17  Currencies

Students learn to…
  • …interpret exchange rates and relate their changes to the relative prices of countries’ goods.
  • …predict the impact of exchange rate changes on business decisions and national economies.
  • …understand the linkage between interest rates and inflation in open economies.
  • …explain the interest rate parity condition and the purchasing power parity assumption.
  • …interpret and evaluate the balances of trade and

An exchange rate indicates the value of one currency in relation to another. Exchange rate fluctuations have a significant impact on the revenues, costs, and profits of businesses; they affect how much you can afford to spend and can even influence job security.

Please work on the questions posed in Exercise 17.1 and Exercise 17.2. They are designed to motivate an introduction the topic.

Exercise 17.1 Exchange rates over time

Figure 17.1: Canadian Dollars to U.S. Dollar Exchange Rate
  1. As can be seen in Figure 17.1, 1 United States Dollar (USD) equals about 1.38 Canadian Dollar (CAD) today. Since January 2002, has the USD depreciated (lost value) or appreciated (gained value) against the CAD? Explain your decision.
  1. To determine whether the USD has depreciated or appreciated against the CAD since January 2002, we need to compare the current exchange rate to the rate from January 2002. The exchange rate in January 2002 was about \[ 1 \text{USD} = 1.6 \text{CAD}.\] The exchange rate in January 2024 is about \[1 \text{USD} = 1.38 \text{CAD}.\]

    That means, if you convert 1 USD in 2024, you get less CAD as compared to converting 1 USD in January 2002. In other words, it takes less CAD in 2024 to get 1 USD compared to the year 2002. Thus, the USD has depreciated against the CAD. In turn, the CAD has appreciated.

  1. Assume that in January 2002, you exchanged a total of 2000 USD to Canadian Dollars (CAD) at a rate of 1.6 CAD per USD. Calculate how much that amount is worth today in USD.
  1. Having exchanged 2000 CAD into USD in 2002 at an exchange rate of $ 1 = 1.6 $ leaves you with \[2000 \ \text{USD} \cdot 1.6 \frac{\text{CAD}}{\text{USD}} = 3200 \, \text{CAD}.\] If you convert these 3200 CAD to USD in 2024 at an exchange rate of \(\text{USD} = 1.38 \text{CAD}\) you end up with \[ 3200 \text{CAD} \cdot \frac{1}{1.38} \frac{\text{USD}}{\text{CAD}} \approx 2318.84\ \text{USD}. \]

    This means that you end up with USD 318.84 more, which corresponds to an increase of around 15.9%. The reason for this gain is that you have invested in a currency that has appreciated. Therefore, holding a currency can be considered a form of investment.

  1. Suppose you have 1000 USD today, that is January 2024, and you plan to invest it in a Canadian fund that assures you a 2% annual interest rate.

    1. Calculate how much USD you’ll have after one year if the exchange rate remains on its current level of 1.38 CAD per USD.
    2. Calculate how much USD you’ll have after one year if the exchange rate slightly chances to 1.42 CAD per USD.
  1. First, you convert your USD to CAD in January 2024: \[1000 \ \text{USD} \cdot 1.38 \frac{\text{CAD}}{\text{USD}} = 1380 \, \text{CAD}.\] Then, you invest the CAD receiving 2% of interest after 1 year: \[1380 \text{CAD} \cdot 1.02 = 1407.6\ \text{CAD}.\] Finally, you convert the CAD back to USD

    1. at the rate 1.38 CAD per USD: \[ 1407.6\ \text{CAD} \cdot \frac{1}{1.38} \frac{\text{USD}}{\text{CAD}} = 1020\ \text{USD}. \]
    2. at the rate 1.42 CAD per USD: \[ 1407.6\ \text{CAD} \cdot \frac{1}{1.42} \frac{\text{USD}}{\text{CAD}} \approx 991.27\ \text{USD}. \]

This means that if you expect the exchange rate to remain unchanged, the Canadian fund could be a reasonable investment, offering a 2% return. However, if you anticipate that the CAD will depreciate by more than 2%, it would not be a profitable investment.

