Cambridge International as and a level Economics Ebook

245
Chapter 9: The macroeconomy 

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In the example above, GDP rises until the $20 billion of 
extra government spending is matched by withdrawals of 
$20 billion. Th
e value of the multiplier is calculated aft er 
the injection by using the formula:
change in in ome
change in injection
c
= Δ
Δ
Y
J
In the example above the multiplier is 
$100bn
$20bn
= 5
Th
e multiplier can also be estimated in advance of the 
change by using the formula:
1
marginal prop nsity to withdraw
e
The multiplier and equilibrium income in two-, 
three- and four-sector economic models
As seen with the circular fl ow, economists oft en seek 
to explain their analysis fi rst in a simplifi ed model and 
then go on to include more variables. Th
is is also the case 
with the multiplier where economists start with a simple 
model of the economy, which only includes two sectors 
and then move on to a model that includes three sectors 
and then fi nally one that includes all four sectors.
Two-sector economy
In a two-sector economy (households and fi rms) there 
is only one withdrawal (saving) (
S
) and one injection 
(investment). In such an economy, the multiplier can be 
found by using the formula:
1
mps
where mps is the 
marginal propensity to save
. It can also 
be calculated by using the formula:
1
1 mps
−
Th
is is because in this model, income is either spent or 
saved. Equilibrium income will occur where aggregate 
expenditure equals output, which in this case is where 
C
+
I
=
Y
and injections equal withdrawals, 
I 
=
S
.
A two-sector economy is sometimes referred to as a 
closed economy without a government sector.