Exchange rates and purchasing-power parity
Nominal and real exchange rates, appreciation and depreciation, and the theory of purchasing-power parity, with its limits.
FinanceThe economy behind your investmentsAbout 5 min: 3 reading, 2 practiceUpdated
General education, not financial advice.
- Tell nominal from real exchange rates and calculate a real exchange rate
- Explain appreciation and depreciation
- Use purchasing-power parity to predict an exchange rate, and explain why it doesn't always hold
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The economy behind your investments: lesson 13 of 16
- The economy behind your investments
- Financial markets and intermediaries 5 min
- The market for loanable funds 5 min
- Banks and the money supply 5 min
- The quantity theory of money 5 min
- The aggregate-demand curve 5 min
- Monetary policy and aggregate demand 5 min
- Aggregate supply and the business cycle 5 min
- Fiscal policy and the multiplier 5 min
- The Phillips curve 5 min
- Expectations and the cost of lower inflation 5 min
- Rules or discretion 6 min
- Deficits and the case for balance 7 min
- Exchange rates and purchasing-power parity 5 min
- Exports, imports and capital flows 5 min
- The market for foreign-currency exchange 5 min
- Policies and shocks in an open economy 5 min
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Pairs with any introductory economics textbook; for example N. Gregory Mankiw, Principles of Macroeconomics (6th ed.), chapter 18
What it is
The nominal exchange rate is the rate at which one currency trades for another. Mankiw's example: 80 yen per dollar. (It can be quoted either way: 80 yen per dollar is 1/80 of a dollar per yen.)
- Appreciation: a currency buys more foreign currency (the dollar goes from 80 to 90 yen).
- Depreciation: it buys less (from 80 to 70 yen).
The real exchange rate is the rate at which goods of one country trade for goods of another:
real exchange rate = (e × P) ÷ P\*
where e is the nominal exchange rate (foreign currency per unit of home currency), P the home price and P\* the foreign price.
Mankiw's example: American rice costs 100 dollars a bushel; Japanese rice costs 16,000 yen. At 80 yen per dollar, American rice costs 8,000 yen, so the real exchange rate is 8,000 ÷ 16,000 = ½ bushel of Japanese rice per bushel of American rice. American rice is half as expensive.
A fall in a country's real exchange rate makes its goods cheaper relative to foreign goods, so its exports rise and imports fall.
Quick check
Tap an answer to check it.
The pound buys 1.30 dollars, then 1.20. Has the pound appreciated or depreciated?
- Appreciation means it buys more foreign currency
Show answer
Depreciated: it buys fewer dollars. Each pound now buys 0.10 dollars less.
Why it matters
Purchasing-power parity (PPP). The simplest theory of exchange rates says a unit of any currency should buy the same quantity of goods in every country. It rests on the law of one price: a good should sell for the same price everywhere, or people would profit by arbitrage, buying where it is cheap and selling where it is dear, until the prices met.
If PPP holds, the nominal exchange rate is the ratio of the two price levels:
e = P\* ÷ P
Mankiw's Big Mac example: a burger costs 3 dollars in the US and 300 yen in Japan, so PPP predicts 100 yen per dollar.
What PPP implies. If a country's prices rise faster (because its central bank prints more money), its currency should depreciate. This explains long-run trends and the collapse of currencies in hyperinflations.
Why it doesn't always hold. Mankiw gives two reasons:
- Many goods can't easily be traded: a haircut in Paris can't be shipped to New York, so price gaps persist.
- Even tradable goods from different countries are not perfect substitutes: some buyers prefer one country's cars or wine to another's, so relative prices can shift.
So PPP is a guide to the long run, not a precise prediction of today's exchange rate.
Worked example
A coffee costs 3.00 euros in Paris and 4.50 dollars in New York. The market exchange rate is 0.90 euros per dollar.
- PPP prediction: e = P\* ÷ P = 3.00 ÷ 4.50 ≈ 0.67 euros per dollar.
- At the actual 0.90, a dollar buys 0.90 ÷ 0.67 ≈ 1.35 times what PPP predicts, so the dollar looks overvalued against the euro by this measure.
- Real exchange rate: (0.90 × 4.50) ÷ 3.00 = 1.35: a New York coffee costs 1.35 Paris coffees.
(Made-up prices; a single good gives only a rough guide.)
Common mistake
Confusing the nominal and real exchange rates. A dollar buying more yen (nominal appreciation) doesn't make American goods dearer if American prices have fallen relative to Japanese ones. What matters for trade is the real exchange rate.
Key terms
- nominal exchange rate
- the rate at which one currency can be traded for another
- real exchange rate
- the rate at which the goods of one country can be traded for the goods of another
- appreciation
- a rise in a currency's value, measured in foreign currency
- depreciation
- a fall in a currency's value, measured in foreign currency
- purchasing-power parity
- the theory that a unit of any currency should buy the same quantity of goods in all countries
- law of one price
- the principle that a good should sell for the same price everywhere
- arbitrage
- buying where a good is cheap and selling where it is dear to profit from the difference
Practise the key terms
Tap a card to turn it over. 7 cards.
| Front | Back |
|---|---|
| nominal exchange rate | the rate at which one currency can be traded for another |
| real exchange rate | the rate at which the goods of one country can be traded for the goods of another |
| appreciation | a rise in a currency's value, measured in foreign currency |
| depreciation | a fall in a currency's value, measured in foreign currency |
| purchasing-power parity | the theory that a unit of any currency should buy the same quantity of goods in all countries |
| law of one price | the principle that a good should sell for the same price everywhere |
| arbitrage | buying where a good is cheap and selling where it is dear to profit from the difference |
Practice
Work it through
A bushel of wheat costs 8 dollars in the US and 1,200 rupees in India. The exchange rate is 90 rupees per dollar.
- 8 × 90
- 720 ÷ 1,200
- 1,200 ÷ 8
Quick quiz
Tap an answer to check it.
Under PPP, a country's money supply grows much faster than other countries'. What happens to its currency?
- Faster price rises mean each unit buys less abroad too
Show answer
It depreciates, as its prices rise faster. e = P* ÷ P: higher P means a lower e.
Why doesn't PPP hold exactly, in Mankiw's account?
- Mankiw's reasons concern goods, not policy
Show answer
Many goods can't be traded, and goods from different countries aren't perfect substitutes. Arbitrage can't close every price gap.
A country's real exchange rate falls. What happens to its net exports?
- That follows a rise in the real exchange rate
Show answer
They rise: its goods become relatively cheaper. Cheaper goods sell more abroad, and home buyers buy fewer imports.
In short
- Nominal exchange rate: currency for currency. Real: goods for goods, (e × P) ÷ P\*.
- Appreciation: a currency buys more foreign currency; depreciation: less.
- PPP: e = P\* ÷ P; faster inflation means a depreciating currency.
- PPP fails for non-traded goods and imperfect substitutes; it is a long-run guide.
Mastery check
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In Mankiw's rice example, what is the real exchange rate?
Show answer
½ bushel of Japanese rice per bushel of American rice.
What exchange rate does PPP predict if a Big Mac costs 3 dollars in the US and 300 yen in Japan?
Show answer
100 yen per dollar.
What is arbitrage?
Show answer
Buying a good where it is cheap and selling it where it is dear, which tends to equalise prices.
Further reading
- N. Gregory Mankiw, Principles of Macroeconomics, 6th ed. (South-Western Cengage, 2012), chapter 18.
- On this site: Exports, imports and capital flows and The quantity theory of money.
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