- Measuring national income — three approaches
- Percentage increase and decrease · coming soon
- Limitations of GDP as a welfare measure
- Measuring inflation — CPI and RPI
- How exchange rates are determined · coming soon
A number that grew more than four times
In 1990, the United Kingdom's GDP was about £673 billion. In 2024 it was about £2 890 billion. That is 4.3 times as much. Did the United Kingdom produce 4.3 times as many goods and services in 2024 as in 1990?
No. Over the same 34 years, prices rose too. A loaf of bread, a bus ticket and a new house all cost far more in 2024 than in 1990. GDP is the market value of what is produced, so it rises when prices rise, even if nothing more is made.
The last lecture ended by saying that GDP leaves out two things: rising prices, and how well people actually live. This lecture deals with the first. The disruption is simple to state. The GDP figure in money mixes two different changes together: more stuff, and the same stuff at higher prices. To know whether an economy has really grown, we have to pull them apart.
Two reasons a money total can rise
The value of anything sold is its price times its quantity. GDP adds up price × quantity for every final good and service. So GDP can rise for two reasons. The quantities can rise, which means the economy produces more. Or the prices can rise, which means the same output is valued at more money. Usually both happen at once.
Nominal GDP values each year's output at that year's prices, called current prices.
Real GDP values each year's output at the prices of one fixed base year, called constant prices. Because the prices are held fixed, real GDP can rise only when output rises.
Real GDP answers a question about quantities: did the economy make more? Nominal GDP answers a question about money: how many pounds, rupees or dollars changed hands? Both are useful. They answer different questions.
Separating the two changes in a small economy
Here is an invented economy that makes only two things: bikes and loaves of bread. The year 2020 is the base year.
| Year | Bikes | Price of a bike | Loaves | Price of a loaf |
|---|---|---|---|---|
| 2020 | 100 | $200 | 5000 | $2.00 |
| 2024 | 110 | $250 | 5200 | $2.40 |
Nominal GDP in 2020: dollars.
Nominal GDP in 2024, at 2024 prices: dollars. That is a rise of about 33.3%.
Real GDP in 2024: the 2024 quantities at the 2020 prices: dollars. Compared with 30 000, that is a rise of exactly 8%.
So output grew by 8%, and the rest of the 33.3% came from prices. The two quantities grew by 10% (bikes) and 4% (bread). Real GDP grew by 8%, between the two, because bikes make up more of the value.
Check: in the base year, real and nominal GDP are the same, 30 000, because the base year's quantities are valued at the base year's prices ✓.
The GDP deflator: one number for "prices"
The ratio of nominal to real GDP measures how much prices have risen since the base year. It is called the GDP deflator:
For the bike economy in 2024, the deflator is . In the base year it is always exactly 100, because nominal equals real. A deflator of 123.4 means that prices are, on average, about 23.4% higher than in the base year.
Look at where 23.4% comes from. Bike prices rose by 25%, and bread prices by 20%. The deflator is an average of the two, and it sits closer to 25% because bikes are the bigger part of the output. This is the meaning of the deflator. It is the average price change of everything the economy produces, weighted by how much of each thing is produced.
Turn the formula round, and it removes inflation from any nominal figure:
Dividing by takes out the price rise. That is why it is called a deflator: it lets the air out of a figure that rising prices have blown up.
Nominal GDP grew by 10% and the deflator rose by 6%. Is real growth exactly 4%?
Show the answer
No, but it is close. Growth factors multiply. Nominal = real × prices, so , and the real factor is . Real growth is about 3.8%. Subtracting (10 − 6 = 4) is a good shortcut when the percentages are small. When prices rise fast, it fails badly, as the real case below shows.
Explore the multiplying yourself.
Last year's GDP is set at 100. Choose how much output grows and how much prices change this year. Watch the two bars, and compare the true real growth with the shortcut "nominal growth − inflation". Try the Türkiye 2022 preset last.
Presets:
Last year's GDP = 100. Real GDP this year = 100 × output factor. Nominal GDP this year = 100 × output factor × price factor.
| Output growth | Price change | Nominal growth | Shortcut: nominal − prices |
|---|---|---|---|
| 2% | 3% | ≈ 5.1% | ≈ 2.1% |
| 8% | 23.4% | ≈ 33.3% | ≈ 9.9% |
| 0% | 10% | 10% | 0% |
| 5.6% | 96% | ≈ 107.0% | ≈ 11.0% |
Real GDP grows by the output growth in every row, whatever happens to prices. Compare the shortcut column with the output growth column: the shortcut is out by about 0.1 points in the first row, 1.9 in the second, 0 in the third and 5.4 in the last. It is close only when prices change slowly.
What should you have seen? Moving output growth changes both bars, because more output is more value at any prices. Moving the price change moves only the nominal bar. Real GDP ignores prices completely. And the shortcut "real ≈ nominal − inflation" is nearly right at low inflation, but at Turkey's 2022 settings it is wrong by more than 5 percentage points.
