The Multiplier Concept

1
The Multiplier Concept

• An exogenous increase or decrease in spending has
  a ripple effect.
• In can be true for a city or a country

2
The Macro Stimulus

• A fall in real interest rates, a wave of
  innovation, or an increase in the demand for U.S.
  exports will lead to an increase in autonomous
  expenditure.

3
The Effect

• The multiplier is the amount by which a change in
  autonomous expenditure is magnified or multiplied
  to determine the change in equilibrium
  expenditure and real GDP.

4
Demonstrating the Multiplier.

• With Business and Households only.
• Three markets.

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SAS
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What happens when there is a permanent increase
in investment of 100?
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100
SAS
100
9
Expenditures are made.

• Output is produced, and
• Income is received.

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SAS
100
100
100
100
100
11
Income is consumed or saved.

• Consumption increases by the increase in income
  times the MPC.
• Saving increases by the increase in income times
  the MPS.

12
Assume that

• The MPC .8, and thus
• The MPS .2

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This generates new consumption expenditures.
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100
SAS
100
100
MPC .8
80
MPS .2
20
100
100
15
The process starts over.
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18
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So far the the increase has been

• 100 80 64 ?
• How much will it be if it goes around enough
  times to be one cent?

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• 100 80 64 51.2 41.0 32.8 26.2 21.0
  19.8 13.4 10.7 8.6 6.9 5.5 4.4 3.5
  2.8 2.3 1.8 ....

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• Or, where a .8,
• 100 100a 100a2 100a3 100a4 100a5 100a6
  100a7 .....
• Or 100 (1 a a2 a3 a4 a5 a6
  a7....)
• Or 100 500

1
1 - a
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The Multiplier
1

• The Multiplier
• When the MPC is .8,
• the multiplier is
• 500 400 100

1 - MPC
1
1


5
.2
1 - .8
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What happens when there are more sectors?

• There are more chances for leakage.
• The multiplier is smaller.

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MPM .0625
SAS
100
100
T
4
100
b
MPC .8
MPS .2
T
11.11
h
MPS
.0625
b
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SS
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The Revised Multiplier

• The percent of the initial injection that creates
  new expenditures is 60.
• Thus the multiplier is 1/(1-.6), or 2.5.

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