Exchange Rates represent the linkage between one country and its partners in the global economy. They affect the relative price of goods being traded (exports and imports), the valuation of assets, and the yield on those assets. In the period of fixed exchange rates these prices, values, and yields were predictable over time. However, since 1973 we have been living in a world of flexible exchange rates where foreign exchange markets determine these rates based on trade flows, interest rate differentials, differing rates of inflation, and speculation about future events.

2.6.1 Nominal Exchange Rates

Exchange rates can be expressed as the foreign price of a domestic currency (i.e., the Euro price of a U.S. dollar) or its reciprocal -- the domestic price of foreign currency. We will express these values using the following notation:

the Euro price of a Dollar: €P$

or

the Dollar price of a Euro: $P/€

Currently this particular ratio of currencies is near parity ($1.30:1). Note that in the table below the rate between the U.S. and Canada is near parity (1:1). The following represents the foreign-exchange value of a U.S. dollar as of April 2013 and 2017 (from here on out, exchange rates will be expressed as the Foreign Price of a Dollar 'FP/$'):

Exchange Rates (04/2013, 11/2017)

* a stronger dollar (weaker foreign currency) between 2013 and 2017

All of the above rates represent Nominal Exchange Rates in that they are the actual posted trading rates on foreign exchange markets. These particular rates can be used to find the domestic price of foreign goods. For example, suppose that we are interested in the price of a litre of whiskey (Suntory) player manufactured in Japan:

P_Japan = ¥ 8,060

if the exchange rate is:

¥124 = $1

then the domestic (U.S.) price of this same good is:

P_U.S. = $65 (8,060/124)

As exchange rates fluctuate, the domestic prices of foreign goods will often be affected:

New exchange rate:	¥140 = $1	(a weaker Yen)
Price of a litre in Japan:	PJapan = ¥ 8,060	(unchanged)
Price of that litre in the U.S.:	PU.S. = $57.60	(less expensive)

The weaker yen (it now takes more yen to buy a U.S. dollar) or stronger dollar (a dollar now buys more yen), has led to a reduction in the price of Japanese exports and U.S. imports. We would expect that this change will lead to an increase in the flow of goods from Japan to the U.S. However, trade flows are affected not by nominal exchange rates, but instead, Real Exchange Rates

2.6.2 Purchasing Power Parity

In order to understand the determination of real exchange rates, we need to examine the concept of Purchasing Power Parity or PPP

Suppose that we compare the price of a common good in two different countries. The Economist magazine often used a McDonald's Big Mac.^™ for this purpose. McDonald's operates in many countries around the world selling products governed by strict specifications and standards. The presentation and taste of a Big Mac.^™ (based on this author's experience) is identical in Beijing, Denver, Jakarta, Singapore, and Seoul. Using this homogeneous worldwide product, we expect the following to be true:

Exchange rate:	¥124 = $1
Price of a Big Mac.™ in the U.S.:	PU.S. = $2.25
Price of Big Mac.™ in Japan:	PJapan = ¥ 279

If Purchasing Power Parity holds then the nominal exchange rate should be:

¥P(Big Mac.^™) / $P(Big Mac.^™) = ¥ 279 / $2.25 = ¥124 : $1

But what if we had the following:

Exchange rate:	¥124 = $1
Price of a Big Mac.™ in the U.S.:	PU.S. = $2.25
Price of Big Mac.™ in Japan:	PJapan = ¥300

In this case,

¥P(Big Mac.^™) / $P(Big Mac.^™) greater than nominal exchange rate.

We could therefore take $1,000 and buy 444 Big Macs.^™; export the Big Macs.^™ to Japan and sell them for ¥300 each. This would generate ¥ 133,200 in revenue. We then sell yen on foreign exchange markets and buy dollars. At the current exchange rate, this would allow us to buy $1074 (¥133,200/¥124) and earn a profit of $74.

However, this process of arbitrage (on a larger scale) should affect Big Mac.^™ prices and the nominal exchange rate. The buying of Big Macs.^™ in the U.S. should push the domestic price upwards. The selling of Big Macs.^™ should drive prices down in Japan. The selling of Yen on foreign exchange markets should weaken the Yen and the buying of Dollars should strengthen the dollar. This activity will continue until the ratio of Big Mac.^™ prices is just equal to the nominal exchange rate.

2.6.3 The Real Exchange Rate

This information between nominal exchange rates and foreign/domestic prices of a common good can be expressed as a single value -- the Real Exchange Rate'ε_r':

ε_r = e.r._nominal[P_domestic / P_foreign]

or

ε_r = (¥P/$)[$P(Big Mac.^™) / ¥P(Big Mac.^™)]

This real exchange rate 'ε_r' is a unit-free measure where, in the case of a single good, its value can be interpreted relative to 1.0 (PPP). In our above example where '¥P/$ = 124:1, the ¥P(Big Mac.^™) = 300, and the $P(Big Mac.^™) = 2.25 we would calculate the real rate to be:

ε_r = (124)[2.25 / 300] = 0.93

or 1 Big Mac.^™ in the U.S. is equivalent to 0.93 Big Macs.^™ in Japan allowing for arbitrage opportunities. Either the Yen must weaken, the price of Big Macs.^™ in the U.S. must increase, or the price of Big Macs.^™ in Japan must fall. However, other economic events or conditions (capital flows, trade barriers, price-making power) may prevent this from happening.

These real exchange rates do provide a foundation for the direction of trade flows such that:

Net Exports 'NX' = f_(-)(ε_r)

The above rate of 0.93 would lead to the export of Big Macs.^™ from the U.S. and imported into Japan.

The calculation of real exchange rates are more-likely based on a basket of goods rather that a single homogeneous commodity. Thus, price indices in different countries are used such that:

ε_r = e.r._nominal[CPI_domestic / CPI_foreign]

In constructing the real exchange rate this way we can then think about how differences in rates of inflation among nations either affect this real rate and thus trade flows or perhaps leads to changes in nominal exchange rates:

if %ΔP_U.S. > %ΔP_Japan then either: ε_r ↑ or e.r._nominal ↓

In using these indices, we can no longer interpret the real exchange rate relative to a unit value (1.0). Instead we are forced to look at the direction of change in the real rate to understand the effect on exports and imports.