A real case: Turkey's GDP more than doubled in one year
The headline. The Turkish Statistical Institute (TurkStat) reported on 1 March 2023 that Türkiye's GDP at current prices in 2022 was about 15.0 trillion lira, a rise of 107.0% on 2021. In money terms, the economy more than doubled in one year.
The prediction from the nominal figure. If you read only that number, you would expect factories, farms and shops to have produced twice as much as a year earlier. That would be an extraordinary boom.
What happened. The same release gave the chain-linked volume measure, which is real GDP: it grew by 5.6%. Output grew, but by a normal amount for a growing economy.
The deflator. Nominal = real × prices, so the price factor is . The GDP deflator rose by about 96% in a single year. Almost all of the 107% was inflation.
Verdict. The nominal figure was correct, and it was useful for some questions, such as how much tax revenue to expect. But as a measure of growth, it was badly misleading: the nominal rise was about nineteen times the real growth. Notice too that the shortcut fails: , but real growth was 5.6%.
Figures as first published in TurkStat's release of 1 March 2023 (reported by MuhasebeNews and Fibre2Fashion, both quoting TurkStat). Later revisions may differ slightly.
Return now to the United Kingdom. Between 1990 and 2024, nominal GDP grew about 4.3 times, but real GDP grew about 1.8 times: an 84% rise in output. Prices, measured by the deflator, rose about 2.3 times. So the British economy really did grow a great deal, but by far less than the money figure suggests.
An invented country has nominal GDP of $500 billion in 2019, its base year. In 2024, nominal GDP is $690 billion and the GDP deflator is 125. How much did real output grow?
Real GDP in 2019 = $500 billion (base year: real = nominal).
Real GDP in 2024 = billion dollars.
Real growth = . Nominal growth was 38%.
Check: ✓. Real growth is smaller than nominal growth, as it must be when prices have risen.
Now find the mistake in another student's working.
The question: an invented country's nominal GDP was $800 billion in 2018, the base year. In 2024 it was $1050 billion, with a GDP deflator of 125. Find real growth. One line of this working is wrong. Tap the line you think is wrong.
A student's working, with the mistake marked.
- In the base year, real GDP = nominal GDP = $800 billion. (Correct.)
- Real GDP in 2024 = 1050 × 125 ÷ 100 = $1312.5 billion. (The error. Multiplying by the deflator adds the price rise instead of removing it. Real GDP = 1050 ÷ 125 × 100 = $840 billion.)
- Real growth = (1312.5 − 800) ÷ 800 ≈ 64%. (The arithmetic follows from line 2, so the answer is wrong. The correct real growth is (840 − 800) ÷ 800 = 5%.)
- So real GDP grew faster than nominal GDP, which grew by 31.25%. (This should have been a warning: real growth can beat nominal growth only if prices fell, and a deflator of 125 means they rose.)
Comparing countries: purchasing power parity
Real GDP solves the problem of prices changing over time. A similar problem appears when we compare countries. To compare GDP in different currencies, the obvious method is to convert everything into one currency, usually US dollars, at the market exchange rate.
The trouble is that many things cost much less in some countries than in others, even after converting the currency. A haircut, a bus ride or a meal in a local restaurant is usually far cheaper in Chennai than in New York. These services are not traded across borders, so their prices do not even out. Converting at the exchange rate values them at local prices, so cheap local services make a country's output look smaller than it is.
Purchasing power parity (PPP) fixes this. Statisticians compare the prices of the same goods and services in every country. From these they build a PPP rate: how much of each currency buys the same basket of goods as one US dollar buys in the United States. GDP converted at PPP rates is measured in "international dollars", and it compares the quantities produced, at a common set of prices.
The World Bank's International Comparison Program found that in 2021, China's GDP at PPP was about $28.8 trillion, 18.9% of the world total, and the United States' was nearly $23.6 trillion, 15.5%. At market exchange rates, China's was about $18.2 trillion and the United States' about $23.7 trillion. India's GDP at PPP was about $11.0 trillion, 7.2% of the world total. The United States' figure is almost the same both ways, because an international dollar is defined to buy what a US dollar buys in the United States.
Which number is right? Both, for different questions. To ask what a country can buy on world markets, such as aircraft, oil or foreign debt repayments, use market exchange rates, because that is the price it actually pays. To compare how much is produced, or how much people can buy at home, use PPP.
Three traps
"Real growth = nominal growth − inflation" is only a shortcut. Growth factors multiply. At low inflation the error is tiny. At Turkey's 2022 inflation, the shortcut gives 11% when the truth was 5.6%. When the numbers are large, divide: real factor = nominal factor ÷ price factor.
A deflator of 125 means prices are 25% higher than in the base year, not 25% higher than last year. To find inflation between two years, compare the two deflators: from 120 to 125 is a rise of .
Both remove the effect of prices, but in different directions. Real GDP compares one country across time, using one year's prices. PPP compares different countries at the same time, using common prices. A comparison of the United Kingdom and Germany in 2024 needs PPP, not real GDP.
