MPC, MPS, and Multipliers

• 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.

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.

Marginal Propensity to Marginal Propensity to ConsumeConsume

• 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

Marginal Propensity to SaveMarginal 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

• 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.

MPC MPC 1/MPS 1/MPS = = M M.90.90 1/.101/.10 = = 1010.80.80 1/.201/.20 = 5= 5.75.75 1/.251/.25 = 4= 4.60.60 1/.401/.40 = 2.5= 2.5.50.50 1/.501/.50 = 2= 2

Spending MultiplierSpending Multiplier = = 1/MPS1/MPS

The First Round of The First Round of GovernmentGovernment Spending Causes The Biggest Spending Causes The Biggest SplashSplash MPC of 75%MPC of 75%G spends $G spends $200200 billion on the billion on the highwayshighways..Highway workers save 25% of $200 Highway workers save 25% of $200 billion billion [$50 [$50

billion] & spend 75% or $150 billion on boats. billion] & spend 75% or $150 billion on boats.

Boat makers save 25% of $150 Boat makers save 25% of $150 bil.bil. [$37.50 bil.] [$37.50 bil.] & & spend 75% or $112.50 bil. on iPod Minis, etc.spend 75% or $112.50 bil. on iPod Minis, etc.

Total Saving has reached $87.50

• 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

USING MULTIPLIERS

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

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

• 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

MPCMPC MPC/MPSMPC/MPS = = M M.90.90 -MPC/.10-MPC/.10 = = -9 -9.80.80 -MPC/.20-MPC/.20 == -4 -4.75.75 -MPC/.25-MPC/.25 == -3 -3.60.60 -MPC/.40-MPC/.40 = = -1.5-1.5.50.50 -MPC/.50-MPC/.50 == -1 -1

Tax MultiplierTax Multiplier = - = -MPC/MPSMPC/MPS

Tax MultiplierTax Multiplier

-4-4

-3-3

-1.5-1.5

-1-1

-9-9

Tax Multiplier = -MPC/MPSTax Multiplier = -MPC/MPSSpending MultiplierSpending Multiplier = = 1/MPS1/MPS

MPCMPC MultiplierMultiplier

.9.9 1010

.8.8 55

.75.75 44

.60.60 2.52.5

.5.5 22The tax multiplier tax multiplier is always smallersmaller thanthan the spending multiplierspending multiplier because a portion of the change in income due to taxes is saved, reducing the overall impact on spending..

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

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.

Step 1: Calculate the MPC and MPSMPC = 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

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.

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.