Question

In Munich a bratwurst costs 5 euros; a hot dog costs \(\$ 4\) at Boston's Fenway Park. At an exchange rate of \(\$ 1.05 /\) per euro, what is the price of a bratwurst in terms of a hot dog? All else equal, how does this relative price change if the dollar depreciates to \(\$ 1.25\) per euro? Compared with the initial situation, has a hot dog become more or less expensive relative to a bratwurst?

Short answer

Initially, a bratwurst costs \(5.25 and is equivalent to 1.3125 hot dogs. After the dollar depreciates to \)1.25 per euro, a bratwurst costs $6.25 and is equivalent to 1.5625 hot dogs. Compared to the initial situation, a hot dog has become less expensive relative to a bratwurst.

Step-by-step solution

Find the price of a bratwurst in dollars

To find out the cost of a bratwurst in dollars, we must multiply its price in euros by the current exchange rate (in dollars per euro). At an exchange rate of \(1.05 per euro, the calculation is: Price in dollars = Price in euros × Exchange rate = 5 euros × \)1.05/euro.

Calculate the number of hot dogs per bratwurst

Now, we divide the price of a bratwurst in dollars by the price of a hot dog in dollars to find out how many hot dogs one bratwurst is worth. Using the price from step 1, we get: Number of hot dogs per bratwurst = Price of bratwurst in dollars / Price of hot dog in dollars.

Adjust the exchange rate for dollar depreciation

If the dollar depreciates and the new exchange rate is \(1.25 per euro, we need to recalculate the price of a bratwurst in dollars using the new exchange rate: New price in dollars = 5 euros × \)1.25/euro. Then we need to calculate the number of hot dogs per bratwurst again using this new price.

Analyze the change in relative price

By comparing the number of hot dogs per bratwurst before and after the dollar's depreciation, we can determine how the relative price has changed. If the number of hot dogs per bratwurst has increased, it means hot dogs have become cheaper relative to bratwursts. If it has decreased, hot dogs have become relatively more expensive.

Key concepts

Currency Depreciation

Understanding currency depreciation is crucial when it comes to determining how goods from one country compare in price to those from another. When we talk about currency depreciation, we refer to the decrease in value of one currency relative to another. For example, if the dollar depreciates against the euro, it means that each dollar now buys fewer euros than before.

In practical terms, this affects not only international trade but also tourism and global market investments, as the relative cost for goods and services changes. In the given exercise, we saw the dollar depreciate from \(1.05/euro\) to \(1.25/euro\). This depreciation indicates that Americans will need to spend more dollars to buy the same amount of euros, which in turn means they will pay more in dollars for goods priced in euros, like the Munich bratwurst. It's a phenomenon reflective of broader economic trends and has a significant impact on purchasing power.

Price Level Comparison

Price level comparison between two different goods from different economies, such as a bratwurst from Munich and a hot dog from Boston, helps us understand the purchasing power of currencies and individuals. The price level comparison is the process of comparing the cost of standardized goods across different countries or cities, after accounting for exchange rates.

In our exercise, the initial price comparison was based on the exchange rate of \(1.05/euro\) to determine how many hot dogs equal the price of one bratwurst. After the dollar's depreciation, with a new exchange rate of \(1.25/euro\), this comparison shifts. It's essential to remember that these comparisons can be influenced by several factors, including inflation, supply and demand, and changes in market sentiment. They are often used as a gauge for the relative cost of living between areas and can give insight into the economic conditions in different countries.

International Economics

The field of international economics deals with how countries interact with one another economically, covering both trade and financial considerations. It involves understanding how currencies, like the dollar and euro, trade against each other and what impacts those exchange rates. Concepts like currency depreciation or appreciation, trade balances, international investments, and movement of capital and labor are all woven into the fabric of international economics.

In cases like our exercise, we analyze the impact of international economic dynamics on everyday items such as bratwursts and hot dogs. The changing exchange rate between the euro and the dollar reflects shifts in economic power, policy decisions by governments and central banks, and global economic health. Events like dollar depreciation against the euro show us the interconnectedness of economies and underline how international economics is an integral part of our daily transactions and overall economic understanding.