Chapter 24
The ISLM
World
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Learning Objectives
• Identify the shift and slope determinants of the LM
curve
• Identity the shift and slope determinants of the IS curve
• Understand how combining the IS and LM curves
determines an equilibrium level of real GDP and
interest rates
• Explain how ISLM analysis is connected to the
aggregate demand curve
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Introduction
• ISLM analysis—a more complex model of GDP
determination
– Shows how monetary and fiscal policy interact
– Shows what determines the relative multiplier effects of each
– Provides a partial integration of the classical and Keynesian
systems into one conceptual framework
– Demonstrates some of the fundamental features
distinguishing classical and Keynesian outlooks
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Introduction (Cont.)
• Initially assume a fixed price level—concerned
with the level of real GDP
• Followed by an analysis of the implications of
flexible wages and prices
• Ultimately the discussion shows how the ISLM
model collapses into an aggregate demand
schedule
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The LM Curve
• Classical economists stressed the transactions demand
for money
• Keynes had a more complex view of the transactions
demand
– Since transactions demand increases with income, the rate of
interest rises as income rises
– Not only does the interest rate help determine income
(classical view), income helps determine the interest rate
(Keynesian)
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The LM Curve (Cont.)
• Keynesian View (Cont.)
– Causation runs both ways—from interest rate to
income and from income to the interest rate
– A reformulation of the model permits determination
of both interest rates and income
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The LM Curve (Cont.)
• Figure 24.1
– Shows three alternative money-demand functions,
each associated with a different level of economic
activity
– Each level of GDP has its own liquidity-preference
function since more money is demanded for
transaction balances at higher income levels
– Therefore, the demand for money is really a function
of two variables—income and interest rate
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FIGURE 24.1 How to derive the LM curve: At higher
levels of income, the demand for money rises and so
do interest rates.
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The LM Curve (Cont.)
• Figure 24.1 (Cont.)
– The equilibrium condition (money demanded =
money supplied) no longer provides a single interest
rate
– There is a combination of income (Y) and interest
rate (r) that satisfies this equilibrium condition,
when the money supply is fixed
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The LM Curve (Cont.)
• Figure 24.2
– A plot of the relationship between Y and r that satisfies
equilibrium conditions in the money market
– Interest rate is on the vertical axis and income on the
horizontal axis
– This relationship is labeled the LM curve since is it the locus
of combinations of Y and r that satisfy the equilibrium
condition
– At different interest rates, shows what the resulting income
would have to be to make demand for money equal to (fixed)
supply
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FIGURE 24.2 The LM curve.
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The LM Curve (Cont.)
• Figure 24.2 (Cont.)
– Tells what the resulting interest rate would have to be at
different income levels to insure demand and supply of
money were equal
– At higher income levels, more transaction money is
desired, so the interest rate must be higher to reduce the
demand to maintain equilibrium with a fixed supply
– However, this relationship by itself does not determine the
actual value of Y and r—need another relationship to interact
with the LM curve
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The Slope of the LM Curve
• Figure 24.3
– Explores the slope of the LM curve
– Assume point A is the initial equilibrium point and
income increases from Y1 to Y2
– At the original interest rate r1, the demand for money
is too great and interest rates must increase to r2 to
restore equilibrium
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FIGURE 24.3 The slope of the LM
curve.
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The Slope of the LM Curve (Cont.)
• Figure 24.3 (Cont.)
– The actual slope of the LM curve is determined by
two factors
• The size of the gap between money demand and supply at
point C—the larger the distance, the greater the required
increase in r and steeper the slope
• The interest-sensitivity of money demanded—the greater
the interest-sensitivity the steeper the slope
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The Slope of the LM Curve (Cont.)
• Monetary Policy and the LM curve
– Figure 24.4
– An increase in the money supply causes the LM curve to shift
to the right
– Therefore, the Federal Reserve can increase the potential
equilibrium level of GDP associated with a given interest rate
(point a to point b)
– However a change in income is not the only way an increase
in the money supply can be absorbed into the economy
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Figure 24.4 An increase in the money
supply shifts the LM curve to the right
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The Slope of the LM Curve (Cont.)
• Monetary Policy and the LM curve
– Since the supply of money exceeds the demand at
the old rate, the interest rate may fall (point a to
point c) to increase the demand
– Therefore, it is possible to increase Y or decrease
r, or some combination of the two
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The IS Curve
• According to classical economists, interest rates are
determined by the interaction between desired saving
and investment
• Figure 24.5 and 24.6 demonstrate the inverse
(negative) relationship between the level of interest and
the level of investment
• Figure 24.6 summarizes the inverse relationship
between interest rate determined in the goods market
and the level of income
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FIGURE 24.5 How to derive the IS curve: At
lower rates of interest the level of investment is
higher,and so is the level of income.
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FIGURE 24.5 How to derive the IS curve: At
lower rates of interest the level of investment is
higher,and so is the level of income. (Cont.)
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Figure 24.6 The investment-demand function.
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The IS Curve (Cont.)
• IS curve (Figure 24.7)—locus of points satisfying the
investment-equals-savings equilibrium condition with
interest (r) on the vertical and income (Y) on the
horizontal
– At lower interest rates, there is more investment, so income
must be higher to increase the amount of savings
– At higher income levels, savings is higher, so the interest
rate must be lowered to encourage the additional savings
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FIGURE 24.7 The IS curve and its
slope.
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The Slope of the IS Curve
• The slope of the IS curve is determined by two
factors—the sensitivity of the investment
function (I versus r) and the marginal propensity
to save (1 – b)
– A highly interest-sensitive investment function will
result in a flat IS curve
– A low marginal propensity to save also implies a flat
IS curve
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The Slope of the IS Curve (Cont.)
• The position of the IS curve is altered by any
change in autonomous spending
– Government spending or taxation
– Private investment that is independent of the rate of
interest, but depends on the expectations of
entrepreneurs
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The Slope of the IS Curve (Cont.)
• Figure 24.8
– Shows the effect of an increase in government spending on
position of IS curve [IS(G1) to IS(G2)]
– This causes each of the total-expenditure functions to shift
upward, producing a higher level of Y for each interest rate
– Starting at point a, shifting the IS curve upward can result in
different outcomes
• An increase in income (point a to point b)
• An increase in interest rates (point a to point c)
• Some combination of the two—higher income and higher interest
rates
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FIGURE 24.8 An increase in government
spending shifts the IS curve to the right
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The Slope of the IS Curve (Cont.)
• Figure 24.8 (Cont.)
– Keynesians argue that an increase in government
spending will significantly increase GDP—
movement toward point b
– However, classical economists feel increased
government spending would result in increased
interest with no increase in GDP—movement toward
point c
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Determination of Income/Interest: IS
and LM Together
• Figure 24.9
– This represents a simultaneous plot of the LM curve (given a
fixed supply of money) and the IS curve (given a level of
autonomous spending)
– The intersection of the two curves (point E) represents the
equilibrium level of income (Y) and interest (r)
– At any other point on the graph, equilibrium conditions are
violated and dynamic forces will move income and interest
rate toward point E.
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FIGURE 24.9 The simultaneous
determination of income and interest
(fantastic!).
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Determination of Income/Interest: IS
and LM Together (Cont.)
• Figure 24.9 (Cont.)
– Point E is a stable equilibrium--as long as nothing shifts the
IS or LM curves, there is no tendency for Y or r to change
– However, this is nothing sacred about income YE—it may
or may not be a full employment level of output
– This opens up the possibility of using monetary or fiscal
policy to shift one or both of the curve to move the economy
to the full employment level
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Monetary and Fiscal Policy
• Monetary Policy
– Figure 24.10—Shifting the LM curve to the right along a
stable IS curve will simultaneously increase Y and decrease r
(Y to Y1 and r to r1)
– Figure 24.11
• Contrasts the effects of the LM curve interacting with a steep IS curve
and a flat IS curve
• A flat IS curve can be due to a highly interest-sensitive investment
function
• Flat IS curve—impact of monetary policy is effective on increasing
GDP, relatively smaller effect on interest
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FIGURE 24.10 An expansionary
monetary policy.
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FIGURE 24.11 Monetary policy is more
effective the flatter the IS curve.
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Monetary and Fiscal Policy (Cont.)
• Monetary Policy (Cont.)
– Figure 24.12
• Contrasts the effects monetary policy with a steep LM
curve versus a flat LM curve interacting with a given IS
curve
• If the demand for money is rather insensitive to changes in
the rate of interest, the LM curve is steeper
• Steep LM curve—larger the decline in the rate of interest
and the greater the increase in GDP
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FIGURE 24.12 Monetary policy is more
effective the steeper the LM curve.
