Lecture Macroeconomics: Lecture 15 - Prof. Dr.Qaisar Abbas

Review of the previous lecture
1.

2.

3.

4.

5.

6.

Long run: prices are flexible, output and employment are always at
their natural rates, and the classical theory applies.
Short run: prices are sticky, shocks can push output and
employment away from their natural rates.
Aggregate demand and supply: a framework to analyze economic
fluctuations
The aggregate demand curve slopes downward.
The long-run aggregate supply curve is vertical, because output
depends on technology and factor supplies, but not prices.
The short-run aggregate supply curve is horizontal, because
prices are sticky at predetermined levels.


Review of the previous lecture
7. Shocks to aggregate demand and supply cause fluctuations in GDP
and employment in the short run.

8. The Fed can attempt to stabilize the economy with monetary policy.

Lecture 15

Aggregate demand – I

Instructor: Prof. Dr. Qaisar Abbas


Lecture Contents

•

the IS curve, and its relation to
–

the Keynesian Cross

–

the Loanable Funds model


The Keynesian Cross
•

•

A simple closed economy model in which income is determined by
expenditure.

(due to J.M. Keynes)

Notation:

I = planned investment
E = C + I + G = planned expenditure
Y = real GDP = actual expenditure

•

Difference between actual & planned expenditure: unplanned inventory
investment


Elements of the Keynesian Cross

C = C (Y − T )

consumption function:

G = G , T =T

govt policy variables:
for now, 
investment is 
exogenous:
planned expenditure:

I =I
E = C (Y − T ) + I + G

Equilibrium condition:

Actual expenditure  =  Planned expenditure
Y = E


Graphing planned expenditure

E

planned

E =C +I +G

expenditure

1

MPC

income, output, Y


Graphing the equilibrium condition

E

E =Y

planned
expenditure

45º

income, output, Y


The equilibrium value of income

E

E =Y

planned

E =C +I +G

expenditure

income, output, Y

Equilibrium
income


An increase in government purchases

E 
=Y

E

At Y1,
there is now an
unplanned drop
in inventory…

E =C +I +G2
E =C +I +G1

G

…so firms
increase output,
and income
rises toward a
new equilibrium

Y

E1 = Y1

Y

E2 = Y2


Solving for

Y = C + I

+ G

∆Y = ∆C + ∆I + ∆G
=

∆C

+ ∆G

= MPC ∆Y + ∆G
Collect terms with  Y  
on the left side of the 
equals sign:

(1 − MPC) ∆Y = ∆G

Y

equilibrium condition
in changes
because I  exogenous
because  C = MPC  Y 
Finally, solve for  Y :

� 1
�
∆Y = �
� ∆G

1 − MPC �
�


The government purchases multiplier
Example: MPC = 0.8

1
∆Y =
∆G
1 − MPC
1
1
=
∆G =
∆G = 5 ∆G
1 − 0. 8
0.2
The increase in G causes income to increase by 5 times as much!


The government purchases multiplier
Definition: the increase in income resulting from a $1 increase in G.
In this model, the G multiplier equals

∆Y
1
=
∆G
1 − MPC

In the example with MPC = 0.8,

∆Y
1
=
= 5
∆G
1 − 0.8


Why the multiplier is greater than 1

•

Initially, the increase in G causes an equal increase in Y:

•

But Y

Y=

C
further Y
further C
further Y

•

So the final impact on income is much bigger than the initial

G.

G.


E 
=Y

An increase in taxes
E

Initially, the tax
increase reduces
consumption, and
therefore E:

E =C1 +I +G
E =C2 +I +G
At Y1, there is now
an unplanned
inventory buildup…

C =  MPC  T

…so firms
reduce output,
and income falls
toward a new
equilibrium

Y

E2 = Y2

Y

E1 = Y1


Solving for

eq’m condition in 
changes

∆Y = ∆C + ∆I + ∆G
= ∆C
= MPC

I  and G  exogenous

( ∆Y

Solving for  Y :

Final result:

Y

− ∆T

)

(1 − MPC) ∆Y = − MPC ∆T
�− MPC �
∆Y = �
� ∆T
1 − MPC �
�


The Tax Multiplier
def: the change in income resulting from
a $1 increase in T :

∆Y
∆T

− MPC
=
1 − MPC

If MPC = 0.8, then the tax multiplier equals

∆Y
∆T

− 0. 8
− 0. 8
=

=
= −4
1 − 0. 8
0. 2


The Tax Multiplier
…is negative:
A tax hike reduces
consumer spending,
which reduces income.

…is greater than one
(in absolute value):
A change in taxes has a
multiplier effect on income.

…is smaller than the govt spending multiplier:
Consumers save the fraction (1-MPC) of a tax cut,
so the initial boost in spending from a tax cut is
smaller than from an equal increase in G.


The Tax Multiplier
…is negative:
An increase in taxes reduces consumer spending, which reduces
equilibrium income.

…is greater than one (in absolute value):
A change in taxes has a multiplier effect on income.

…is smaller than the govt spending multiplier:
Consumers save the fraction (1-MPC) of a tax cut, so the initial boost in
spending from a tax cut is smaller than from an equal increase in G.


Exercise:

•

Use a graph of the Keynesian Cross to show the impact of an
increase in investment on the equilibrium level of
income/output.


The IS curve
def: a graph of all combinations of r and Y that result in goods market
equilibrium,
i.e. actual expenditure (output)
= planned expenditure
The equation for the IS curve is:

Y = C (Y − T ) + I ( r ) + G


Deriving the IS curve
E =Y

E
r

E =C +I (r1 )+G

I

  E
  Y

E =C +I (r2 )+G

I

r

Y1

Y

Y2

r1
r2
IS 
Y1

Y2

Y

Understanding the IS curve’s slope

•

•

The IS curve is negatively sloped.

Intuition:
A fall in the interest rate motivates firms to increase investment spending,
which drives up total planned spending (E ).

To restore equilibrium in the goods market, output (a.k.a. actual
expenditure, Y ) must increase.


The IS curve and the Loanable Funds model

The L.F. model

(a)
r

S2

r

S1

r2

r2
r1

(b)  The IS  curve

I (r  ) 

r1
IS

S, I

Y2

Y1

Y


Fiscal Policy and the IS curve

•

•

We can use the IS-LM model to see how fiscal policy (G and T
) can affect aggregate demand and output.

Let’s start by using the Keynesian Cross to see how fiscal policy

shifts the IS curve…