest rate and is the inflation rate.
When inflation is higher than the interest rate, the real interest rate is negative. Savers lose buying power, and borrowers repay less buying power than they received.
Lenders lose, borrowers gain
Look again at Tendai. A debt is a promise to pay a fixed amount of money. Inflation does not change the amount, but it does change what the amount is worth. So when prices rise, every debt written in money shrinks in real terms.
Suppose someone owes $200 000 for five years, and prices rise by 5% each year. After five years the price level is times higher. So the $200 000 is worth only about dollars in the prices of the first year. The borrower pays nothing extra, and the real debt is about $43 000 smaller.
Every debt has two sides. What the borrower gains, the lender loses. The buying power moves from the people who are owed money to the people who owe it. That is why economists say that inflation redistributes income and wealth.
The surprise is what moves the money
This is the hard part of the lecture. Spend time here. If inflation always helps borrowers, why would anyone lend?
The answer is that lenders are not foolish. Suppose a lender wants to earn 3% a year in real terms, and everyone expects 10% inflation. Then the lender will ask for about interest. If inflation does turn out to be 10%, the real interest rate is exactly the 3% both sides planned. Nobody gains and nobody loses. This idea, that the nominal interest rate includes the inflation people expect, is named after the American economist Irving Fisher.
So it is not inflation itself that moves buying power. It is unexpected inflation: the gap between the inflation people planned for and the inflation that happened. Rosa and Tendai lost and gained because 10% was a surprise. Try the gap yourself.
A lender lends $10 000 for 5 years, repaid at the end with interest. The lender wants 2% a year in real terms, so the interest rate is set to cover the inflation that both sides expect. Choose the expected inflation, then the inflation that actually happens. Watch where the buying power goes. (An invented loan.)
Try:
An invented $10 000 loan for 5 years. The interest rate covers 2% real return plus the inflation expected. The table shows the real value of the repayment, in the prices of the day the loan was made.
- 5% expected, 5% happens. Interest rate 7.1%. The repayment is worth $11 041 in old prices, exactly as planned. No one gains.
- 2% expected, 10% happens. Interest rate 4.0%. The repayment is worth only $7 569. The borrower gains $3 472 of buying power.
- 8% expected, 2% happens. Interest rate 10.2%. The repayment is worth $14 693. The lender gains $3 652 of buying power.
What should you have seen? Whenever the two sliders matched, the lender got exactly the planned $11 041 of buying power, however high inflation was. When inflation was higher than expected, the borrower gained. When it was lower, the lender gained. That is it. That is the whole idea of this lecture. Inflation moves buying power when an amount is fixed in money and the inflation was not expected.
Two countries have had 6% inflation every year for ten years. In one of them, it has never been above or below 6%. In the other, it has been 0% in some years and 12% in others. In which country does inflation move more buying power between lenders and borrowers?
Show the answer
The second. In the first country everyone expects 6%, so it is built into every interest rate and wage deal. In the second, inflation keeps surprising people in both directions, so lenders and borrowers keep gaining and losing. The level of inflation matters less than how predictable it is. This is one reason central banks try so hard to keep inflation steady and to be believed.
Who else loses: fixed incomes, slow pay and cash
The same idea, an amount fixed in money, explains the other losers.
Workers whose pay rises late. Pay is usually agreed once a year. When prices jump between pay rises, real pay falls. In the United Kingdom, average regular pay fell by 3.0% in real terms in the year to April–June 2022, the largest fall since comparable records began in 2001 (ONS, August 2022). The fall was not shared equally. In July–September 2022, regular pay grew by 6.6% in the private sector but by only 2.2% in the public sector (ONS, November 2022). Workers whose pay was set slowly fell further behind.
People on benefits and pensions with a time lag. The measuring-inflation lecture showed that UK benefits rise each April with the CPI of the September before. In April 2022 they rose by 3.1%, the CPI rate for September 2021, while CPI inflation was 9.0% (DWP, 2022 and 2023). For a year, their real value fell. In April 2023 they rose by 10.1% and caught up. Indexation protected these households in the end, but the lag left them a year behind.
People holding cash. Notes and coins earn no interest, so cash loses buying power at the rate of inflation. People respond by holding less cash and moving money more often. Economists call this effort the shoe-leather cost, from the picture of walking to the bank more often.
Who gains? Borrowers with fixed-rate debts, as long as their incomes keep up with prices. Owners of houses often see their prices rise with inflation. And one borrower is larger than all the rest.
The largest borrower of all: the government
Governments borrow by selling bonds. A bond with a fixed interest rate is a debt fixed in money. So unexpected inflation cuts the real value of government debt, and the people who hold the bonds pay for that gain.