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Monetary and Fiscal Policy (Cont.)
• Fiscal Policy
– Figure 24.13
• Shifting the IS curve upward will simultaneously increase
income and interest rates (Y to Y1 and r to r1)
• In previous chapters, the multiplier effect on GDP
resulting from an increase of government spending
ignored the impact of increasing interest rates—shown by
a movement from Y to Yn
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FIGURE 24.13 An expansionary
fiscal policy.
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Monetary and Fiscal Policy (Cont.)
• Fiscal Policy (Cont.)
– Figure 24.13 (Cont.)
• Crowding-out effect
– Increased government borrowing to finance the spending will
increase interest rates
– Higher interest rates will reduce investment spending which will
tend to reduce the increase in GDP
– Therefore, the net effect of increased government spending
will be diminished by the reduction in investment spending
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Monetary and Fiscal Policy (Cont.)
• Fiscal Policy (Cont.)
– Figure 24.14
• Shows two LM curves—the flatter the curve, the smaller
the interest-sensitivity of liquidity preferences—
interacting with a given shift of the IS curve
• The flatter the LM curve, the less the increase in interest
rates and the greater the increase in GDP—smaller
crowding-out effect
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FIGURE 24.14 Fiscal policy is more
effective the flatter the LM curve.
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Monetary and Fiscal Policy (Cont.)
• Fiscal Policy (Cont.)
– Figure 24.15
• Shows two IS curves—the flatter the curve, the greater the
interest-sensitivity of the investment function—interacting
with a fixed LM curve
• The flatter the IS curve, the less the increase in interest
rates and the greater the increase in GDP—smaller
crowding-out effect
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FIGURE 24.15 Fiscal policy is more
effective the steeper the IS curve.
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What about Velocity
• While it appears the Keynesian analysis does not
utilize the concept of velocity, it is actually
embedded in the LM function
• Given a fixed money supply, as one moves up
along an LM function, the income velocity of
money is necessarily going up since Y is
increasing
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What about Velocity (Cont.)
• Figure 24.16
– Rightward shifts of the IS curve caused by increased
government spending results in raising GDP through
increased velocity
– This occurs since the demand for money is sensitive
to the rate of interest and the increased interest
induces public to hold less speculative balances,
freeing more cash to be used for transactions
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FIGURE 24.16 When the IS curve shifts,
both income and velocity rise.
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What about Velocity (Cont.)
• Figure 26.17
– If the demand for money were totally insensitive to
the interest, velocity would be constant and GDP
would not be affected by shifts in autonomous
spending
– This results in a perfectly vertical LM curve at that
level of GDP
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Figure 24.17 When the LM curve is vertical,
shifts in the IS curve raise neither income
nor velocity.
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What about Velocity (Cont.)
• Figure 26.17 (Cont.)
– In this case, increased government spending results
only in higher interest rates and no increase in GDP
– Complete crowding-out—the increase in interest
reduces investment spending by the same amount as
the increase in government spending
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What about Velocity (Cont.)
• ISLM curves—integration of classical and
Keynesian economics
– Keynesian theory—the rate of interest is
determined by the supply of and demand for
money—LM curve
– Classical theory—the rate of interest is determined
exclusively by savings and investment—IS curve
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When Will Full Employment Prevail?
• The question remains—why do not variations in
interest automatically result in full employment in
Keynesian system
• Nothing in the analysis will permit the automatic
shifting of the IS or LM curves without additional
autonomous spending
• The Keynesian analysis states that the only way to push
the economy toward full employment is to increase
economic activity through additional government
spending
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When Will Full Employment Prevail?
(Cont.)
• Classical adjustment with ISLM curves
(Figure 24.18)
– If prices are permitted to vary, the ISLM analysis will
permit the automatic adjustment
– Under conditions of less than full employment, both
prices and wages would fall
– Since real income would remain the same, this
suggests there would be no automatic change in real
factors
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FIGURE 24.18 The classical position: Lower
prices shift the LM curve to the right and
automatically produce full employment.
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When Will Full Employment Prevail?
(Cont.)
• Classical adjustment with ISLM curves
(Cont.)
