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 multiplierStep 3: Calculate the Spending and/or Tax

MultiplierStep 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.