There is an exception, and the UK in 2022 shows it. About a quarter of UK government debt, £503.7 billion in March 2022, was in index-linked gilts (ONS). These bonds pay interest, and repay their value, in line with the RPI. In June 2022 the interest the UK government owed on its debt was £19.4 billion in a single month. That was the highest since monthly records began in 1997, and £16.7 billion of it came from the rise in the RPI (ONS, July 2022). On index-linked debt, inflation gives the government no gain at all. The lenders are protected, so the cost stays with the government.
Sort the cases below, using one test for each: is the amount fixed in money, and was the inflation expected?
Inflation turns out higher than people expected. Put each person or organisation in a box. Read the reason after each choice.
Each case, with where it belongs and why, when inflation turns out higher than expected.
- Gains: a family repaying a fixed-rate mortgage (the debt is fixed in money); a government that borrowed with fixed-interest bonds (its debt shrinks in real terms).
- Loses: a retired teacher with a fixed private pension; the bank that lent the fixed-rate mortgage; a household keeping cash at home.
- Loses: a worker whose pay rises 4% when prices rise 9%. Real pay falls by about 4.6%.
- Neither: a pensioner whose pension rises every month with the price index; an investor holding index-linked bonds; a lender whose interest rate already included the inflation that happened.
Tax that rises without a vote
Income tax is usually charged on income above a threshold. If the threshold is a fixed amount of money, inflation raises taxes by itself. Pay rises with prices, so more of each person's income is above the threshold, and more people cross into higher tax bands. Their real income has not grown, but their real tax bill has. This is called fiscal drag, or "bracket creep".
Lina earns $30 000. Income above a tax-free allowance of $12 000 is taxed at 20%. Prices rise by 10% and her pay rises by 10% to $33 000, but the allowance stays at $12 000. What happens to her real tax bill?
Before: tax = dollars, which is 12% of her pay.
After: tax = dollars, which is about 12.7% of her pay.
In old prices her new tax is dollars. So her real tax rose by about 6.1%, while her real pay did not change at all.
Check: if the allowance had risen by 10% to $13 200, her tax would be , and . ✓ Her real tax would not have changed.
A real case: freezing tax thresholds (UK, 2021 onwards)
The policy. In March 2021 the UK government froze the income tax personal allowance at £12 570 and the higher-rate threshold at £50 270, from 2022–23 to 2025–26. By law these amounts normally rise with inflation each year.
The prediction. The Office for Budget Responsibility (OBR) estimated that the freeze would raise about £8.2 billion in 2025–26, and bring about 1.3 million more people into income tax (OBR, March and October 2021). That forecast assumed low inflation: 1.9% in 2022–23 (IFS, 2026).
What happened. Inflation in 2022–23 reached 10.0% (IFS, 2026). The higher inflation and pay growth made the same freeze far larger. The freeze was extended, first to 2027–28 and then to 2030–31. By November 2025 the OBR estimated the effect of all the threshold freezes since 2022–23. By 2030–31 they would bring 5.2 million more people into income tax, and move 4.8 million more into the higher rate (OBR, November 2025). In 2026–27, the allowance would be £16 070 if it had risen with inflation since April 2021 (IFS, August 2026).
The verdict. A frozen threshold is a tax rise whose size is decided by inflation, not by a vote. With low inflation the freeze was modest. When inflation surprised everyone, the same decision became one of the largest tax rises in decades. Unexpected inflation moved buying power from taxpayers to the government.
Costs that do not move to anyone
Not every effect of inflation is a transfer. Some are pure losses, where nobody gains.
- Menu costs. Firms spend time and money changing prices: price lists, websites, labels and computer systems. Each change is small, but across a whole economy it adds up.
- Shoe-leather costs. Time spent managing money to avoid holding cash.
- Uncertainty. When future prices are hard to predict, lenders ask for extra interest to cover the risk. Firms find it harder to judge whether an investment will pay, so they invest less, and capacity grows more slowly.
There is also an effect on trade. If a country's prices rise faster than its trading partners' prices, its goods become dearer abroad.
Country A has 10% inflation. Its main trading partner has 2%. The exchange rate does not change. By how much do A's goods become dearer compared with its partner's?
Divide the growth factors: . So A's goods become about 7.8% dearer. Exports tend to fall and imports to rise.
For A's goods to cost the same as before, A's currency would have to buy about 7.3% less foreign currency: . That fall makes imports dearer. The last lecture showed how a falling currency pushes prices up again, through imported inflation.
Check: . ✓
When money stops working: hyperinflation
At very high rates, inflation stops being a transfer and becomes a collapse. Economists usually call it hyperinflation when prices rise by more than 50% in a month.
In Germany, prices rose by about 29 500% in October 1923 alone, so they doubled about every 3.7 days (Hanke and Krus). Savings built over a lifetime became worthless, and debts could be repaid with almost worthless paper. A new currency was introduced in November 1923.