– However, falling prices would increase the real
value of the supply of money
– This in turn would tend to shift the LM curve to the
right, lowering interest rates and increasing desired
investment until full employment was restored
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When Will Full Employment Prevail?
(Cont.)
• Keynesian attack on the above:
– Inflexibility of prices and wages would not permit
the adjustment
– Liquidity trap (Figure 24.19)
• The LM curve is perfectly horizontal
• Increase in the money supply (though lowering of prices)
would not lower the interest rate
• No automatic increase in investment/output and
employment would remain below full employment levels
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FIGURE 24.19 An extreme
Keynesian position: A liquidity trap.
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When Will Full Employment Prevail?
(Cont.)
• Keynesian attack on the above: (Cont.)
– Interest-insensitive investment function (Figure
24.20)
• The IS curve is very steep
• Therefore, declining prices and the reduction in interest
rates will not be able to raise investment sufficiently to
generate full employment levels
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FIGURE 24.20 Another extreme Keynesian
position: Investment unresponsive to the
interest rate.
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When Will Full Employment Prevail?
(Cont.)
• Wealth effect of lowering prices (classical
counter)
– Falling prices increase both liquidity and wealth
– Increased wealth will raise desired consumption
function at every level of income
– This acts like any autonomous increase in spending
and will automatically shift the IS curve to the right
toward full employment
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ISLM and Aggregate Demand
• The aggregate demand curve relates the price
level to demand for real output
• The ISLM analysis focuses on the relation
between interest and demand for real output
• Therefore, it is relatively straightforward to
generate a complete aggregate demand schedule
from the ISLM model
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ISLM and Aggregate Demand
(Cont.)
• Figure 24.21
– Different price levels are associated with a family of
LM curves
– Lowering the price levels will cause the LM curves
to shift to the right
– The equilibrium level of output (Y) of the different
LM curves and a fixed IS curve will trace out an
aggregate demand that relates prices to output
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Figure 24.21 Deriving aggregate
demand from ISLM.
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Figure 24.21 Deriving aggregate
demand from ISLM. (Cont.)
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ISLM and Aggregate Demand
(Cont.)
• Figure 24.21 (Cont.)
– Additionally, a shifting of the IS curve, coupled with
different LM curves generated by different price
levels, will trace out a different aggregate demand
curve
– Less obvious, but also true, an increase in the stock
of money shifts the aggregate demand to the right
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TABLE 24.1 A Summary of Monetary
and Fiscal Policy Effectiveness
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Appendix
THE SIMPLE
ALGEBRA
OF INCOME
DETERMINATION
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APPENDIX—THE SIMPLE ALGEBRA
OF INCOME DETERMINATION
• Much of ISLM analysis can be summarized in
equation form
• The economy is divided into two sectors
– The goods or product markets, comprising the
demand for goods and services
– The monetary sector, comprising the demand for and
supply of money
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APPENDIX—THE SIMPLE ALGEBRA
OF INCOME DETERMINATION (Cont.)
• The Model
– The product market can be described by four functional
relationships (behavior equations) and one equilibrium
condition (an identity)
• All functional relationships are assumed to be linear
• The functional relationships (numbers shown in the textbook)
– (1) Consumption (C) function
– (2) Investment (I) function
– (3) Tax (T) function
– (4) government spending (G)
• The equilibrium condition
– (5) C + I + G + Y or S + T = I + G
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APPENDIX—THE SIMPLE ALGEBRA
OF INCOME DETERMINATION (Cont.)
– The monetary sector of the economy consists of
two functional relationships and one equilibrium
condition
• Functional relationships
– (6) Liquidity preference (L) or demand-for-money function
– (7) Money supply (M)
• Equilibrium condition
– (8) L = M
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APPENDIX—THE SIMPLE ALGEBRA
OF INCOME DETERMINATION (Cont.)
– The IS and LM functions
• By solving equations (1) through (5), we find the IS function: equation
(9)
• By solving equations (6) through (8), we find the LM function:
equation (10)
– Equilibrium Income and Interest
• By solving equations (9) and (10) simultaneously, we obtain:
– equilibrium income (Y): equation (11)
– interest rate (r): equation (12)
– Multiplier Effects on Income and Interest Rates
• From equation (11) we can derive the multiplier effects on income:
equations (13) through (15)
• From equation (12) we can derive the multiplier effects on the interest
rate: equations (16) through (18)
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