### The Multiplier Effect

```The Multiplier Effect
Multiplier Effect
• “the impact on real GDP of a change in any of
the components of aggregate spending (C, I ,
G , X-M).”
• The multiplier effect results in a larger change
in real GDP than the initial change in any of
the four components of aggregate spending
Mathematically speaking….
Multiplier = change in real GDP/
initial change in expenditure
Or…
Initial change in expenditure X multiplier =
change in real GDP
So you’re saying….
• That a \$1 increase in spending by C, or I, or G,
or X-M might lead to a greater than \$1
increase in real GDP? How does that work?
It’s like a chain reaction!
The Chain Reaction Explained
• Suppose I increases by \$8,000,000
(autonomous expenditure) . Real GDP goes
up by the same amount, but that’s not all that
happens. Induced expenditures follow,
because the \$8,000,000 is also income
received by the factors of production, which in
turn makes possible increased consumption
spending (C)
It’s kinda like dominoes…
• As we know, increased income that flows to
the owners of factors of production isn’t
always entirely spent.
• A portion of the additional income will be
spent (these are injections to the circular
flow), but the other portion will be saved
(leakages to the circular flow)
Marginal Propensity to Consume
• MPC is the fraction of additional income that
households spend on consumption of
domestically produced goods and services.
• So if MPC =3/4, and real income increases by
\$8,000,000….
• how much new consumption will result?
• how much will leak out as savings?
Marginal propensity to save and
friends
• MPS (marginal propensity to save) is one of the ways
new income can leak from the circular flow.
• MPT (marginal propensity to tax) represents how
much of new income must be paid in taxes
• MPI (marginal propensity to import) represents how
much of new income will be spent on imports
So if you add ‘em all up….
• MPC + MPS + MPT + MPI = 1
• Makes sense because every \$1 of additional
income is either consumed, saved, taxed or
spent on imports.
So let’s do some math
• Let’s assume I has increased by \$8,000,000.
• So the initial increase to income is
\$8,000,000. Then what happens? Let’s assume
the MPC is .75…..
Calculating the value of the Multipler
Change in income
Induced change in
consumption
1st round
\$8,000,000
¾X8=6
2nd round
\$6,000,000
¾ X 6 = 4.5
3rd round
\$4,500,000
¾ X 4.5 = 3.38
4th round
\$3,380,000
¾ X 3.38 = 2.5
And on and on
And on
And on…..
Total
\$32,000,000
¾ X 32 = 24
Initial increase in
investment expenditure of
\$8,000,000
• An increase of \$8,000,000 in I will lead to an
increase in income (real GDP) of \$32,000,000
when MPC = .75.
• \$8,000,000 of that is from the initial increase
in I, the other \$24,000,000 comes from the
increase in induced consumption spending
So the value of the Multipier is….
• Multiplier = Change in real GDP/
initial change in expenditure
\$32,000,000/\$8,000,000 = 4
More relationships…
• Multiplier = 1/1-MPC
• Multiplier = 1/1-.75
• Multiplier = 1/.25
• Multiplier = 4
• So in order to calculate the multiplier, all we
need to know is the marginal propensity to
consume
Moral of the story….
• The larger the marginal propensity to
consume, the larger the value of the multiplier
will be.
• Increases to any of the components of AD will
have the same effect
• It works in the opposite way too, decreases in
spending will lead to a larger decrease in total
income
The multiplier and fiscal policy
• Obviously, the value of the multiplier plays an
important role in the effect of expansionary or
contractionary fiscal policy. If government
pursues expansionary fiscal policy, knowing
the value of the multiplier will give us a better
idea of how much real GDP will actually
increase.
Tax cuts vs. government spending
• Remember that increased government
spending will have a greater effect on real GDP
than tax cuts. Does anybody remember why
this happens?
Tax cuts vs. government spending
• If the multiplier = 4 (MPC= .75), a \$1 increase
in government spending leads to \$4 in
• If the multiplier = 4 (MPC= .75), a \$1 tax cut
increased savings
• Increases in government spending have a
greater effect on AD than tax cuts but are less
popular
Final thoughts on the multiplier
• The multiplier is difficult to calculate because:
• It takes months for spending to cycle through
the economy
• Changes to MPS, MPI, and MPT can cause the
size of the multiplier to fluctuate
Final thought on the multiplier
• Beware the effect of the price level! When in
the horizontal portion of the Keynesian AS
curve, increases in AD will increase output
without increasing the price level. However,
as we move towards the upwards sloping
portion of the Keynesian AS curve, increases