In Zimbabwe, the peak came in mid-November 2008, with an estimated monthly rate of 79.6 billion per cent (Hanke). Prices doubled about every day. In 2009 the country stopped using its own currency, and people used foreign currencies, such as the US dollar, instead.
Both cases had the same root. A government paid its bills by creating money, and people stopped believing the money would keep its value. Then buying power is not moved from one group to another. It is destroyed.
Three classic mistakes
Moderate inflation mainly moves buying power. For every lender who loses, a borrower gains. The real costs, such as menu costs and uncertainty, exist, but a strong answer separates them from the transfers and names who gains as well as who loses.
"Nominal minus inflation" is only a shortcut. With 50% interest and 40% inflation, the real rate is , not 10%. Divide the growth factors.
Only from inflation that was not expected, and only on debts with a fixed rate. If the inflation was expected, it was built into the interest rate. If the loan has a variable rate, the interest rate can rise with inflation, and the borrower may lose.
Work each one on paper first. Open a hint only when you are stuck.
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Kwame keeps $20 000 in a savings account paying 2% interest for one year. Inflation is 6%. Find the money amount at the end of the year, its real value in start-of-year prices, and the exact real interest rate. Compare with the shortcut.
Hint 1
First find the money amount. Then divide by the growth factor of prices.
Hint 2
The real interest rate is .
Full answer
Money amount: dollars. Real value: dollars. Real interest rate: . The shortcut gives , close because the rates are small. Check: . ✓
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People expected 3% inflation, but it turned out to be 8%. Who gains, who loses and who is protected? (a) A borrower with a one-year loan at a fixed 5%. (b) A worker whose contract raises pay each month in line with the price index. (c) Someone with $5 000 in an account paying no interest.
Hint 1
For each one, ask: is the amount fixed in money, and does it adjust when prices rise?
Hint 2
Use for (a) and (c).
Full answer
(a) Gains. The real rate is , instead of the planned . (b) Protected: pay keeps up with prices month by month. (c) Loses: , so the money buys about 7.4% less. Check (a): the lender, on the other side, loses exactly what the borrower gains.
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A tax-free allowance of $10 000 is frozen for 3 years. Prices and pay both rise by 8% a year. Ali earns $25 000 at the start, and income above the allowance is taxed at 20%. By what percentage does his real tax bill rise? What would it be if the allowance rose with prices?
Hint 1
After 3 years, pay is .
Hint 2
Find the new tax, then divide it by to put it in start-of-year prices.
Full answer
Tax at the start: dollars. After 3 years, pay is dollars, so tax is dollars. In start-of-year prices: dollars. His real tax rose by about 13.7%, while his real pay did not change. With an allowance raised to dollars, the tax would be about dollars, which is . So his real tax would be unchanged. ✓
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A government owes $100 billion in bonds paying a fixed 2% a year, and $40 billion in index-linked bonds paying 0.5% a year in real terms. Everyone expected 2% inflation, but it is 10% this year. (a) At the end of the year, how much buying power has the government gained on each kind of debt, compared with what was planned? (b) Why might a government still choose to sell index-linked bonds?
Hint 1
For the fixed bonds, the government repays $102 billion. Compare its real value at 2% inflation with its real value at 10%.
Hint 2
An index-linked bond repays billion dollars. Divide by 1.10.
Full answer
(a) Fixed bonds: planned real value billion; actual billion. The government gains about $7.3 billion of buying power, and the bondholders lose it. Index-linked bonds: it repays billion, worth billion, exactly as planned. No gain. (b) Lenders accept a lower interest rate when they are protected from inflation, so index-linked debt can be cheaper when inflation stays low. It also shows that the government does not plan to inflate its debt away. The risk is the one the UK met in 2022: when inflation rises, the cost of this debt rises with it. Check: the index-linked bonds are of the debt, close to the UK's quarter.
Most promises in an economy are written in money: wages, pensions, loans, rents, tax thresholds and government bonds. Inflation changes what every one of those promises is worth, and unexpected inflation does it without anyone voting or signing. So the question "who should bear the cost?" sits inside every inflation, and it is a political question as well as an economic one. Indexation, and central banks that keep inflation low and predictable, are both ways of keeping money promises honest.
The next lecture turns the picture upside down. When prices fall, every debt grows in real terms, and borrowers become the losers.
- The real value of a money amount is the amount divided by the price index, and the real interest rate is found by dividing growth factors, .
- Unexpected inflation moves buying power from people who are owed fixed amounts of money, such as savers and lenders, to people who owe them, such as borrowers and governments.
- Inflation that is fully expected is built into interest rates and pay deals, so it moves little buying power, which is why predictable inflation matters as much as low inflation.
- People with incomes fixed in money or adjusted with a lag lose, while indexation protects them, and fixed tax thresholds raise real taxes through fiscal drag.
- Some costs of inflation, such as menu costs, shoe-leather costs and uncertainty, are losses for everyone, and hyperinflation destroys the value of money completely.