Prof. Gustavo Indart
Department of Economics
University of Toronto
ECO209
MACROECONOMIC THEORY
Chapter 11
MONEY, INTEREST, AND INCOME
Discussion Questions:
1. The model in Chapter 9 assumed that both the price level and the interest rate were fixed.
But the IS-LM model lets the interest rate fluctuate and determines the combination of
output demanded and the interest rate for a fixed price level. It should be noted that while
the upward-sloping AD-curve in Chapter 9 (the [C+I+G+NX]-line in the Keynesian cross
diagram) assumed that interest rates and prices were fixed, the downward-sloping AD-curve
that is derived at the end of Chapter 10 from the IS-LM model lets the price level fluctuate
and describes all combinations of the price level and the level of output demanded at which
the goods and money sector simultaneously are in equilibrium.
2.a. If the expenditure multiplier (α) becomes larger, the increase in equilibrium income caused
by a unit change in intended spending also becomes larger. Assume investment spending
increases due to a change in the interest rate. If the multiplier α becomes larger, any
increase in spending will cause a larger increase in equilibrium income. This means that the
IS-curve will become flatter as the size of the expenditure multiplier becomes larger.
If aggregate demand becomes more sensitive to interest rates, any change in the
interest rate causes the [C+I+G+NX]-line to shift up by a larger amount and, given a certain
size of the expenditure multiplier α, this will increase equilibrium income by a larger amount.
As a result, the IS-curve will become flatter.
2.b. Monetary policy changes affect interest rates and this leads to a change in intended
spending, which is reflected in a change in income. In 2.a. it was explained that a steep IScurve means either that the multiplier α is small or that desired spending is not very interest
sensitive. Therefore, an increase in money supply will reduce interest rates. However, this
does not result in a large increase in aggregate demand if spending is very interest
insensitive. Similarly, if the multiplier is small, then any change in spending will not affect
output significantly. Therefore, the steeper the IS-curve, the weaker the effect of monetary
policy changes on equilibrium output.
2
3. Assume that money supply is fixed. Any increase in income will increase money demand
and the resulting excess demand for money will drive the interest rate up. This, in turn, will
reduce the quantity of money balances demanded to bring the money sector back to
equilibrium. But if money demand is very interest insensitive, then a larger increase in the
interest rate is needed to reach a new equilibrium in the money sector. As a result, the LMcurve becomes steeper.
Along the LM-curve, an increase in the interest rate is always associated with an
increase in income. This means that an increase in money demand (due to an increase in
income) has to be offset by a decrease in the quantity of money demanded (due to an
increase in the interest rate) to keep the money sector in equilibrium. But if money demand
becomes more income sensitive, a smaller change in income is required for any specific
change in the interest rate to keep the money sector in equilibrium. Therefore, the LM-curve
becomes steeper as money demand becomes more income sensitive.
4.a. A horizontal LM-curve implies that the public is willing to hold whatever money is supplied
at any given interest rate. Therefore, changes in income will not affect the equilibrium
interest rate in the money sector. But if the interest rate is fixed, we are back to the analysis
of the simple Keynesian model used in Chapter 9. In other words, there is no offsetting
effect (or crowding-out effect) to fiscal policy.
4.b. A horizontal LM-curve implies that changes in income do not affect interest rates in the
money sector. Therefore, if expansionary fiscal policy is implemented, the IS-curve shifts to
the right, but the level of investment spending is no longer negatively affected by rising
interest rates, that is, there is no crowding-out effect. In terms of Figure 10-3, the interest
rate not longer serves as the link between the goods and assets markets.
4.c. A horizontal LM-curve results if the public is willing to hold whatever money balances are
supplied at a given interest rate. This situation is called the liquidity trap. Similarly, if the
Bank of Canada is prepared to peg the interest rate at a certain level, then any change in
income will be accompanied by an appropriate change in money supply. This will lead to
continuous shifts in the LM-curve, which is equivalent to having a horizontal LM-curve, since
the interest rate will never change.
5. From the material presented in the text we know that when intended spending becomes
more interest sensitive, then the IS-curve becomes flatter. Now assume that an increase in
the interest rate stimulates saving and therefore reduces the level of consumption. This
means that now not only investment spending but also consumption is negatively affected
by an increase in the interest rate. In other words, the [C+I+G+NX]-line in the Keynesian
cross diagram will now shift down further than previously and the level of equilibrium income
will decrease more than before. In other words, the IS-curve has become flatter.
This can also be shown algebraically, since we can now write the consumption function
as follows:
C = C* + cYD - gi
In a simple model of the expenditure sector without income taxes, the equation for
aggregate demand will now be
AD = Ao + cY - (b + g)i.
From Y = AD ==> Y = [1/(1 - c)][Ao - (b + g)i] ==>
3
i = [1/(b + g)]Ao - [(1 - c)/(b + g)]Y
Therefore, the slope of the IS-curve has been reduced from (1 - c)/b to (1 - c)/(b + g).