Work each one on paper first. Open a hint only when you are stuck.
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An invented island grows only rice. In 2021 (the base year) it grows 1000 tonnes, sold at $500 a tonne. In 2025 it grows 1080 tonnes, sold at $600 a tonne. Find nominal GDP in both years, real GDP in 2025, real growth and the 2025 deflator.
Hint 1
Nominal uses each year's own price. Real uses the 2021 price for both years.
Hint 2
Real GDP in 2025 = 1080 × 500. The deflator = nominal ÷ real × 100.
Full answer
Nominal 2021 = 1000 × 500 = $500 000. Nominal 2025 = 1080 × 600 = $648 000, a rise of 29.6%. Real 2025 = 1080 × 500 = $540 000, a rise of 8%, which matches the 8% more rice. Deflator = 648 000 ÷ 540 000 × 100 = 120, which matches the 20% rise in the rice price. Check: 1.08 × 1.20 = 1.296 ✓.
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An invented country's nominal GDP was $1.00 trillion in 2020, the base year. In 2025 it was $1.32 trillion, and the deflator was 110. By what percentage did real output grow?
Hint 1
In the base year, real GDP equals nominal GDP.
Hint 2
Real GDP in 2025 = 1.32 ÷ 110 × 100.
Full answer
Real 2025 = 1.32 ÷ 1.10 = $1.20 trillion (in 2020 prices). Real growth = (1.20 − 1.00) ÷ 1.00 = 20%. Nominal growth was 32%, and prices rose by 10%. Check: 1.20 × 1.10 = 1.32 ✓. The shortcut 32 − 10 = 22% would overstate growth by 2 percentage points.
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In an invented country, nominal GDP fell by 2% in one year, and the GDP deflator fell from 100 to 95. A newspaper says "the economy shrank". Is that right?
Hint 1
A falling deflator means prices fell. Prices can fall, as well as rise.
Hint 2
Real factor = nominal factor ÷ price factor = 0.98 ÷ 0.95.
Full answer
Real factor = 0.98 ÷ 0.95 ≈ 1.032, so real GDP rose by about 3.2%. The economy produced more. The money total fell only because prices fell by 5%. The newspaper has confused nominal with real. Falling prices are called deflation, and a later lecture explains why they can be a problem even when output grows.
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Two invented countries. In Arland, a basket of everyday goods and services costs $1000. In Bervia, the same basket costs 30 000 bervs. The market exchange rate is 60 bervs to the dollar. Bervia's GDP is 3000 billion bervs. Find Bervia's GDP in dollars at the market rate and at PPP (take Arland's prices as the common standard). Which figure should Bervia's government use when planning to buy foreign aircraft, and which when comparing living standards?
Hint 1
The PPP rate is the number of bervs that buy what $1 buys in Arland: 30 000 ÷ 1000.
Hint 2
At market rates, divide by 60. At PPP, divide by 30.
Full answer
Market rate: 3000 ÷ 60 = $50 billion. PPP rate: 30 bervs per dollar, so 3000 ÷ 30 = $100 billion (international dollars). Bervia's output buys twice as much at home as the exchange rate suggests, because its prices are half of Arland's: the basket costs 30 000 ÷ 60 = $500 at the market rate. For buying foreign aircraft, use $50 billion: the aircraft are priced in dollars, and Bervia must pay the market rate. For comparing living standards, use $100 billion, because people live on what their income buys at home prices. Check: 50 × 2 = 100 ✓.
A fixed base year has a weakness. Prices of different goods change at different rates. Computers, for example, have become far cheaper compared with haircuts over the last few decades. Valuing today's output at the prices of a year long ago gives old relative prices too much weight. So statistical offices now update the prices every year and link the years together, like links in a chain. The UK's Office for National Statistics publishes "chained volume measures", and the United States publishes real GDP in "chained dollars". TurkStat's "chain-linked volume" in Worked Example 2 is the same idea. The principle is unchanged: hold prices still, and measure what changes.
The GDP deflator is not the only price measure. The consumer price index, the subject of a later lecture, follows a basket of things households buy, including imports. The deflator covers everything produced inside the country, including investment goods, government services and exports, and it leaves imports out. That is why the two can differ.
Real GDP tells you how much an economy produces. It does not yet tell you how well its people live. The next lecture asks that question.
- Nominal GDP values output at current prices, so it rises when output rises or when prices rise.
- Real GDP values output at the fixed prices of a base year, so it rises only when output rises, and it is the measure of economic growth.
- The GDP deflator is nominal GDP ÷ real GDP × 100, an average price change of everything produced, equal to 100 in the base year.
- Growth factors multiply, so real growth = nominal factor ÷ price factor − 1, and subtracting percentages is only a shortcut for low inflation.
- Purchasing power parity converts GDP into international dollars at common prices, so it suits comparisons of output and living standards between countries.