The Equilibrium Interest Rate: The Interaction
of Money Supply and Demand
As you might expect from other economics courses you’ve taken, the money market is
in equilibrium when the money supply set by the central bank equals aggregate money
demand. In this section we see how the interest rate is determined by money market
equilibrium, given the price level and output, both of which are temporarily assumed to
be unaffected by monetary changes.
Equilibrium in the Money Market
If is the money supply, the condition for equilibrium in the money market is
(15-3)
After dividing both sides of this equality by the price level, we can express the money
market equilibrium condition in terms of aggregate real money demand as
(15-4)
Given the price level, P, and the level of output, Y, the equilibrium interest rate is the one
at which aggregate real money demand equals the real money supply.
In Figure 15-3, the aggregate real money demand schedule intersects the real money
supply schedule at point 1 to give an equilibrium interest rate of . The money supply
schedule is vertical at because is set by the central bank while P is taken as given.
Let’s see why the interest rate tends to settle at its equilibrium level by considering what
happens if the market is initially at point 2, with an interest rate, R2, that is above R1.
Ms/P Ms
R1
Ms/P = L(R, Y).
Ms = Md.
Ms
Y1
L(R, Y2) L(R, Y1) Y2
Y1 Y2
Interest
rate, R
Aggregate real
money demand
L(R, Y 1)
Increase in
real income
L(R, Y 2)
Figure 15-2
Effect on the Aggregate Real
Money Demand Schedule of a
Rise in Real Income
An increase in real income from
Y1 to Y2 raises the demand for real
money balances at every level of
the interest rate and causes the
whole demand schedule to shift
upward.
CHAPTER 15 Money, Interest Rates, and Exchange Rates 361
At point 2 the demand for real money holdings falls short of the supply by , so
there is an excess supply of money. If individuals are holding more money than they desire
given the interest rate of , they will attempt to reduce their liquidity by using some
money to purchase interest-bearing assets. In other words, individuals will attempt to get
rid of their excess money by lending it to others. Since there is an aggregate excess supply
of money at , however, not everyone can succeed in doing this: There are more people
who would like to lend money to reduce their liquidity than there are people who would
like to borrow money to increase theirs. Those who cannot unload their extra money try to
tempt potential borrowers by lowering the interest rate they charge for loans below .
The downward pressure on the interest rate continues until the rate reaches . At this
interest rate, anyone wishing to lend money can do so because the aggregate excess supply
of money has disappeared; that is, supply once again equals demand. Once the market
reaches point 1, there is therefore no further tendency for the interest rate to drop.4
Similarly, if the interest rate is initially at a level below , it will tend to rise. As
Figure 15-3 shows, there is excess demand for money equal to at point 3.
Individuals therefore attempt to sell interest-bearing assets such as bonds to increase
their money holdings (that is, they sell bonds for cash). At point 3, however, not everyone
can succeed in selling enough interest-bearing assets to satisfy his or her demand
for money. Thus, people bid for money by offering to borrow at progressively higher interest
rates and push the interest rate upward toward . Only when the market has
reached point 1 and the excess demand for money has been eliminated does the interest
rate stop rising.
R1
Q3 - Q1
R3 R1
R1
R2
R2
R2
Q1 - Q2
Real money supply
Interest
rate, R
Aggregate real
money demand,
L(R, Y)
Real money
holdings
Q2
R3
R1
R2
Q3
2
1
3
Ms
P
(= Q1)
Figure 15-3
Determination of the Equilibrium
Interest Rate
With P and Y given and a real
money supply of MS/P, money
market equilibrium is at point 1.
At this point, aggregate real
money demand and the real
money supply are equal and the
equilibrium interest rate is R1.
4 Another way to view this process is as follows: We saw in the last chapter that an asset’s rate of return falls
when its current price rises relative to its future value. When there is an excess supply of money, the current
money prices of illiquid assets that pay interest will be bid up as individuals attempt to reduce their money holdings.
This rise in current asset prices lowers the rate of return on nonmoney assets, and since this rate of return is
equal to the interest rate (after adjustment for risk), the interest rate also must fall.
362 PART THREE Exchange Rates and Open-Economy Macroeconomics
We can summarize our findings as follows: The market always moves toward an interest
rate at which the real money supply equals aggregate real money demand. If there is
initially an excess supply of money, the interest rate falls, and if there is initially an excess
demand, it rises.
Interest Rates and the Money Supply
The effect of increasing the money supply at a given price level is illustrated in Figure 15-4.
Initially the money market is in equilibrium at point 1, with a money supply and an
interest rate . Since we are holding P constant, a rise in the money supply to increases
the real money supply from to . With a real money supply of , point 2 is
the new equilibrium and is the new, lower interest rate that induces people to hold the increased
available real money supply.