Exercise 17.2 Our relations are not good

Figure 17.2: Trump doubles metal tariffs on Turkey by 20%

Source: Twitter

Why is Trump implicitly expressing concerns about the weak Lira and the strong Dollar? Would he prefer a “strong” Turkish Lira and a “weak” Dollar? What factors actually contribute to his satisfaction? Can you understand the logic behind President Trump’s decision to double metal tariffs in response to the decline of the Turkish Lira (see Figure 17.2)? Discuss.

17.1 Exchange rates

The most important economic indicators frequently discussed in the media and politics are Gross Domestic Product (GDP)1, the policy rate2, and the inflation rate3. These measures are designed to explain the functioning of economic markets and guide policymakers. However, the exchange rate is used less frequently in political and public debates, which I believe is a significant oversight for several reasons.

1 The total value added of a country in a given period

2 The interest rate set by a central bank that influences the lending and borrowing rates of commercial banks to control inflation, manage employment levels, and stabilize the currency

3 The percentage increase in the general price level of goods and services in an economy over a given period

Firstly, similar to the aforementioned measures, exchange rate movements have a substantial impact on both markets and individuals. Moreover, the exchange rate serves as an accurate measure that reflects real market movements more quickly than most other indicators. Overall, a solid understanding of exchange rates is crucial for making informed decisions, managing financial risks, optimizing operations, and strategically positioning companies in the global marketplace.

Before I explain this in greater detail, let me share my explanations for why the exchange rate is relatively unnoticed in public debates:

  • Complexity of interpretation: It is comparatively difficult to interpret. GDP should be rising, while the inflation and policy rates should ideally be low. In contrast, the exchange rate is not so straightforward because there isn’t a universally optimal exchange rate that everyone hopes for. The ideal rate depends on many factors, such as whether you want to buy goods from abroad or sell them to the rest of the world. Different stakeholders and investors will have varying preferences about the exchange rate. Many people, especially politicians, avoid the complexities of “it depends” arguments because it is challenging to make convincing cases based on intricate relationships.
  • Volatility: The exchange rate is comparatively volatile, and its changes are difficult to predict.
  • Multiple exchange rates: There isn’t just one exchange rate; there are many, as any currency can be exchanged for any other currency. This means that a country’s exchange rate may rise against currency A but fall against currency B.
  • Limited political influence: The power of politics to directly and measurably influence a country’s exchange rate is limited.
  • Understanding requirements: The impact of exchange rate movements on our lives requires a solid understanding of economic markets, which many people lack.

While I cannot change the factors that contribute to the limited discussion of exchange rates, I can work to help you make sense of this topic. Before discussing the importance of the exchange rate in Section 17.3, let’s first define the rate:

Exchange Rate

The price of one currency in terms of another is called an exchange rate. Exchange rates allow us to compare the prices of goods and services across countries, determining a country’s relative prices for exports and imports.

To define the rate more formally, suppose the Euro (€) is the home currency and Turkish Lira (₺) the foreign currency, then the exchange rate in direct quotation (Preisnotierung) is \[E^{\frac{\text{€}}{\text{₺}}}=\frac{X \text{€}}{Y \text{₺}}\] and the exchange rate in indirect quotation (Mengennotierung) is \[E^{\frac{\text{₺}}{\text{€}}}=\frac{Y \text{₺}}{X \text{€}}.\]

Both rates contain the same information, but have different interpretations:

  • \(E^{\frac{\text{€}}{\text{₺}}}\) tells that we have to give X to receive Y , whereas
  • \(E^{\frac{\text{₺}}{\text{€}}}\) tells that we have to give Y to receive X .

Alternative interpretations:

  • \(E^{\frac{\text{€}}{\text{₺}}}\) tells that we have to give \(\frac{X}{Y} \text{€}\) to receive 1 , whereas
  • \(E^{\frac{\text{₺}}{\text{€}}}\) tells that we have to give \(\frac{Y}{X} \text{₺}\) to receive 1 .
Appreciation / Depreciation

A currency can appreciate or depreciate relative to other currencies.

