Kenneth R. Szulczyk

euroUS

S

euro

USeuro

S

US

euro

US

M V Y

M V Y

P

P

S=  ( 1 3)

Economists utilize a mathematical trick to convert the absolute levels of Equation 13 into
percentage change, yielding Equation 14. We switched the variables to lower case with a dot
above each one to indicate a percentage change for that variable.

s=mUSS meuroS vUSveuroyeuroyUS (14)

Economists can apply Equation 14 to many situations. For example, the real GDP is
growing in Eurozone by 4% per year while the United States is experiencing a 3% real GDP
growth. Furthermore, the European Central Bank expanded the money by 2% while the Federal
Reserve expanded the money supply by 3%. If the velocities for money do not change (i.e. equal
zero), subsequently, the euro should appreciate by 2% against the U.S. dollar. Consequently, the
higher real income and a slower expanding money supply strengthen the euro. Remember, the
denominator of the fraction defines the domestic currency.

International Fisher Effect

The Fisher Effect relates the nominal interest rate to the rate of inflation and real interest
rate. We define the terms as the following:

 Real interest rate equals r.

 Nominal interest rate equals i.

 Expected inflation rate equals .

We define the Fisher Effect by Equation 15:

݅+ 1 =( 1 +ݎ)( 1 +ߨ) (15)

Many economists use algebra to reduce the Fisher Effect to Equation 16, which becomes an
approximation. They set the cross term, r × , to zero.

݅=( 1 +ݎ)( 1 +ߨ)− 1 = 1 +ݎ+ߨ+ߨݎ− 1 ≈ݎ+ߨ (16)

As long as the expected inflation and real interest rates are small, then the approximation
will be accurate. For example, if the expected inflation, , is 10% and nominal interest rate, i,
equals 5%, subsequently, the real interest rate is approximately - 5%. Cross term, r × , is
roughly 0.5%. Consequently, all prices in a society rise by 10% while your nominal investment