Intermediate
Macroeconomics
Tutorial 1
Chapter 1: Review of the AD-AS Model
- Labour Demand & Money Supply
- Demand for Money
- Economic Schools of Thought
,T1 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9
1.1 Short questions
Consider a closed economy in which the central bank adjusts the money supply such that the interest
rate 𝑅 is constant. Derive the slope of the AD curve. Show what happens to the LM curve as a result of
the central bank’s policy.
Recap
The monetary authority changes money supply such the desired interest rate level is achieved. If there
is a monetary expansion, then 𝑀 ! ↑. This causes the vertical line to shift out at a lower equilibrium
level of interest rates. At the original interest rate, there is now excess supply of (real) money. This
leads to a decrease in the equilibrium interest rate (since people will try to buy bonds with their excess
money, driving bond prices up and yields/interest rates down*).
*To earn interest on this excess money, people buy bonds,
increasing demand for bonds and pushing bond prices up. Since
bond yields (interest rates) move inversely to prices, higher
bond prices mean lower yields, leading to a drop in market
interest rates.
Suppose that the price level decreases, the curve reacts idem. A
lower price level increases the real money supply. Because the
same nominal money supply can now buy more goods and
services. This shifts the real money supply curve to the right, just
like a nominal money supply increase.
Such a shift would then also move the LM curve that states the relation of interest and the output
level. Since the LM curve shows all combinations of output and interest rates where money demand
equals money supply, a lower 𝑖 for any given 𝑦 means the LM curve shifts to the right.
The aggregate demand curve is directly affected by shifts in the LM curve. If the central bank increases
money supply, lowering interest rates, this stimulates investment and consumption, increasing
aggregate demand for goods and services at every price level. Consequently, the AD curve also shifts
rightward, reflecting higher output demand across the economy. However, if prices fall without a
policy change, the economy simply moves downward along the existing AD curve rather than shifting
it.
1
,T1 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9
Again: Consider a closed economy in which the central
bank adjusts the money supply such that the interest
rate 𝑅 is constant. Derive the slope of the AD curve.
Show what happens to the LM curve as a result of the
central bank’s policy.
The LM curve 𝑀 = 𝑙(𝑅∗ , 𝑌)
This equation represents the money market
equilibrium at the given world interest rate 𝑅∗ . Since
the monetary authority changes money supply such
that the interest rate is constant, it is independent of
output. This indicates that the LM curve in this case is
horizontal. Since investment and consumption depend
only on the fixed 𝑅∗ , aggregate demand becomes
independent of the price level. Thus, the AD curve is
vertical.
What do we mean with the notion that capital and labour are cooperative production factors? Can you
give an example where this holds true?
More capital increases the marginal productivity of labour, and more labour increases the marginal
productivity of capital. Consider construction Workers with Cranes: more cranes (capital) allow
workers to lift heavy materials faster, raising their output per hour. Up to some point where it does
not raise productivity because then you would first need more workers.
What are the two most important differences between the views of the classical and the Keynesian
economists?
Classical economist Maybe the government can affect the economy
The government should not stabilize the economy
Keynesian The government can affect the economy
The government should stabilize the economy
2
, T1 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9
Assume that a firm investment depends only weakly on the interest rate. Does that make the IS curve
very steep or relatively flat?
%$ ['()]
𝑌 = 𝐶(𝑌) + 𝐼(𝑅) + 𝐺 𝑑𝑌 = 𝐶# ∙ 𝑑𝑌 + 𝐼$ ∙ 𝑑𝑅 [1 − 𝐶]𝑑𝑌 = 𝐼$ ∙ 𝑑𝑅 =−
%# +!
The IS curve describes the equilibrium on the demand side of the goods market. To determine whether
the curve is steep or flat we must derive its slope. So, we derive 𝑑𝑅/𝑑𝑌 to understand how changes
in output 𝑌 affect the interest rate 𝑅. It is given that changes in the interest rate have little effect on
investment (investment depends only weakly on the interest rate) this indicates that 𝐼$ (the derivative
indicating how a change in investment impacts the change of income) is very small.
Following the derivative, then 𝑑𝑅(𝑙𝑎𝑟𝑔𝑒)/𝑑𝑌(𝑠𝑚𝑎𝑙𝑙) is very large. Meaning that a small increase in
𝑌 produces a large reduction in 𝑅 and the IS-curve is almost vertical (very steep). In other words, to
maintain equilibrium in the goods market, larger changes in the interest rate are required to balance
out changes in output when investment is not responsive to interest rate fluctuations.
So, when investment weakly dependent on the interest rate, the IS curve becomes steep because
changes in output (income) have a substantial impact on the interest rate needed to maintain
equilibrium in the goods market.
Using intuition, we know that on the vertical axis is the interest rate and the horizontal axis the output
level. If investment is only weakly related to the interest rate, then there is a large difference in interest
rate necessary to affect investment which in turn is positively related to output. Therefore, it makes
sense that we need a large increase in the interest rate to affect output slighty. Thus, the curve is
steep.
Consider usual diagram with the real wage on the vertical axis and employment on the horizontal axis.
Perfectly competitive firms use capital and labour to produce output. Why must competitive labour
demand functions be downward sloping? Why must capital and labour be cooperative factors of
production?
,
Competitive labour demand functions A)
= 𝐹. (𝑁, 𝐾 A) < 0
𝐹.. (𝑁, 𝐾
-
,
They slope downward in the D - , 𝑁E space because there are diminishing returns to the labour
input. With constant returns to scale and only two factors of production, it must be the case that
𝐹./ > 0.
3
Macroeconomics
Tutorial 1
Chapter 1: Review of the AD-AS Model
- Labour Demand & Money Supply
- Demand for Money
- Economic Schools of Thought
,T1 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9
1.1 Short questions
Consider a closed economy in which the central bank adjusts the money supply such that the interest
rate 𝑅 is constant. Derive the slope of the AD curve. Show what happens to the LM curve as a result of
the central bank’s policy.
Recap
The monetary authority changes money supply such the desired interest rate level is achieved. If there
is a monetary expansion, then 𝑀 ! ↑. This causes the vertical line to shift out at a lower equilibrium
level of interest rates. At the original interest rate, there is now excess supply of (real) money. This
leads to a decrease in the equilibrium interest rate (since people will try to buy bonds with their excess
money, driving bond prices up and yields/interest rates down*).
*To earn interest on this excess money, people buy bonds,
increasing demand for bonds and pushing bond prices up. Since
bond yields (interest rates) move inversely to prices, higher
bond prices mean lower yields, leading to a drop in market
interest rates.
Suppose that the price level decreases, the curve reacts idem. A
lower price level increases the real money supply. Because the
same nominal money supply can now buy more goods and
services. This shifts the real money supply curve to the right, just
like a nominal money supply increase.
Such a shift would then also move the LM curve that states the relation of interest and the output
level. Since the LM curve shows all combinations of output and interest rates where money demand
equals money supply, a lower 𝑖 for any given 𝑦 means the LM curve shifts to the right.
The aggregate demand curve is directly affected by shifts in the LM curve. If the central bank increases
money supply, lowering interest rates, this stimulates investment and consumption, increasing
aggregate demand for goods and services at every price level. Consequently, the AD curve also shifts
rightward, reflecting higher output demand across the economy. However, if prices fall without a
policy change, the economy simply moves downward along the existing AD curve rather than shifting
it.
1
,T1 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9
Again: Consider a closed economy in which the central
bank adjusts the money supply such that the interest
rate 𝑅 is constant. Derive the slope of the AD curve.
Show what happens to the LM curve as a result of the
central bank’s policy.
The LM curve 𝑀 = 𝑙(𝑅∗ , 𝑌)
This equation represents the money market
equilibrium at the given world interest rate 𝑅∗ . Since
the monetary authority changes money supply such
that the interest rate is constant, it is independent of
output. This indicates that the LM curve in this case is
horizontal. Since investment and consumption depend
only on the fixed 𝑅∗ , aggregate demand becomes
independent of the price level. Thus, the AD curve is
vertical.
What do we mean with the notion that capital and labour are cooperative production factors? Can you
give an example where this holds true?
More capital increases the marginal productivity of labour, and more labour increases the marginal
productivity of capital. Consider construction Workers with Cranes: more cranes (capital) allow
workers to lift heavy materials faster, raising their output per hour. Up to some point where it does
not raise productivity because then you would first need more workers.
What are the two most important differences between the views of the classical and the Keynesian
economists?
Classical economist Maybe the government can affect the economy
The government should not stabilize the economy
Keynesian The government can affect the economy
The government should stabilize the economy
2
, T1 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9
Assume that a firm investment depends only weakly on the interest rate. Does that make the IS curve
very steep or relatively flat?
%$ ['()]
𝑌 = 𝐶(𝑌) + 𝐼(𝑅) + 𝐺 𝑑𝑌 = 𝐶# ∙ 𝑑𝑌 + 𝐼$ ∙ 𝑑𝑅 [1 − 𝐶]𝑑𝑌 = 𝐼$ ∙ 𝑑𝑅 =−
%# +!
The IS curve describes the equilibrium on the demand side of the goods market. To determine whether
the curve is steep or flat we must derive its slope. So, we derive 𝑑𝑅/𝑑𝑌 to understand how changes
in output 𝑌 affect the interest rate 𝑅. It is given that changes in the interest rate have little effect on
investment (investment depends only weakly on the interest rate) this indicates that 𝐼$ (the derivative
indicating how a change in investment impacts the change of income) is very small.
Following the derivative, then 𝑑𝑅(𝑙𝑎𝑟𝑔𝑒)/𝑑𝑌(𝑠𝑚𝑎𝑙𝑙) is very large. Meaning that a small increase in
𝑌 produces a large reduction in 𝑅 and the IS-curve is almost vertical (very steep). In other words, to
maintain equilibrium in the goods market, larger changes in the interest rate are required to balance
out changes in output when investment is not responsive to interest rate fluctuations.
So, when investment weakly dependent on the interest rate, the IS curve becomes steep because
changes in output (income) have a substantial impact on the interest rate needed to maintain
equilibrium in the goods market.
Using intuition, we know that on the vertical axis is the interest rate and the horizontal axis the output
level. If investment is only weakly related to the interest rate, then there is a large difference in interest
rate necessary to affect investment which in turn is positively related to output. Therefore, it makes
sense that we need a large increase in the interest rate to affect output slighty. Thus, the curve is
steep.
Consider usual diagram with the real wage on the vertical axis and employment on the horizontal axis.
Perfectly competitive firms use capital and labour to produce output. Why must competitive labour
demand functions be downward sloping? Why must capital and labour be cooperative factors of
production?
,
Competitive labour demand functions A)
= 𝐹. (𝑁, 𝐾 A) < 0
𝐹.. (𝑁, 𝐾
-
,
They slope downward in the D - , 𝑁E space because there are diminishing returns to the labour
input. With constant returns to scale and only two factors of production, it must be the case that
𝐹./ > 0.
3