  • If the appreciates, \(E^{\frac{\text{€}}{\text{₺}}}\) decreases and \(E^{\frac{\text{₺}}{\text{€}}}\) increases.
  • If the depreciates, \(E^{\frac{\text{€}}{\text{₺}}}\) increases and \(E^{\frac{\text{₺}}{\text{€}}}\) decreases.
Conventions to talk about exchange rates:
  • Euro to Dollar means \(\frac{\text{€}}{\$}\) (This is especially confusing and it can also be understood the other way round but the first currency mentioned is usually interpreted as the numerator)
  • Euro per Dollar means \(\frac{\text{€}}{\$}\)
  • Euro in Dollar means \(\frac{\$}{\text{€}}\)
  • 1 Euro costs X Dollars means X \(\frac{\$}{\text{€}}\)

Exercise 17.3 Interpret the exchange rate representations shown in Figure 17.3. Consider the Euro as the home currency and write the most recent currency rates of the four figures in direct quotation.

Figure 17.3: Euro to Dollar
(a)
(b)
(c)
(d)

Source: Subfigures (c) and (d) are taken from Google.

The exchange rate in direct quotation is:

  1. \[E^{\frac{\text{€}}{\text{\$}}}=\frac{X \text{€}}{Y \text{\$}} = \frac{1 \text{€}}{1,0212 \text{\$}}=0.97924011 \frac{\text{€}}{\text{\$}} \] Figure 17.3 (a) is denoted in indirect quotation. From April 2014 to July 2022 the Euro depreciated as one Euro was equivalent to 1.3823 Dollar in April 2014 and only 1.0212 Dollar in July 2022.

  2. \[E^{\frac{\text{€}}{\text{\$}}}=\frac{X \text{€}}{Y \text{\$}} = 1 \] Figure 17.3 (b) is denoted in direct quotation. From early 2018 to mid 2022 the Euro depreciated as one Dollar was equivalent to 0.80 Euro in early 2018 and 1.00 Euro in mid 2022.

  3. \[E^{\frac{\text{€}}{\text{\$}}}=\frac{X \text{€}}{Y \text{\$}} = \frac{1 \text{€}}{1,1050 \text{\$}}=0.904977376 \frac{\text{€}}{\text{\$}} \] Figure 17.3 (c) is denoted in indirect quotation. From the beginning of the graph somewhen 2019 till 9th of September 2024 the Euro depreciated as one Euro was equivalent to 1.1680 Dollar in 2019 and is now worth 1.1050 Dollar in July 2022.

  4. \[E^{\frac{\text{€}}{\text{\$}}}=\frac{X \text{€}}{Y \text{\$}} = \frac{1 \text{€}}{1,0212 \text{\$}}= 0.904731747\frac{\text{€}}{\text{\$}} \] Figure 17.3 (d) is denoted in indirect quotation. For example, from the 2nd of January 2021 to the 9th of September 2024 the Euro depreciated as one Euro was equivalent to 1.2011 Dollar in January 2021 and 1.1053 Dollar in July 2022.

Please note that Googles “EUR / USD” notation is misleading as it does not mean that the exchange rate is denoted in direct quotation, that is, \(\frac{X \text{€}}{Y \text{\$}}\).

Exercise 17.4 Exchange currencies

Suppose 1 US Dollar (USD) is equivalent to 1.20 Euros (EUR).

  1. Calculate the equivalent amount in Euros if a person exchanges 500 US Dollars.
  2. If the exchange rate changes to \(1.15 \frac{USD}{EUR}\), recalculate the equivalent amount in Euros for the same 500 US Dollars.
  3. If the exchange rate changes to \(1.15 \frac{USD}{EUR}\), has the Euro appreciated or depreciated?
  4. A European tourist plans to spend 1,000 Euros during a trip to the United States. Calculate the equivalent amount in US Dollars at the exchange rate of \(1.15 \frac{EUR}{USD}\).
  1. The equivalent amount in Euros for exchanging 500 US Dollars at the initial exchange rate of (1.20 , ) is given by: \[ \text{Equivalent Euros} = \frac{500 \, \text{USD}}{1.20 \, \text{USD/EUR}} \]

  2. If the exchange rate changes to (1.15 , ), the new equivalent amount in Euros is: \[ \text{New Equivalent Euros} = \frac{500 \, \text{USD}}{1.15 \, \text{USD/EUR}} \]

