1. The Multipliers Homework
1. Marginal Propensity to Consume (MPC) = ∆ consumption (C)/ ∆ Disposable Income (DI)
DI and Disposable Personal Income (DPI) can be used interchangeably.
2. Marginal Propensity to Save (MPS) = ∆ savings (S)/ ∆ Disposable Income (DI)
MPC + MPS = 1.

2. 3. Autonomous Expenditure Multiplier (The Multiplier) 1/ 1-MPC OR 1/MPS OR ∆ Real GDP/ ∆ Autonomous Expenditure (C, I, or G)

3. 4. Government Spending/ Purchases Multiplier = Same as the Multiplier!
WARNING! If the government changes transfer payments (Social Security, Welfare, Student Loans) only then the multiplier will be smaller because the recipients of the payments will consume some of the payments and SAVE some of the payments.

4. 5. Transfer Payments Multiplier = MPC X Multiplier OR Transfer Payments Multiplier = MPC/MPS.
6. Tax Multiplier = -MPC X Multiplier OR Tax Multiplier = -MPC/MPS.

5. What happens when people get a tax cut?
Their DI increases!
What happens when people get a tax increase?
Their DI decreases!
b. What two things can you do with income? Spend (Consume) it or save it!
c. If people save some of their tax cut the tax multiplier will not be as great as the government purchases multiplier. Conversely if their taxes are raised they will consume less AND save less.

6. 7. Balanced Budget Multiplier =
Government Purchases Multiplier + Tax Multiplier = 1
An increase in government spending (G) that is met with an equal increase in taxes (T) in order to maintain a balanced budget will boost the GDP by an equal amount. Equal increases in G and T will expand GDP by an amount equal to that increase.

7. 8. Net Exports Multiplier = 1/ (MPS + MPM)
MPM = Marginal Propensity to iMport = ∆ Imports/ ∆GDP
As economy enters a recession Expansionary Fiscal Policy (↑ G OR ↑ TP OR ↓ T)  ↑ AD
BUT...
↑ AD  ↑ D for Money (borrowing)  ↑ Domestic Interest Rates  ↑ Foreign Demand for $  $ appreciates  NX ↓  AD ↓  contractionary offset to the expansionary fiscal policy!

8. If economy has inflation  Contractionary Fiscal Policy (↓ G OR ↓ TP OR ↑ T)  ↓ in AD
BUT...
↓ in AD  ↓ D for Money (borrowing)  ↓ Domestic Interest Rates  ↓ Foreign Demand for $  $ depreciates  NX ↑  AD ↑  expansionary offset to the contractionary fiscal policy!

9. Calculate the marginal propensities to consume, save, import, and the various multipliers (#1-8) using the chart below.
2003
2004
Disposable Income (DI)
1000
1200
Consumption (C)
800
920

10. Calculating the MPC and MPS
2003
2004
Disposable Income (DI)
1000
1200
Consumption (C)
800
920
MPC = ∆C/ ∆DI
120 ÷ 200 = .6
MPS = 1- MPC
1- .6 = .4

11. Then answer these questions:
1. A $1,000,000 increase in autonomous expenditure would increase GDP by how much? Show your work!
Multiplier = 1/ 1-MPC OR 1/ MPS
MPS = .4
MPC =.6
1÷ (1- .6) = 1 ÷ .4 = 2.5
$1,000,000 x 2.5 = $2,500,000

12. 2. A $1,000,000 increase in government spending would increase GDP by how much? Show your work!
Government Spending Multiplier is the same as the Multiplier so it equals 2.5.
$1,000,000 x 2.5 = $2,500,000

13. 3. A $1,000,000 increase in transfer payments would increase GDP by how much? Show your work!
TP Multiplier = MPC x Multiplier OR
TP Multiplier = MPC/ MPS
.6 x 2.5 = 1.5 OR .6 ÷ .4 = 1.5
$1,000,000 x 1.5 = $1,500,000

14. 4. A $1,000,000 decrease in taxes would increase GDP by how much
4. A $1,000,000 decrease in taxes would increase GDP by how much? Show your work!
Tax Multiplier = -MPC x Multiplier OR
Tax Multiplier = -MPC/ MPS
- .6 x 2.5 = -1.5 OR -.6 ÷ .4 = -1.5
$-1,000,000 x -1.5 = $1,500,000

15. 5. A $1,000,000 increase in government spending accompanied by a $1,000,000 increase in taxes would increase GDP by how much? Show your work!
Balanced Budget Multiplier =
Government Purchases Multiplier + Tax Multiplier
2.5 + (-1.5) = 1.0
$1,000,000 x 1 = $1,000,000

16. 6. A $1,000,000 increase in government spending would increase GDP by how much if the marginal propensity to import were .1 ? Show your work!
Net Exports Multiplier = 1 ÷ (MPS + MPM)
MPM = .1
MPS = .4
1 ÷ ( ) = 2.0
$1,000,000 x 2.0 = $2,000,000