6. In the IS-LM model, a simultaneous decline in interest rates and income can only be caused
by a shift of the IS-curve to the left. This shift in the IS-curve could have been caused by a
decrease in private spending due to negative business expectations or a decline in
consumer confidence. In 1991, the economy was in a recession and firms did not want to
invest in new machinery and, since consumer confidence was very low, people were not
expected to increase their level of spending. In the IS-LM diagram the adjustment process
can be described as follows:
Io ↓ ==> Y ↓ (the IS-curve shifts left) ==> md ↓ ==> i ↓ ==> I ↑ ==> Y ↑.
Effect: Y ↓ and i ↓ .
i
i1
ISo
LM
IS1
i2
0
Y2
Y1
Y
Application Questions:
1.a. Each point on the IS-curve represents an equilibrium in the expenditure sector. Therefore
the IS-curve can be derived by setting
Y = C + I + G = (0.8)[1 - (0.25)]Y + 900 - 50i + 800 = 1,700 + (0.6)Y - 50i ==>
(0.4)Y = 1,700 - 50i ==> Y = (2.5)(1,700 - 50i) ==> Y = 4,250 - 125i.
1.b. The IS-curve shows all combinations of the interest rate and the level of output such that
the expenditure sector (the goods market) is in equilibrium, that is, intended spending is
equal to actual output. A decrease in the interest rate stimulates investment spending,
making intended spending greater than actual output. The resulting unintended inventory
decrease leads firms to increase their production to the point where actual output is again
equal to intended spending. This means that the IS-curve is downward sloping.
1.c. Each point on the LM-curve represents an equilibrium in the money sector. Therefore the
LM-curve can be derived by setting real money supply equal to real money demand, that is,
M/P = L ==> 500 = (0.25)Y - 62.5i ==> Y = 4(500 + 62.5i) ==> Y = 2,000 + 250i.
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1.d. The LM-curve shows all combinations of the interest rate and level of output such that the
money sector is in equilibrium, that is, the demand for real money balances is equal to the
supply of real money balances. An increase in income will increase the demand for real
money balances. Given a fixed real money supply, this will lead to an increase in interest
rates, which will then reduce the quantity of real money balances demanded until the money
market clears. In other words, the LM-curve is upward sloping.
1.e. The level of income (Y) and the interest rate (i) at the equilibrium are determined by the
intersection of the IS-curve with the LM-curve. At this point, the expenditure sector and the
money sector are both in equilibrium simultaneously.
From IS = LM ==> 4,250 - 125i = 2,000 + 250i ==> 2,250 = 375I ==> i = 6
==> Y = 4,250 - 125*6 = 4,250 - 750 ==> Y = 3,500
Check: Y = 2,000 + 250*6 = 2,000 + 1,500 = 3,500
i
125
IS
LM
6
0
2,000
3,500
4,250
Y
2.a. As we have seen in 1.a., the value of the expenditure multiplier is α = 2.5. This multiplier α
is derived in the same way as in Chapter 9. But now intended spending also depends on the
interest rate, so we no longer have Y = αAo, but rather
Y = α(Ao - bi) = (1/[1 - c + ct])(Ao - bi) ==> Y = (2.5)(1,700 - 50i) = 4,250 - 125i.
2.b. This can be answered most easily with a numerical example. Assume that government
purchases increase by ∆G = 300. The IS-curve shifts parallel to the right by
==> ∆IS = (2.5)(300) = 750.
Therefore IS': Y = 5,000 - 125i
From IS' = LM ==> 5,000 - 125i = 2,000 + 250i ==> 375i = 3,000 ==> i = 8
==> Y = 2,000 + 250*8 ==> Y = 4,000 ==> ∆Y = 500
When interest rates are assumed to be constant, the size of the multiplier is equal to α = 2.5,
that is, (∆Y)/(∆G) = 750/300 = 2.5. But when interest rates are allowed to vary, the size of
the multiplier is reduced to α1 = (∆Y)/(∆G) = 500/300 = 1.67.
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2.c. Since an increase in government purchases by ∆G = 300 causes a change in the interest
rate of 2 percentage points, government spending has to change by ∆G = 150 to increase
the interest rate by 1 percentage point.
2.d. The simple multiplier α in 2.a. shows the magnitude of the horizontal shift in the IS-curve,
given a change in autonomous spending by one unit. But an increase in income increases
money demand and the interest rate. The increase in the interest rate crowds out some
investment spending and this has a dampening effect on income. The multiplier effect in 2.b.
is therefore smaller than the multiplier effect in 2.a.
3.a. The LM-curve becomes flatter as money supply becomes interest sensitive. Any increase in
income will lead to an increase in money demand, which will drive up the interest rate. But
the higher interest rates will not only reduce the demand for money but also increase the
supply of money. Thus a smaller increase in the interest rate than before is required to bring
the money sector back into equilibrium. This means that the LM-curve is flatter.
3.b. If the central bank believes that private spending is very interest sensitive, it is more likely to
pursue policies that are intended to keep interest rates from fluctuating. If the central bank
believes that most economic disturbances result from changes in money demand (causing
the LM-curve to shift), then it is more likely to increase money supply in response to higher
interest rates. In other words, if the Bank of Canada accommodates an increase in money
demand by increasing money supply, then neither income nor the interest rate will be
affected. On the other hand, a disturbance can also come from the expenditure sector, in
which case the IS-curve will shift. If interest rates increase due to higher desired spending,
then the rise in interest rates can again be kept in check if the Bank of Canada responds by
increasing money supply. This time, however, the overall increase in the level of output
demanded will now be even larger due the expansionary monetary policy and this may not
be desirable.
4.a. An increase in the income tax rate (t) will reduce the size of the expenditure multiplier (α).
But as the multiplier becomes smaller, the IS-curve becomes steeper. As we can see from
the equation for the IS-curve, this is not a parallel shift but rather a rotation around the
vertical intercept.
Y = α(Ao - bi) = [1/(1 - c + ct)](Ao - bi) ==> i = (1/b)Ao - (α/b)Y = (1/b)Ao - (1/b)[1 - c + ct]Y
4.b. If the IS-curve shifts to the left and becomes steeper, the equilibrium income level will
decrease. A higher tax rate reduces private spending and this will lower national income.
4.c. When the income tax rate is increased, the equilibrium interest rate will also decrease. The
adjustment to the new equilibrium can be expressed as follows (see graph on the next
page):
t up ==> C down ==> Y down ==> md down ==> i down ==> I up ==> Y up.
Effect: Y ↓ and i ↓
6
i
IS1
ISo
LM
i1
i2
0
Y2
Y1
Y
5.a. If money demand is less interest sensitive, then the LM-curve is steeper and monetary
policy changes affect equilibrium income to a larger degree. If money supply is assumed to
be fixed, the adjustment to a new equilibrium in the money sector has to come solely
through changes in money demand. If money demand is less interest sensitive, any
increase in money supply requires a larger increase in income and a larger decrease in the
interest rate in order to bring the money sector into a new equilibrium.
i
i
IS
LM1
LM2
IS
LM1
i1
i1
i2
i2
0
Y1
Y2
Y
0
LM2
Y1
Y2
Y
The adjustment process in each of the two diagrams is the same; however, in the case of a
more interest-sensitive money demand (a flatter LM-curve), the change in Y and i will be
smaller.
(M/P) up ==> i down ==> I up ==> Y up ==> md up ==> i up
Effect: Y↑ and i ↓
Section 10-5 derives the equation for the LM-curve and the equation for the monetary policy
multiplier as
i = (1/h)[kY - (M/P)] and (∆Y)/∆(M/P) = (b/h)γ
respectively. If money demand becomes more interest sensitive, the value of h becomes
larger and the slope of the LM-curve becomes flatter, while the size of the monetary policy
multiplier becomes smaller.
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5.b. An increase in money supply drives interest rates down. This decrease in interest rates will
stimulate intended spending and thus income. If money demand becomes less interest
sensitive, a larger increase in income is required to bring the money sector into equilibrium.
But this implies that the overall decrease in the interest rate has to be larger, given that the
interest sensitivity of spending has not changed.
6. The price adjustment, that is, the movement along the AD-curve, can be explained in the
following way: With nominal money supply (M) fixed, real money balances (M/P) will
decrease as the price level (P) increases. There is an excess demand for money and
interest rates will rise. This will lead to a decrease in investment spending and thus the level
of output demanded will decrease. In other words, the LM-curve will shift to the left as real
money balances decrease.
7. In the classical case, the AS-curve is vertical. Therefore, any increase in aggregate demand
due to expansionary monetary policy will, in the long run, not lead to any increase in output
but simply lead to an increase in the price level. An increase in money supply will first shift
the LM-curve to the right. This implies a shift of the AD-curve to the right. Therefore we have
excess demand for goods and services and prices will begin to rise. But as the price level
rises, real money balances will begin to fall again, eventually returning to their original level.
Therefore, the shift of the LM-curve to the right due to the expansionary monetary policy and
the resulting shift of the AD-curve will be exactly offset by a shift of the LM-curve to the left
and a movement along the AD-curve to the new long-run equilibrium due to the price
adjustment. At this new long-run equilibrium, the level of output and interest rates will not
have changed while the price level will have changed proportionally to the nominal money
supply, leaving real money balances unchanged. In other words, money is neutral in the
long run (the classical case).
8.a. An increase in the demand for money will shift the LM-curve to the left, raising the interest
rate and lowering the level of output demanded. As a result, the AD-curve will also shift to
the left. In the Keynesian case, the price level is assumed to be fixed, that is, the AS-curve
is horizontal. In this case, the decrease in income in the AD-AS diagram is equivalent to the
decrease in income in the IS-LM diagram, since there is no price adjustment, that is, the real
balance effect does not come into play.
8.b. An increase in the demand for money will shift the LM-curve to the left, raising the interest
rate and lowering the level of output demanded. As a result, the AD-curve will also shift to
the left. In the classical case, the level of output will not change, since the AS-curve is
vertical. In this case, the shift in the AD-curve will simply be reflected in a price decrease,
but the level of output will remain unchanged. The real balance effect causes the LM-curve
to shift back to its original level, since the price decrease causes an increase in real money
balances.