NUIG Macro
Based Primarily on Mankiw Chapter 10
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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

Planned Expenditure, E
Actual Expenditure, Y=E
Planned expenditure,
E = C(Y-T*) + I* + G* a + I* + G*
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Y *
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.
Income,
Output
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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.
– 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).
– In effect, the government can exploit the multiplier process and improve output and employment in the economy.
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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.
–
–
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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 To determine how income changes when the interest rate changes, we can combine the investment function with the Keynesian cross diagram.
–
–
–
–
–
Because investment is inversely related to the interest rate, an increase in the interest rate from r of investment from I(r
1
) to I(r
2
).
1 to r
2 reduces the quantity
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 Y
1 to Y
2
.
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 causality involved in constructing an IS curve is as follows
– 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
8 the IS curve relatively steeper.

 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*
I(r) = Y - C(Y - T*) - G* 9



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 downward sloping in {r, Y} space.
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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.
»
»
»
The following slide uses the Keynesian cross to show how an increase in government spending from G
1 to G
2 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 Y
1 to Y
2
.
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 shift the IS curve inward (to the left).
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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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