# Lesson Summary: Exchange rates

## Lesson summary

If someone from Hamsterville came up to you and tried to buy an old book from you, and tried to pay you in their currency — the Hamsterville snark ($SN$) — you’d tell them “no thanks!”
Why? Because the Hamsterville snark is worthless to you since you can’t buy anything with it in your country. Instead, you want to be paid in your own currency. That means that someone from Hamsterville would need to exchange their currency for the currency used in your country.
The exchange rate of a currency is how much of one currency can be bought for each unit of another currency. A currency appreciates if it takes more of another currency to buy it, and depreciates if it takes less of another currency to buy it.

## Key terms

Key termDefinition
exchange ratethe price of one currency in terms of another currency; for example, if the exchange rate for the euro (€) is $132$ yen (¥), that means that each Euro that is purchased will cost $132$ yen.
appreciatewhen a currency becomes more valuable relative to another currency; a currency appreciates when you need more of another currency to buy a single unit of a currency.
depreciatewhen the value of a currency decreases relative to another currency; a currency depreciates when you need less of another currency to buy a single unit of a currency.
floating exchange rateswhen the exchange rates of currencies are determined in free markets by the interaction of supply and demand

## Key takeaways

### The exchange rate is the price of one currency in terms of the other

Currencies are traded in the foreign exchange market. Like any other market, when something is exchanged there is a price. In the foreign exchange market, a currency is being bought and sold, and the price of that currency is given in some other currency. That price is expressed as an exchange rate.
For example, in the market for the Hamsterville snark, the exchange rate of the snark to the U.S. dollar ($US\$) is $US\5$ per snark. That means in order to buy a single snark, someone from the United States would need to pay for it with $US\5$.
On the other hand, someone from Hamsterville who wants dollars would buy those dollars with snarks. So, the exchange rate of the dollar is the inverse of the exchange rate of the snark:
\begin{aligned} \text{Exchange rate for snark}&=\5 \text{ per } 1SN\\\\ \text{Exchange rate for dollar}&=1SN \text{ per } \5\end{aligned}

### If a currency appreciates it is more valuable; if a currency depreciates it is less valuable

When an exchange rate changes, the value of one currency will go up while the value of the other currency will go down. When the value of a currency increases, it is said to have appreciated. On the other hand, when the value of a currency decreases, it is said to have depreciated.
For example, if it now takes $USD\10$ to buy a single Hamsterville snark instead of $\5$, the snark has appreciated and its value has increased. If prices in the United States haven’t changed, this is great news for Hamstervillians! Now the snark can buy more goods and services from the United States.
But, this is bad news for Americans who want to buy Hamsterville’s goods and services. Each U.S. dollar now buys only $0.1 SN$ instead of $0.2 SN$ as it did before. The dollar has depreciated against the snark and everything from Hamsterville just got a lot more expensive.

## Key equations

### Exchange rates

The exchange rate of a currency is expressed as the units of another currency needed to buy a single unit of the currency. For example, the exchange rate for currency A is given below:
$\text{Exchange rate}_A=\dfrac{\#\text{ of units of currency}B}{\text{ unit of currency }A}$

### Calculating the cost of something with exchange rates

To find the cost of something in the value of another currency, divide that cost by the exchange rate. For example, it takes 300 galactic credits ($GC$) to buy a smoothie on Tatooine. If the exchange rate means that $CAD\1$ buys $5 GC$, then the cost of a Tatooine smoothie to a Canadian tourist is:
\begin{aligned}\text{cost of a good in CAD\} &=\dfrac{\text{cost of good in GC}}{\text{cost of a galactic credit in CAD\}}\\\\ &=\dfrac{300}{ CAD\5}\\\\ & = \60\end{aligned}
Therefore a Tatooine smoothie costs $CAD\60$ to a Canadian.

## Common misperceptions

• We are used to thinking about buying things with a currency, so many new learners are confused about what the price should be in the market for a currency. Buthe price of an orange is never given in oranges; it’s given in some other currency. Just like an orange, a dollar can’t be bought with itself, but instead, it needs to be bought with some other currency.
• A common misperception is that a strong currency is always what is best for a country. On the one hand, if a currency appreciates, all of its imported goods get a lot cheaper. If a country tends to import a lot more goods than they export, then an appreciated currency might be desirable. But on the other hand, if a country relies heavily on exports, an appreciating currency isn’t such a great thing. When a currency appreciates, the exports from a country that use that currency will decrease because all of those goods are more expensive to countries other currencies.

## Questions for review

The Ghanaian cedi currently trades for 20 Icelandic kroné.
1. What is the exchange rate of the kroné? What is the exchange rate for the cedi? SHOW YOUR WORK.
2. If the trading price changes to 25 kroné per cedi, what has happened to:
(a) the kroné? Explain.
(b) the cedi? Explain.
1. If the cost of a fermented shark sandwich in Iceland is 1500 kroné, what is its cost in cedi to a tourist from Ghana based on a trading price of 1 cedi for 20 kroné? Show your work.