Real Exchange RateStylized Example

Set UpOnly two countries US and Canada Only two goods Grain and SaltComparison between monetary and non monetary economy 1) Barter economySuppose that people from the US and Canada meet at the border to exchange Grain with Salt once a year

Real Exchange RateSuppose that at t=01 kg of Grain is exchanged with 1 kg of Salti.e. 1 kg of Grain = 1 kg of Salt

The real exchange rate is: e0(Grain/Salt)real = e0(US/CANADA)real =1

Monetary EconomySuppose that the prices are as follows:1 kg of Grain = USD 11 kg of Salt = CAD 1.5Given the prices and the real exchange rate :1 kg of Grain *USD 1 = 1 kg of Salt *CAD 1.5, that is: USD 1 = 1.5 CAD => e0(CAD/USD)nominal=1.5

After 1 Period, at t=1Suppose that Grain crops was bad last year, so there is less offer of Grain. Salt production is unchanged. Now the new real exchange after one year is:kg of Grain = 1.1 kg of Salt The new real exchange rate is: e1(Grain/Salt)real = e1(US/CANADA)real =1.1

Case 1: No change in domestic prices in USD and CADIf the price are unchanged, we can compute the nominal exchange rate as before:1 kg of Grain *USD 1 = 1.1 kg of Salt *CAD 1.5At t=1 the forex rate is USD 1 = 1.5 CAD => e1(CAD/USD)nominal=1.65

Case 2: Assume inflation in both countriesAssume that the new price of the two goods are:1 kg of Grain = USD 1.03 (inflation at 3%)1 kg of Salt = CAD 1.575 (inflation at 5%)Given the real exchange rate of 1.1, the new nominal exchange rate is:1 kg of Grain *USD 1* (1+3%) = 1.1 kg of Salt *CAD 1.5 (1+5%)

Nominal Exchange rateThe new prices will imply that the nominal exchange rate is also changed.

This in our usual notation implies:e1(CAD/USD)nominal =1.68

ConclusionThis is to show how real and nominal exchange rate are linked and to retrieve the formula we have used to compute the real exchange rates: