Transcript Topic 1: Introduction to Economics 1 (The Price System)

NUIG Macro
Lecture 17: The IS/LM Model (1)
Based Primarily on Mankiw Chapter 10
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Introduction & Learning Objectives
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Today we will derive an IS curve and examine what
determines the slope and position of the IS curve.
– There are two ways to do this: using either the
Keynesian cross model (traditional way), or using
the neoclassical model (simpler). We will consider
both derivations in turn.
In the next lecture we will derive an LM curve and
examine what determines its slope and position.
After this, we will put the two curves together and
present the complete IS/LM model.
– This model is the basis for the claim made earlier
that in the short-run both the goods market and the
money market simultaneously determine r and Y. 2
The Keynesian Cross (1)
Planned Expenditure, E
Actual Expenditure, Y=E
Planned expenditure,
E = C(Y-T*) + I* + G*
Using the Keynesian cross diagram we can see
that the economy’s equilibrium income level is
Y*. Whenever the economy is away from
equilibrium, firms experience unplanned stock
accumulation which acts as a signal for them to
change production.
a + I* + G*
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Y*
Income,
Output
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The Keynesian Cross (2)
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The Keynesian cross is useful because it
shows how the spending plans of households,
firms and the government determine the
economy’s income.
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We also noted in the last lecture how fiscal policy
(changes in taxes and spending) can move the
economy from a “bad” equilibrium (one with a low
level of Y) to a good equilibrium (one with a level of
Y closer to the natural rate of output).
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In effect, the government can exploit the multiplier
process and improve output and employment in the
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economy.
Theoretical Weakness
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Although the Keynesian cross is useful, it
makes the simplifying assumption that the
level of planned investment in the economy, I,
is fixed at I*. This is unrealistic.
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As we saw in earlier lectures, an important
macroeconomic relationship is that planned
investment depends on the real interest rate, r.
I = I(r) and it is assumed that whenever r rises then
I falls. dI/dr < 0.
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Constructing The IS Curve
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To determine how income changes when the interest
rate changes, we can combine the investment function
with the Keynesian cross diagram.
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Because investment is inversely related to the interest rate, an
increase in the interest rate from r1 to r2 reduces the quantity
of investment from I(r1) to I(r2).
The reduction in planned investment, in turn, shifts the
planned-expenditure function downward. The shift in the
planned-expenditure function causes the level of income to
fall from Y1 to Y2.
Hence, an increase in the interest rate lowers income.
The IS curve summarises the relationship between the
interest rate and the level of income.
The IS curve is downward sloping in {r, Y} space.
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The Slope Of The IS Curve
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The causality involved in constructing an IS
curve is as follows
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r changes  I changes  planned expenditure
changes  Y changes.
Thinking about this causality carefully, we can see
that the slope of the IS curve will depend upon the
interest elasticity of investment and the multiplier.
For any given value of the multiplier, an increase in
the interest elasticity of investment will make the IS
curve relatively flatter.
Similarly, if the interest elasticity of investment is
held constant, a reduction in the multiplier will make
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the IS curve relatively steeper.
Second Derivation
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An simpler derivation comes from the neoclassical
model.
– Y = C + I + G
– C = C(Y - T)
– I = I(r)
– G = G*
– T = T*
Previously we would be assuming Y = Y* = F(K*, L*).
However, in the short-run (Keynesian model) Y is a
variable.
– Y = C(Y - T*) + I(r) + G*
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– I(r) = Y - C(Y - T*) - G*
Second Derivation (continued)
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RHS of equation is Y - C(Y - T*) - G*
As Y rises (by Y), the first term on the RHS gets
larger as does the second term (C(Y - T*)). However,
the second term only increases by MPC  Y < Y.
Given that G is fixed the whole RHS increases in value
when Y rises.
To preserve the equality the LHS must rise in value
too. This means that I must rise. The only way this
can happen is if r falls.
This is easy to see when we recall our basic
equilibrium diagram from the neoclassical model and
remove the restriction that Y is fixed at Y*. Again, IS is
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downward sloping in {r, Y} space.
Fiscal Policy And The IS Curve
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The IS curve is drawn under the assumption that fiscal
policy is held constant.
– When we draw the IS curve, G and T are held fixed.
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The following slide uses the Keynesian cross to show how
an increase in government spending from G1 to G2 shifts
the IS curve. This figure is drawn for a given interest rate
and thus for a given level of planned investment. The
Keynesian cross shows that this change in fiscal policy
raises planned expenditure and thereby increases
equilibrium income from Y1 to Y2 .
Therefore, an increase in government spending shifts the
IS curve outward (to the right). The same is true of a tax
cut.
Reduced government spending and increased taxes will
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shift the IS curve inward (to the left).
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Summary of IS Curve
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The IS curve shows the combinations of r and Y
that are consistent with equilibrium in the goods
market.
The IS curve has a negative slope because
reductions in r increase planned investment
spending and thus, through the Keynesian cross,
raise the level of income/output Y.
The multiplier and the interest elasticity of
investment influence the slope of the IS curve.
Fiscal policy is one factor that influences the
position of the IS curve.
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