MPC, MPS, and Multipliers

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• MPC, MPS, and Multipliers

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The Multiplier Effect
The Multiplier Effect
The Multiplier Effect

• Any increase in spending will result in an even
  larger increase in GDP due to the fact that every
  dollar spent is spent again multiple times.
• Any money spent is someone elses income and
  therefore subject to spending.

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Decisions to Save and Spend

• How strong the multiplier effect will be is
  determined by our decisions to save and spend.
• As our income changes we will spend a portion and
  save a portion of this change.

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Marginal Propensity to Consume

• The portion we spend is known as our Marginal
  Propensity to Consume (MPC)
• It is found by dividing the change in
  Consumption by the change in Disposable Income
• For example if we receive a 10 an hour raise and
  we spend 9 of it and save 1, then our MPC is .9
• C / DI MPC so 9/10 .9

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Marginal Propensity to Save

• The portion we save is known as our Marginal
  Propensity to Save (MPS)
• It is found by dividing the change in Savings by
  the change in Disposable Income
• For example if we receive a 10 an hour raise and
  we spend 9 of it and save 1, then our MPS is .1
• S / DI MPS so 1/10 .1
• The MPC MPS is always equal to 1

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The Multiplier Effect
The Multiplier Effect
The Multiplier Effect

• The limiting factor for the multiplier effect is
  savings.
• For every additional dollar spent a portion of it
  will be saved (the MPS).
• The multiplier is the reciprocal of the MPS or
  1/MPS or 1/1- MPC.
• The larger the MPC (the smaller the MPS) the
  larger the multiplier will be.

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MPC 1/MPS M .90 1/.10 10 .80 1/.20
5 .75 1/.25 4 .60 1/.40
2.5 .50 1/.50 2
Spending Multiplier 1/MPS
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The First Round of Government Spending
Causes The Biggest Splash MPC
of 75G spends 200 billion on the highways.
Highway workers save 25 of 200 billion 50
billion spend 75 or 150 billion on boats.
Boat makers save 25 of 150 bil. 37.50 bil.
spend 75 or 112.50 bil. on iPod Minis, etc.
Total Spending has already reached 462.50b
Total Saving has reached 87.50
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USING MULTIPLIERS

• The multiplier can be used to calculate how any
  change in spending will change total spending
  (AD) or income (GDP).
• The formula used is Change in Spending x
  Multiplier Change in AD/GDP.
• Ex G 1b x 4 4b in AD/GDP

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USING MULTIPLIERS

• Since any change in GDP is the result of the
  change in spending x multiplier, you can find the
  multiplier by dividing the change in AD/GDP by
  the change in spending.
• Ex 4b AD/GDP / 1b in G
• multiplier of 4

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USING MULTIPLIERS

• Knowing that any change in spending will have a
  multiplied effect government can calculate how
  much to change spending by dividing the needed
  change in GDP by the multiplier.
• Ex GDP is 4b below full employment
• 4b needed / 4 1b in G

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Tax Multipliers
Tax Multipliers
Tax Multipliers

• A change in taxes also has a multiplied effect,
  but the tax multiplier is smaller than the
  spending multiplier.

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Tax Multipliers
Tax Multipliers
Tax Multipliers

• Tax Multiplier (note its negative because tax
  increases reduce spending)
• -MPC/1-MPC or -MPC/MPS
• If there is a tax-CUT, then the multiplier is ,
  because there is now more money in the circular
  flow

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Tax Multiplier -MPC/MPS
MPC MPC/MPS M .90 -MPC/.10
-9 .80 -MPC/.20 -4 .75 -MPC/.25
-3 .60 -MPC/.40 -1.5 .50 -MPC/.50 -1
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Tax Multiplier -MPC/MPS
Spending Multiplier 1/MPS
Tax Multiplier
MPC
Multiplier
.9 10
-9
.8 5
-4
.75 4
-3
.60 2.5
-1.5
.5 2
-1
The tax multiplier is always smaller than the
spending multiplier because a portion of the
change in income due to taxes is saved, reducing
the overall impact on spending.
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The Balanced Budget Multiplier

• When government spending increases are matched
  with equal size increases in taxes, the change
  ends up being to the change in government
  spending
• Why?
• 1/MPS -MPC/MPS 1- MPC/MPS MPS/MPS 1
• The balanced budget multiplier always 1

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Multiplier Practice

• Assume US citizens spend .90 for every extra 1
  they earn.
• Further assume that the real interest rate (i)
  decreases, causing a 50 billion increase in
  Investment (I).
• Calculate the effect of this increase in spending
  on AD.

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• Step 1 Calculate the MPC and MPS
• MPC C / DI
• MPS 1- MPC
• Step 2 Determine which multiplier to use, and
  whether its or
• The problem mentions an increase in I, use a ()
  spending multiplier
• Step 3 Calculate the Spending and/or Tax
  Multiplier
• Step 4 Calculate the Change in AD
• ( C, I, G or NX) Spending or Tax Multiplier

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More Practice

• Assume Germany raises taxes on its citizens by
  200b.
• Assume that Germans save 25 of the change in
  their disposable income.
• Calculate the effect of these taxes on the
  German economy.

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More Practice

• Assume the Japanese spend 4/5 of their disposable
  income.
• Assume that the Japanese government increases its
  spending by 50 trillion and in order to
  maintain a balanced budget simultaneously
  increase taxes by 50t.
• Calculate the effect of these changes on the
  Japanese Aggregate Demand.