  3. The equivalent amount in US Dollars for spending 1,000 Euros at the initial exchange rate is: \[ \text{Equivalent USD} = 1,000 \, \text{EUR} \times 1.20 \, \text{USD/EUR} \]

  4. If the European tourist exchanges their money at the changed rate of (1.15 , ), the new equivalent amount in US Dollars is:

\[ \text{New Equivalent USD} = 1,000 \, \text{EUR} \times 1.15 \, \text{USD/EUR} \]

17.2 Relative prices and exchange rates

After understanding the concept of exchange rates, let us consider how trade in goods between two countries operates when each country uses a different currency as its legal tender.

Let us consider a stylized example: Assume the home country produces beer and the foreign country produces wine. If you want to exchange a beer for wine, the relative price indicates the amount of beer you need to provide in order to receive a unit of wine (in direct quotation) or the quantity of wine you will receive for a unit of beer (in indirect quotation).

For example, a relative price of 1 means you can exchange 1 liter of beer for 1 liter of wine. However, if we assume that beer is measured in 500 ml cans and wine in 1-liter bottles, the relative price denoted with \(P^{\frac{beer}{wine}}\) would be represented as:

\[P^{\frac{beer}{wine}}= \frac{2 \text{ cans of beer}}{1 \text{ bottle of wine}}.\]

This means you can exchange 2 cans of beer for one bottle of wine.

If the relative price increases, you will need to provide more beer to receive a bottle of wine. Conversely, if the relative price decreases, you will need to provide less beer to obtain a bottle of wine.

Relative prices

Relative prices determine the relative price of commodities across countries. For example, an increase in the price of foreign commodities makes imported commodities relatively more expensive and home commodities relatively cheaper for buyers at home.

Relative prices are (directly) determined by exchange rates. To logically prove this statement, let us assume for simplicity an exchange rate of 1, \[E^{\frac{\text{₺}}{\text{€}}}=E^{\frac{\text{€}}{\text{₺}}}=1\] and that a liter of beer costs 1 € at home and a wine costs 1 ₺ abroad. Thus, we can buy both a wine or a beer for 1 €. Due to the fact that we must pay the wine producer with ₺, we must convert the € beforehand. The process goes like visualized in Figure 17.4:

Figure 17.4: One wine per Euro

Now, assume that the € appreciates and the exchange rate becomes \(E^{\frac{\text{€}}{\text{₺}}}=0.5\) and \(E^{\frac{\text{₺}}{\text{€}}}=2\), respectively. Then, you receive more than one wine if we assume that the price of wine in ₺ remains unchanged. The process is visualized in Figure 17.5:

Figure 17.5: Two wine per Euro

That means, exchange rates determine the relative prices. If the home currency appreciates (depreciates), buying goods and services abroad becomes relative cheaper (more expensive).

Of course, if many people now buy wine and aim to convert €  to ₺, this may impact the exchange rate and the price of wine. We come back to that later.

Exchange rates and relative prices

The exchange rate determines the relative price of commodities across countries. For example, an appreciation of a currency makes commodities more expensive for foreign buyers and in turn makes foreign commodities cheaper for buyers at home.

17.3 The importance of exchange rates

Here is an incomplete list of arguments to emphasize the importance of exchange rates for economies, businesses, and individuals:

  • Import/export costs: Exchange rate fluctuations determine the relative prices and hence affect the cost of importing goods and materials and the global demand for domestic products. An appreciation of the home currency makes imports relatively cheaper but exports more expensive for the rest of the world, while depreciation has the opposite effect.
  • Revenue conversion: Multinational companies earn revenues in multiple currencies. Exchange rate changes can significantly impact the value of these revenues when converted back to the home currency, affecting overall profitability.
  • Foreign investments: Companies investing in foreign assets or operations need to understand exchange rates to forecast returns accurately and manage exchange rate risk.
  • Risk management: Knowledge of exchange rates enables businesses to hedge against currency risk using financial instruments like forwards, futures, options, and swaps. This is crucial for stabilizing cash flows and protecting profit margins.
  • Market competitiveness: Exchange rates affect the relative cost competitiveness of goods and services in international markets. Companies need to understand these implications to price their products competitively and make strategic decisions about entering or exiting markets.
  • Macroeconomic insights: Exchange rates are influenced by and also affect economic indicators such as inflation, interest rates, and economic growth. Understanding these relationships helps in making informed predictions about market conditions.
  • Contractual agreements: Businesses engaged in international trade must understand exchange rates to negotiate and structure contracts effectively, determining terms such as the currency of payment and exchange rate clauses.
  • Government and Policy Understanding: Exchange rates are often influenced by governmental and central bank policies. Understanding the dynamics between exchange rates and policy decisions is vital for anticipating regulatory changes and their potential impact on business operations.

17.4 Trump, relative prices, and trade policy

Let’s return to Trump’s Twitter message . Steel producers in the U.S. (and Donald Trump himself) are unhappy about a strong dollar (and a weak Turkish Lira) because it makes their products relatively expensive for Turkish buyers while making Turkish steel relatively cheap for U.S. consumers.

Trump had two options to address this issue: altering the exchange rates or adjusting the relative prices of goods between countries. Changing the exchange rate directly is a challenging task. Although buying or selling currencies on the foreign exchange market can influence exchange rates, the market is so large that the actions Trump could take as President would have minimal impact (see Section 17.5). Adjusting policy rates could influence exchange rates more effectively, as we will discuss in Chapter 18. However, the Federal Reserve, which sets policy rates and thus has an impact on interest rates, operates independently from political orders. Consequently, Trump’s influence over their decisions is limited.

As a result, Trump chose to increase the price of foreign steel in the U.S. by introducing or raising tariffs. The approach works, American steel producing companies get protected from foreign competition and might sell more domestically. However, there many negative consequences that detoriate the overall welfare. Foremost, everybody in the U.S. must pay more for steel (and for products made with steel and aluminum). David Boaz, Executive Vice President of the Cato Institute, a libertarian think tank, highlights this issue in his response on Twitter (see Figure 17.6).

Figure 17.6: Who wins in the end?

Source: Twitter

To quantify the costs of Mr. Trumps’s tariffs, let me quote the well-written article by Amiti et al. (2019) (p. 188-189):

Amiti, M., Redding, S. J., & Weinstein, D. E. (2019). The impact of the 2018 tariffs on prices and welfare. Journal of Economic Perspectives, 33(4), 187–210.

We find that by December 2018, import tariffs were costing US consumers and the firms that import foreign goods an additional $3.2 billion per month in added tax costs and another $1.4 billion per month in deadweight welfare (efficiency) losses. Tariffs have also changed the pricing behavior of US producers by protecting them from foreign competition and enabling them to raise prices and markups, and we estimate that the combined effects of input and output tariffs have raised the average price of US manufacturing by 1 percentage point, which compares with an annual average rate of producer price inflation from 1990 to 2018 of just over 2 percentage points. US tariffs and the foreign retaliatory tariffs also affect international supply chains, and we estimate that if the tariffs that were in place by the end of 2018 were to continue, approximately $165 billion of trade per year will continue to be redirected in order to avoid the tariffs. We also show that the rise in tariffs has reduced the variety of products available to consumers.

In addition, it can be argued that increased tariffs might actually make the dollar stronger. If buyers stop purchasing steel from Turkey due to higher tariffs, they will need fewer Turkish lira and therefore will exchange fewer U.S. dollars for Turkish lira. This reduced demand for Turkish lira could lead to a stronger dollar.

While raising tariffs and initiating trade disputes could be a strategy to gain political support and possibly get re-elected, there is a general consensus among economists that raising tariffs usually leads to economic losses and detrimental outcomes for all countries involved.

17.5 The FOREX

17.5.1 The market

In a market, individuals exchange goods and services, offering something to receive something else in return. In the FOREX (foreign exchange market), participants exchange currencies. Like all markets, the price here is influenced by the supply and demand dynamics of currencies.

