• 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 else’s income and therefore subject to spending.

• 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.

• 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

• 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

• 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.

Spending Multiplier = 1/MPS
MPC 1/MPS = M
.90
1/.10
.80
.75
.60
.50
1/.20
1/.25
1/.40
1/.50
= 10
= 5
= 4
= 2.5
= 2

The First Round of Government
Spending Causes The Biggest Splash
MPC of 75%
G 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 Saving has reached $87.50

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

• 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

• 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

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

• Tax Multiplier (note: it’s 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

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

Spending Multiplier
=
1/MPS
MPC
.9
.8
.75
Multiplier
10
5
-4
4
-3
Tax Multiplier = -MPC/MPS
Tax Multiplier
-9
.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.

• 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

• 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.

 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

• 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.

• 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.