The process through which the interest rate falls is by now familiar. After is increased
by the central bank, there is initially an excess real supply of money at the old
equilibrium interest rate, , which previously balanced the market. Since people are
holding more money than they desire, they use their surplus funds to bid for assets that
pay interest. The economy as a whole cannot reduce its money holdings, so interest rates
are driven down as unwilling money holders compete to lend their excess cash balances.
At point 2 in Figure 15-4, the interest rate has fallen sufficiently to induce an increase in
real money demand equal to the increase in the real money supply.
By running the above policy experiment in reverse, we can see how a reduction of the
money supply forces interest rates upward. A fall in causes an excess demand for
money at the interest rate that previously balanced supply and demand. People attempt to
sell interest-bearing assets—that is, to borrow—to rebuild their depleted real money holdings.
Since they cannot all be successful when there is excess money demand, the interest
rate is pushed upward until everyone is content to hold the smaller real money stock.
We conclude that an increase in the money supply lowers the interest rate, while a fall
in the money supply raises the interest rate, given the price level and output.
Ms
R1
Ms
R2
M1/P M2/P M2/P
R1 M2
M1
M1
P
Interest
rate, R
Real money
holdings
2
1
L(R, Y)
R1
R2
Real money
supply
Real money
supply increases
M2
P
Figure 15-4
Effect of an Increase in the
Money Supply on the Interest
Rate
For a given price level, P, and real
income level, Y, an increase in
the money supply from M1 to M2
reduces the interest rate from R1
(point 1) to R2 (point 2).
CHAPTER 15 Money, Interest Rates, and Exchange Rates 363
Output and the Interest Rate
Figure 15-5 shows the effect on the interest rate of a rise in the level of output from to
, given the money supply and the price level. As we saw earlier, an increase in output
causes the entire aggregate real money demand schedule to shift to the right, moving the
equilibrium away from point 1. At the old equilibrium interest rate, , there is an excess
demand for money equal to (point ). Since the real money supply is given, the
interest rate is bid up until it reaches the higher, new equilibrium level (point 2). A fall
in output has opposite effects, causing the aggregate real money demand schedule to shift
to the left and therefore causing the equilibrium interest rate to fall.
We conclude that an increase in real output raises the interest rate, while a fall in real
output lowers the interest rate, given the price level and the money supply.
of Money Supply and Demand
As you might expect from other economics courses you’ve taken, the money market is
in equilibrium when the money supply set by the central bank equals aggregate money
demand. In this section we see how the interest rate is determined by money market
equilibrium, given the price level and output, both of which are temporarily assumed to
be unaffected by monetary changes.
Equilibrium in the Money Market
If is the money supply, the condition for equilibrium in the money market is
(15-3)
After dividing both sides of this equality by the price level, we can express the money
market equilibrium condition in terms of aggregate real money demand as
(15-4)
Given the price level, P, and the level of output, Y, the equilibrium interest rate is the one
at which aggregate real money demand equals the real money supply.
In Figure 15-3, the aggregate real money demand schedule intersects the real money
supply schedule at point 1 to give an equilibrium interest rate of . The money supply
schedule is vertical at because is set by the central bank while P is taken as given.
Let’s see why the interest rate tends to settle at its equilibrium level by considering what
happens if the market is initially at point 2, with an interest rate, R2, that is above R1.
Ms/P Ms
R1
Ms/P = L(R, Y).
Ms = Md.
Ms
Y1
L(R, Y2) L(R, Y1) Y2
Y1 Y2
Interest
rate, R
Aggregate real
money demand
L(R, Y 1)
Increase in
real income
L(R, Y 2)
Figure 15-2
Effect on the Aggregate Real
Money Demand Schedule of a
Rise in Real Income
An increase in real income from
Y1 to Y2 raises the demand for real
money balances at every level of
the interest rate and causes the
whole demand schedule to shift
upward.
CHAPTER 15 Money, Interest Rates, and Exchange Rates 361
At point 2 the demand for real money holdings falls short of the supply by , so
there is an excess supply of money. If individuals are holding more money than they desire
given the interest rate of , they will attempt to reduce their liquidity by using some
money to purchase interest-bearing assets. In other words, individuals will attempt to get
rid of their excess money by lending it to others. Since there is an aggregate excess supply
of money at , however, not everyone can succeed in doing this: There are more people
who would like to lend money to reduce their liquidity than there are people who would
like to borrow money to increase theirs. Those who cannot unload their extra money try to
tempt potential borrowers by lowering the interest rate they charge for loans below .