Figure 17.7: Example of a foreign exchange market
  • When the Euro (€) is considered strong, the exchange rate \(E^{\frac{\text{€}}{\text{₺}}}\) is low:
    • At this lower exchange rate, there’s a high demand for Turkish Lira (₺) (point C), but the supply of ₺ is scarce (point E).
    • Consequently, the Euro faces depreciation pressure, leading to an increase in the exchange rate \(E^{\frac{\text{€}}{\text{₺}}} \uparrow\).
  • Conversely, when the Euro (€) is weak, the exchange rate \(E^{\frac{\text{€}}{\text{₺}}}\) is high:
    • With the exchange rate high, the demand for ₺ drops (point A), while its supply burgeons (point F).
    • As a result, the Euro is under appreciation pressure, causing the exchange rate to decrease \(E^{\frac{\text{€}}{\text{₺}}} \downarrow\).
  • Point B represents the equilibrium exchange rate, where the demand for ₺ meets its supply. At this juncture, holders of ₺ are unwilling to part with more, and similarly, Euro holders are not inclined to exchange more.

In 2022, the daily (!) traded volume of currencies averaged approximately $ 7,506 billion, as highlighted in Table 17.1.

Table 17.1: Daily turnover of global foreign exchange market from 2001 to 2022 (in billion U.S. dollars)
name 2001 2004 2007 2010 2013 2016 2019 2022
Total 1.239 1.934 3.324 3.973 5.357 5.066 6.581 7.506
USD 1.114 1.702 2.845 3.371 4.662 4.437 5.811 6.639
EUR 470 724 1.231 1.551 1.790 1.590 2.126 2.292
JPY 292 403 573 754 1.235 1.096 1.108 1.253
GBP 162 319 494 512 633 649 843 968
CNY 0 2 15 34 120 202 285 526
AUD 54 116 220 301 463 349 446 479
CAD 56 81 143 210 244 260 332 466
CHF 74 117 227 250 276 243 326 390
All others combined 170 251 568 786 1124 1223 1921 2093

Note: All others combined are: HKD, SGD, SEK, KRW, NOK, NZD, INR, MXN, TWD, ZAR, BRL, DKK, PLN, THB, ILS, IDR, CZK, AED, TRY, HUF, CLP, SAR, PHP, MYR.
Source: https://github.com/TheEconomist/big-mac-data (July 18, 2018).

17.5.2 Actors on the FOREX

As indicated in Figure 17.8, there are several major players involved in trading on the foreign exchange market. In particular, commercial banks, multinational corporations and non-bank financial institutions, such as investment funds, play an important role in trading and speculation. Central banks also play a crucial role as they intervene to stabilize their national currency and thus influence the direction of the market.

Figure 17.8: Players on the foreign exchange market

17.5.3 The vehicle currency

Instead of converting directly between two less common currencies, it’s more efficient to use a broadly accepted and stable currency as a vehicle. That means, if you want to exchange currency A to B. You do not exchange currency A directly to B but you convert currency A first to the vehicle currency C and then from C to B.

As depicted in Figure 17.9, around 32% of all currency transactions included the Euro while a notable 88% involved the U.S. Dollar which makes the Dollar the standard vehicle currency. The Dollar acts as a medium in transactions between currencies that do not directly trade with high volume. This can reduce transaction costs and streamline the process.

Figure 17.9: Market share of leading foreign exchange currencies in 2019

17.6 Purchasing power parity assumption

The Purchasing Power Parity (PPP) assumption is also know as the law of one price. It says that in competitive markets with zero transportation costs and no trade barriers, identical goods have the same price all over the world when expressed in terms of the same currency. The idea behind this is that if differences in prices exist, profits can be made through international arbitrage, that is, the process of buying a good cheap in one country and selling the good with a profit in another country. This process can quickly equalize real price differences across countries.

