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Long-Run Equilibrium
Output, Wages, Prices and the
Exchange Rate in the Long Run
Aggregate Demand & Aggregate
Money Stock and the Economy
• Money and the real output in the long run
The quantity theory of money:
(The equation of exchange)
P.Q* = M .V
• Money and the price level
M/P = L ( Q , i)
• Money and the interest rate
Money, Price, and the Interest Rate
Mo/Po = M1/P1
D M/P =L (Q,i)
Real Money
Money and the X Rate
• The X rate is simply the price of foreign currency
in terms of the domestic currency; it is a price.
P = e . P*
• The doubling of M leading to a doubling of the P
in the long run (the equation of exchange) would
cause the expected future spot rate to increase
(expected depreciation of the home currency),
shifting the demand for FX to the right.
The FX Market
DFX (i,i*,ee1)
DFX (i,i*,eeo)
Purchasing Power Parity and the Law of One Price
• Arbitrage and the law of one price
Ph = e . P f
• Why doesn’t it hold?
• Transaction/transportation costs
• Trade barriers
• Perceived quality differentials
• The PPP theory of foreign exchange
e = P /P*
%Δ e = %Δ P – %Δ P*
%Δ P = %Δ e + %Δ P*
or P =
e + P*
Why PPP May Not Hold
(A Second Look)
• Transportation/transaction costs
• CPI measurement problems
Tradables vs. nontradables
Different consumer baskets
Changing relative prices within each country
Trade barriers
Absolute vs. relative PPP
PPP and Inflation
Let us recall:
%Δ P = %Δ e + %Δ P*
This equation can be rearranged as:
%Δ e = %Δ P - %Δ P*
e = P – P*
Are inflation rates really important in determining
the X rate?
The Big Mac Index:
The Monetary Approach to the
Exchange Rate
• David Hume’s Specie-Flow Mechanism
Adjustments to full-employment output
Price adjustments
Mercantilists’ accumulation of gold will result in
increases in the price level (lower gold prices), thus,
reducing exports and increasing imports
A Simple Model
• Recall that the equilibrium in the money market
requires that real money stick be equal to the
demand for money:
M/P = L ( Q, i), where Q is constant.
We can then write:
M – P = L or P = M- L
That simply means that inflation rate is equal to
the difference between the growth rate of money
stock and the growth rate of the demand for
We can write the same equation for
the foreign country(*):
P* = M*- L*
Subtracting one form the other:
P – P* = (M - L) – (M*- L*)
P – P = (M - M*) – ( L - L*)
Now recalling e = P – P* (relative PPP)
e = (M – M*) – ( L – L*)
Assuming no changes in the demand for money (L and
L*), a difference in the money stock growth rates would
result in a change in the exchange rate; e = 0
PPP and Inflation
Let us now recall what we learned earlier in
the semester about the relationship between
the exchange rate and the interest rate:
i – i* = (ee – e)/e = ee (Expected rate of change in X rate)
From e = P – P* we write: ee = Pe – Pe*
Thus we write:
ee = Pe – Pe* = i – i*
Now think about how an increase in the money stock at home (ceteris
paribus) could affect the exchange rate.
An alternative approach to the same concept:
Real interest rate = r = i – p or re = i – pe
Or, pe = i – re
For the foreign country: p*e = i* – r*e
Subtracting one from the other:
(pe– p*e) = (i – i*) – ( re –re*)
Assuming the real interest rates at home and
abroad are equal (under free capital flows),
(i – i*) = (pe– pe*) = ee
The Real Exchange Rate
Now recall:
R = P/ (e P*)
We write the equation in terms of % changes:
R = P – e – p* = (P – P* ) – e
Or, e = (P – P*) – R
Note that here R is in fact the real “exchange
rate”. If PPP holds R will not change; R = 0
When PPP does not hole R = 0
R = e - (P – P*)
The Real Exchange Rate and the Real
Interest Rate
We had:
(i – i*) = ( pe – p*e) = ee
From the previous analysis we can write:
ee = (pe – p*e) – Re
Substituting (i – i*) for ee, (i – i*) = ( pe – p*e) - Re
Now from the real interest rate equations we write:
(re – re*) = (i –i*) – ( pe – p*e)
Now substituting ( pe – p*e) – Re for (i –i*), the equation
will simplify to:
(re – re*) = - R e ,
linking the real interest rate to the real exchange rate .