Question

Steve, an American in London, wants to buy a British-made sweater. The current price of the sweater is $\pounds 40.$ Would Steve be better off if the exchange rate is 1 dollar=$\pounds 0.87$ or 1 dollar =£ 0.77 ?Explain your answer.

Short answer

Steve would be better off if the exchange rate is 1 dollar=£ 0.87 because the sweater costs less in US dollars at this rate.

Step-by-step solution

Convert the sweater price using the first exchange rate

Using the exchange rate of 1 dollar=£ 0.87, we divide the price of the sweater in pounds (£40) by the exchange rate (0.87). The formula is $\frac{40}{0.87}$ which equals approximately $45.98.

Convert the sweater price using the second exchange rate

Using the exchange rate of 1 dollar=£ 0.77, we divide the price of the sweater in pounds (£40) by the exchange rate (0.77). The formula is $\frac{40}{0.77}$ which equals approximately $51.95.

Compare the two results

Comparing Step 1 and Step 2, we can see that with an exchange rate of 1 dollar = £0.87, the sweater costs Steve approximately $45.98, while with an exchange rate of 1 dollar = £0.77, the sweater costs him approximately $51.95. Therefore, Steve would be better off with an exchange rate of 1 dollar = £0.87 as the sweater costs less in US dollars at this rate.

Key concepts

Currency Conversion

Currency conversion is all about translating the value of one currency into another. This is essential when comparing prices across different countries, like when Steve wants to know how much a British sweater costs in US dollars. The exchange rate is the key factor here. It determines how much of one currency you need to spend to get another. To convert a price, you divide the price in local currency by the exchange rate for each foreign currency unit. For example:

• Price of sweater in pounds (£40)
• Exchange rate for \(1 = £0.87
• Conversion: $$\begin{gathered} \frac{40}{0.87}\approx 45.98 \\ ) \end{gathered}$$

This calculation shows how much Steve would pay in dollars. A higher exchange rate means less spending in your currency, while a lower exchange rate implies more spending. Understanding these conversions helps in evaluating purchasing decisions in foreign markets.

Purchasing Power

Purchasing power refers to the value of currency expressed in terms of the amount of goods or services one unit of currency can buy. When exchange rates change, so does purchasing power. In Steve's example, his purchasing power in the UK is affected by the current exchange rate. If the exchange rate is 1 dollar = £0.87, Steve can buy more with his dollars than if the rate is 1 dollar = £0.77.
This is because:

• A dollar converts to more pounds (£) at £0.87 than at £0.77, giving Steve more purchasing power in the first scenario.
• When Steve's purchasing power increases, he spends fewer dollars for the same sweater (£40).

Being aware of how purchasing power fluctuates with exchange rates helps consumers and businesses make informed spending decisions in international contexts.

International Trade

International trade involves buying and selling goods and services across borders. Exchange rates significantly influence this trade by determining the cost of transactions in different currencies. For businesses and individuals like Steve, understanding these rates is crucial for assessing product affordability from another country.
Considerations for international trade include:

• Exchange rates impact profit margins for sellers who export goods.
• Consumers need favorable exchange rates to benefit economically from buying foreign products.
• Countries with stronger currencies may find exports less competitive but imports cheaper.

In Steve's case, a more favorable exchange rate makes it viable for him to purchase the sweater while traveling, thereby contributing to international trade relations by expanding consumer choice across national boundaries.