However, in the real world, prices differ substantially across countries (see the Big Mac Index in Table 17.2 and Exercise 17.5). The assumptions of the PPP do mostly not hold perfectly in reality: some goods and services are not trade-able, firms might have different degrees of market power across countries, and the transaction costs are not zero. Here are more reasons, why the PPP does not always apply, especially in the short run:

  • Transportation costs are not zero. Shipping goods can be time consuming and expensive.
  • Many goods and services, such as real estate or personal services, cannot be traded.
  • International markets may be segmented due to regulatory barriers, tariffs and other trade restrictions.
  • Countries have different consumption preferences. That means, the same basket of goods is not necessarily equally demanded. The willingness to pay for goods vary across countries often significantly.
  • Countries impose different taxes and provide different subsidies on goods and services, which affects their prices and leads to deviations from PPPs.
  • Short-term fluctuations in exchange rates may deviate from the values predicted by PPPs due to speculation, interest rate differentials and other factors.
  • Differences in inflation rates between countries may lead to deviations from PPP, especially in the short run.
  • The same product may be perceived differently in different countries due to brand names, quality differences or local customization, resulting in different prices.
  • Regulations like warranty and product classifications are different and have an impact on the product and the willingness to pay for it.
  • Political instability, war or economic sanctions can affect currency values and prices and lead to deviations from PPP.
  • Prices of goods and services do not always adjust immediately to changes in the exchange rate, leading to short-term deviations from PPP.

Exercise 17.5 Big Mac Index

The differences of prices across countries can be illustrated with the Economist’s Big Mac Index. It indicates the price of a Big Mac in different countries in terms of the US Dollar. Table 17.2 shows some countries with on average expensive and cheap Big Macs.

Table 17.2: The price of a Big Mac across countries
Country Price
Switzerland $6.57 (6.50 CHF)
Sweden $5.83 (51.00 SEK)
United States $5.51 (5.51 USD)
Norway $5.22 (42 NOK)
Canada $5.08 (6.65 CAD)
Euro area $4.75 (4.56 EUR)
Egypt $1.75 (31.37 EGP)
Ukraine $1.91 (50 UAH)
Russia $2.09 (130 RUB)
Malaysia $2.10 (8.45 MYR)
Indonesia $2.19 (31,500 IDR)
Taiwan $2.27 (69 TWD)

Source: https://github.com/TheEconomist/big-mac-data (July 18, 2018).

  1. Read Wikipedia’s page on the Big Mac Index and discuss the Big-Mac-Index critically. Is it really a reasonable real-world measurement of purchasing power parity?
  2. Compare the Big-Mac-Index to the Mac-Index (see: themacindex.com) looking for price differences of the Mac mini M1 256GB. Why are the price differences for Apple products so much smaller compared to McDonald’s Big Mac? In case the website offline, here is a snapshot of it.)
  3. Using the data of Table 17.2, calculate the exchange rate of Euros (EUR) to Swiss Francs (CHF) in both the direct and the indirect quotation. Interpret your result.
  4. Calculate how many Dollars you can buy with 100€. Then, use that dollars to buy Swiss Francs. How many Swiss Francs do you get?
  5. Multiple choice: Which of the following statements is true?
    1. The table indicates that the Purchasing Power Parity Assumption is fulfilled.
    2. The exchange rate of US Dollar to Swiss Franc (CHF) is close to one.
    3. The exchange rate of US Dollar to the Russian Ruble (RUB) is about \(62.2 \frac{\$}{RUB}\).
    4. The exchange rate of Canadian Dollar (CAD) to the Euro (EUR) is about \(0.73\).
    5. With one Canadian Dollar (CAD) you can buy \(0.73\) US Dollars.
  1. Please take part in the discussion in class.

  2. Please take part in the discussion in class.

  3. The exchange rate of Euros to Swiss Francs in direct quotation is: \[E^{\frac{\text{ EUR}}{\text{ CHF}}}=\frac{4.56 \text{ EUR}}{4.75 \text{ USD}} \cdot \frac{6.57 \text{ USD}}{6.50 \text{ CHF}} = \frac{29.9592 \text{ EUR}}{30.875 \text{ CHF}} \approx 0.9703 \frac{\text{ EUR}}{\text{ CHF}}\] and in indirect quotation: \[E^{\frac{\text{ CHF}}{\text{ EUR}}} \approx 1.0305 \frac{\text{ CHF}}{\text{ EUR}}.\] That means, we have to pay about 0.97 Euro for one Swiss Franc or one Euro costs about 1.03 Swiss Franc.

