Short on time? This page is the recap. For explanations, the round-by-round table and worked examples, use the full study guide.
Recap
- A change in autonomous spending (C, I, G or NX) becomes someone’s income, which is partly spent again. Total spending and output change by more than the first change.
- The MPC is the share of an extra unit of disposable income that is spent; the MPS is the share saved.
- The expenditure multiplier gives the change in AD per VD 1 change in autonomous spending.
- The tax multiplier gives the change in AD per VD 1 change in taxes. It is negative and smaller in size, because a tax change works through disposable income and part of it is saved first.
- Both multipliers depend only on the MPC: a higher MPC means bigger multipliers.
Key relationships
| Relationship | Formula | Use it to |
|---|---|---|
| MPC | ΔC ÷ ΔDI | find how much of extra income is spent |
| MPS | ΔS ÷ ΔDI = 1 − MPC | find how much of extra income is saved |
| Spending multiplier | 1 ÷ MPS = 1 ÷ (1 − MPC) | multiply a change in C, I, G or NX |
| Tax multiplier | −MPC ÷ MPS | multiply a change in taxes |
| Transfer change | +MPC ÷ MPS | multiply a change in transfer payments |
| Change in AD | multiplier × initial change | find the size of the AD shift |
| Change needed | target change in AD ÷ multiplier | work backwards to a policy |
Quick reference: MPC 0.5 → 2 and −1; MPC 0.75 → 4 and −3; MPC 0.8 → 5 and −4; MPC 0.9 → 10 and −9.
Assumptions behind the numbers
- The MPC is constant in every round.
- Saving is the only leakage (imports and income taxes are ignored).
- The price level does not change, so the shift in AD equals the change in real GDP.
Mistakes to avoid
- Writing the spending multiplier as 1 ÷ MPC.
- Using totals (C ÷ DI) instead of changes for the MPC.
- Using the spending multiplier for a tax change.
- Losing the sign: a tax rise lowers AD.
- Saying a balanced-budget rise in spending and taxes has no effect. It raises AD by the amount of the spending change.
- Saying a higher MPS makes the multiplier bigger. It makes it smaller.
Quick self-check
VD is the valda, the currency of the fictional country Valdoria used in the study guide.
- The MPS is 0.2. What are the spending and tax multipliers? (5 and −4)
- With MPS 0.2, government spending falls by VD 10 billion. What is the change in AD? (−VD 50 billion)
- The MPC is 0.6 and taxes rise by VD 20 billion. What is the change in AD? (−VD 30 billion: tax multiplier −1.5)
Next: practice questions.