1. Foreign Exchange Markets,
Purchasing Power Parity, and Real Interest Parity
ECO Money & Banking - Dr. D. Foster

2. Purchasing Power Parity
Where . . .
transportation costs are zero.
tax differentials do not exist.
there are no trade restrictions.
goods are homogeneous.
Law of One Price: A unit of goods in one country trades for the same price in another country.

3. Example - Apples in U.S. & Britain
Purchasing Power Parity
Example - Apples in U.S. & Britain
U.S. price = $.50; British = £.75
If exchange rate is .667 ($/£) then the apple sells for the same price in both.
What if the exchange rate is .75?
Sell apple in Britain for .75 (£) and convert to $: (£.75)*(.75) = $.562 for a 6.2 cent profit!

4. Purchasing Power Parity
Different PPP models
Absolute PPP: E = (CPIUS)/(CPIBrit)
Relative PPP: %ΔE = %Δ(CPIUS) - %Δ(CPIBrit)
differences in inflation rates explain . . .
appreciating/depreciating exchange rates.
Long-run data tends to confirm this.

5. Buying Future Dollars Let iUS=6% and iBrit=8% with E=1.2
E aka “spot rate.”
Let the forward rate be Ef=1.18
With $1200, should you invest in US bonds or British bonds?
US bonds earn $1200*1.06 = $1272.
For British bonds: $1200/1.2 = £1000;
in one year, bond earns £1080;
converts back at (1.18)*(1080) = $ 

6. (Ee - E)/E = (ius-reUS) - (iBrit-reBrit)
Buying Future Dollars
In US terms, the British bond earns:
iBrit + [(Ef - E)/E]
With well functioning markets in equilibrium, this equals ius
Noting relative PPP: %Ee = eUS - eBrit
where e=expected and =inflation.
Using “r” to represent real interest, rewrite as:
(Ee - E)/E = (ius-reUS) - (iBrit-reBrit)

7. Real Interest Rate Parity
Substituting for iUS
(Ee - E)/E = (iBrit + [(Ef - E)/E] -reUS) - (iBrit-reBrit)
We can cancel out both iBrit
If Ee=Ef, we can cancel them out
reUS = reBrit

8. Foreign Exchange & Monetary Policy
Gold Standard
Fixed X∆ rates, K flows, $ policy
Bretton Woods System
Fixed X∆ rates, K flows, $ policy
Unmanaged free floating rates
Volatile X∆ rates, K flows, $ policy
Managed rates
Semi-fixed X∆ rates, K flows, ???$ policy

9. Foreign Exchange Markets,
Purchasing Power Parity, and Real Interest Parity
ECO Money & Banking - Dr. D. Foster