  4. For 100 Euro we get \[100 \text{ EUR} \cdot \frac{4.75 \text{ USD}}{4.56\text{ EUR}} \approx 104.16 \text{ USD}\] and these can be converted to \[104.16 \text{ USD} \cdot \frac{6.50 \text{ CHF}}{6.57\text{ USD}} \approx 103.05 \text{ CHF}\]

  5. Here are the answers:

    1. is false: The price of a Big Mac in $ is different across countries.
    2. is correct.
    3. is false: 1 Ruble costs 0.0160 Dollar: \[ \frac{2.09\text{ USD}}{130 \text{ RUB}} = 0.016\frac{\text{ USD}}{\text{RUB}}.\]
    4. is incorrect: \[ \underbrace{\frac{6.65 \text{ CAD}}{5.08 \text{ USD}}}_{\approx 1.309}\cdot \underbrace{\frac{4.75 \text{ USD}}{4.56 \text{ EUR}}}_{\approx 1.0416} \approx 1.36\frac{\text{ CAD}}{\text{EUR}}. \]
    5. is incorrect: \[ \frac{6.05 \text{ CAD}}{5.08 \text{ USD}} \approx 0.76 \frac{\text{ CAD}}{\text{ USD}}. \] Thus, with one Canadian Dollar you can buy 0.76 U.S. Dollar.

Exercise 17.6 International arbitrage

Table 17.3: Table of price variations across countries
Country Price of Good 08/15
Germany $2
Switzerland $6
United States of America $6
  1. Consider a scenario where the good 08/15 is freely tradeable across countries without any cost (akin to digital software). You have $100, and upon examining the prices of 08/15 in three different countries, you notice discrepancies as depicted in Table 17.3. Discuss how you could profit from international arbitrage, the practice of exploiting price differences of a good across countries. Describe the potential impact on the prices of the good once arbitrage begins.

  2. Assuming 08/15 can be traded freely across borders like software, imagine your arbitrage efforts have harmonized the prices of the good worldwide, as illustrated in the Table 17.4:

Table 17.4: Table of prices and currencies across countries post-arbitrage
Country Price in USD Price in Local Currency
Germany $4 EUR 2
Switzerland $4 CHF 6
United States of America $4 -

Now, calculate and elucidate the following exchange rates:

  • \(\frac{\text{USD}}{\text{EUR}}\)
  • \(\frac{\text{EUR}}{\text{USD}}\)
  • \(\frac{\text{USD}}{\text{CHF}}\)
  • \(\frac{\text{CHF}}{\text{USD}}\)
  • \(\frac{\text{CHF}}{\text{EUR}}\)
  • \(\frac{\text{EUR}}{\text{CHF}}\)
  1. International arbitrage strategy

    • Strategy: Buy 50 units of good 08/15 in Germany for $2 each with your $100. Then, sell these units in Switzerland or the USA for $6 each, making a total of $300. This is a classic arbitrage strategy.
    • Impact on Prices: Consider that you repeat that winning strategy to buy in Germany and sell in some other country, prices will change: The increased demand in Germany will cause the price there to rise, while the increased supply in Switzerland and the USA will cause the price to drop. Eventually, the price differences will equalize, eliminating the arbitrage opportunity.
  2. Calculating exchange rates

  • USD to EUR: \(\frac{4 USD}{2 EUR} = 2\frac{USD}{EUR}\)

  • EUR to USD: \(0.5 \frac{EUR}{USD}\)

  • USD to CHF: \(\frac{2}{3} \frac{USD}{CHF}\)

  • CHF to USD: \(1.5 \frac{CHF}{USD}\)

  • CHF to EUR: \(\frac{3}{1} \frac{CHF}{USD}\)

  • EUR to CHF: \(\frac{1}{3} \frac{EUR}{CHF}\)

Exercise 17.7 Brexit and the exchange rate

Examine Figure 17.10 and discuss the reasons behind the depreciation of the British pound since June 2016.

Figure 17.10: The Price of the British Pound (€/£)

Source: Süddeutsche Zeitung am Wochenende, 17./18. November 2018, year 74, week 46, No. 265, p. 1 (front page).