We begin with the previously developed equations of stock
and flow equilibrium respectively:
1. r*
= − (1/θ) M/P + γ/θ −
τ + (ε/θ) Y
2. Y
= ( a + δ
+ ΦBT + DSB)/(s + m)
− μ/(s + m) r*
+ m*/(s + m) Y*
− σ/(s + m) Q
If you are not completely familiar with the derivation and meaning of
these equations and their presentation in graphical form you should
review the previous module.
Consider first the less-than-full-employment case. Since
the domestic price level is fixed by construction and the price
level in the rest of the world is independent of what happens in
the domestic economy, fixing of the nominal exchange rate implies
a fixed level of the real exchange rate Q . This can be
seen from the definition of the real exchange rate
3. Q
= P / Π P*
In Equation 2, when Q is fixed
there is only one level of Y consistent with flow or goods
market equilibrium, given that r* and Y* are determined
in the rest of the world. This equilibrium level of Y is obviously
independent of asset equilibrium because the asset
equilibrium given in Equation 1 does not enter into its determination.
When we plug this equilibrium level of Y into the asset equilibrium
equation, it can be rearranged to yield
1a. M/P
= − θ (r* + τ) + γ
+ ε Y .
Given the level of Y, there is only one level
of the nominal money stock consistent with stock or asset equilibrium at
the fixed price level and the world-determined real interest rate.
Consider now the full-employment case. Output is fixed at its
full-employment level and the price level responds to market conditions.
When we replace Y in Equation 2 with its full-employment
level YF and take into account that the real
interest rate is determined by conditions abroad, there is only
one level of Q consistent with flow equilibrium.
2a. Q
= a + δ
+ ΦBT + DSB −
(s + m) YF − μ r*
+ m* Y*
Now fix the nominal exchange rate. Taking into account that the
price level in the rest of the world is fixed by conditions
abroad, the equilibrium level of Q implies from Equation 3
an equilibrium level of P.
Thus, under fixed exchange rates with full employment the
domestic price level is determined by the condition of domestic
commodity market equilibrium combined with the real interest rate
(and output and price level) determined in the rest of the world---the
domestic money supply is not a determinant of the domestic
price level. It can now be seen from a slight modification of
Equation 1a to replace Y with YF
1b. M/P
= − θ (r* + τ) + γ
+ ε YF
that given the above-determined domestic price level, the
internationally determined real interest rate and domestic full-employment
level of income, there is only one level of the domestic nominal money
stock consistent with domestic asset equilibrium. Once they fix the
exchange rate, the domestic authorities lose control over the domestic money
supply.
The important result of the above analysis is that under
fixed exchange rates the equilibrium levels of prices and employment in
the domestic economy are determined by the conditions of domestic flow
equilibrium at the levels of the domestic real interest rate and
foreign output and prices determined by conditions abroad. The condition of
domestic asset equilibrium does not figure in domestic output and price level
determination. And the domestic money supply is therefore endogenously
determined by rest-of-world determined domestic interest rate and the levels
of domestic output and prices, independently of the desires of the domestic
authorities.
The question immediately arises as to the mechanism by which the equilibrium
level of the domestic money supply is established? In what way are the
authorities forced to provide the equilibrium nominal money stock? We
consider this issue in the next topic.
Now it is time for a test. Think up your own answers before looking at the
ones provided.
You have learned that under flexible exchange rates
equilibrium output and prices in the small open economy are
determined by the world interest rate and the condition of asset
equilibrium, with the exchange rate adjusting endogenously to
maintain commodity market equilibrium. We now show that under
fixed exchange rates equilibrium is determined by the world
interest rate and the condition of goods market equilibrium, with
the money supply adjusting endogenously to maintain asset equilibrium.
In this case the money supply becomes independent of the policy intentions of
the monetary authorities and monetary policy becomes impotent.