The downward pressure on the interest rate continues until the rate reaches . At this
interest rate, anyone wishing to lend money can do so because the aggregate excess supply
of money has disappeared; that is, supply once again equals demand. Once the market
reaches point 1, there is therefore no further tendency for the interest rate to drop.4
Similarly, if the interest rate is initially at a level below , it will tend to rise. As
Figure 15-3 shows, there is excess demand for money equal to at point 3.
Individuals therefore attempt to sell interest-bearing assets such as bonds to increase
their money holdings (that is, they sell bonds for cash). At point 3, however, not everyone
can succeed in selling enough interest-bearing assets to satisfy his or her demand
for money. Thus, people bid for money by offering to borrow at progressively higher interest
rates and push the interest rate upward toward . Only when the market has
reached point 1 and the excess demand for money has been eliminated does the interest
rate stop rising.
R1
Q3 - Q1
R3 R1
R1
R2
R2
R2
Q1 - Q2
Real money supply
Interest
rate, R
Aggregate real
money demand,
L(R, Y)
Real money
holdings
Q2
R3
R1
R2
Q3
2
1
3
Ms
P
(= Q1)
Figure 15-3
Determination of the Equilibrium
Interest Rate
With P and Y given and a real
money supply of MS/P, money
market equilibrium is at point 1.
At this point, aggregate real
money demand and the real
money supply are equal and the
equilibrium interest rate is R1.
4 Another way to view this process is as follows: We saw in the last chapter that an asset’s rate of return falls
when its current price rises relative to its future value. When there is an excess supply of money, the current
money prices of illiquid assets that pay interest will be bid up as individuals attempt to reduce their money holdings.
This rise in current asset prices lowers the rate of return on nonmoney assets, and since this rate of return is
equal to the interest rate (after adjustment for risk), the interest rate also must fall.
362 PART THREE Exchange Rates and Open-Economy Macroeconomics
We can summarize our findings as follows: The market always moves toward an interest
rate at which the real money supply equals aggregate real money demand. If there is
initially an excess supply of money, the interest rate falls, and if there is initially an excess
demand, it rises.
Interest Rates and the Money Supply
The effect of increasing the money supply at a given price level is illustrated in Figure 15-4.
Initially the money market is in equilibrium at point 1, with a money supply and an
interest rate . Since we are holding P constant, a rise in the money supply to increases
the real money supply from to . With a real money supply of , point 2 is
the new equilibrium and is the new, lower interest rate that induces people to hold the increased
available real money supply.
The process through which the interest rate falls is by now familiar. After is increased
by the central bank, there is initially an excess real supply of money at the old
equilibrium interest rate, , which previously balanced the market. Since people are
holding more money than they desire, they use their surplus funds to bid for assets that
pay interest. The economy as a whole cannot reduce its money holdings, so interest rates
are driven down as unwilling money holders compete to lend their excess cash balances.
At point 2 in Figure 15-4, the interest rate has fallen sufficiently to induce an increase in
real money demand equal to the increase in the real money supply.
By running the above policy experiment in reverse, we can see how a reduction of the
money supply forces interest rates upward. A fall in causes an excess demand for
money at the interest rate that previously balanced supply and demand. People attempt to
sell interest-bearing assets—that is, to borrow—to rebuild their depleted real money holdings.
Since they cannot all be successful when there is excess money demand, the interest
rate is pushed upward until everyone is content to hold the smaller real money stock.
We conclude that an increase in the money supply lowers the interest rate, while a fall
in the money supply raises the interest rate, given the price level and output.
Ms
R1
Ms
R2
M1/P M2/P M2/P
R1 M2
M1
M1
P
Interest
rate, R
Real money
holdings
2
1
L(R, Y)
R1
R2
Real money
supply
Real money
supply increases
M2
P
Figure 15-4
Effect of an Increase in the
Money Supply on the Interest
Rate
For a given price level, P, and real
income level, Y, an increase in
the money supply from M1 to M2
reduces the interest rate from R1
(point 1) to R2 (point 2).
CHAPTER 15 Money, Interest Rates, and Exchange Rates 363
Output and the Interest Rate
Figure 15-5 shows the effect on the interest rate of a rise in the level of output from to
, given the money supply and the price level. As we saw earlier, an increase in output
causes the entire aggregate real money demand schedule to shift to the right, moving the
equilibrium away from point 1. At the old equilibrium interest rate, , there is an excess
demand for money equal to (point ). Since the real money supply is given, the
interest rate is bid up until it reaches the higher, new equilibrium level (point 2). A fall
in output has opposite effects, causing the aggregate real money demand schedule to shift
to the left and therefore causing the equilibrium interest rate to fall.
We conclude that an increase in real output raises the interest rate, while a fall in real
output lowers the interest rate, given the price level and the money supply.
No comments:
Post a Comment