What this lesson teaches
I can explain how a change in AD has a multiplied effect on national income.
Syllabus 9570, 3.1.2(e). Aggregate Demand and Aggregate Supply: How changes in the components of AD can have a multiplied effect on national income
Make a guess
In one country, 40 cents of each extra dollar leaks out as saving, tax and imports. In another, 80 cents leaks out. Where does a new $1 billion of spending raise income more?
- Where 40 cents leaks, because more is spent each round.
- The same in both, because the first spending is the same.
- Where 80 cents leaks, because more money moves around.
Show the answer
Where 40 cents leaks, because more is spent each round.
The multiplier is 1 / MPW. With MPW = 0.4, k = 2.5; with MPW = 0.8, k = 1.25.
k = 1 / MPW. The more that leaks out, the smaller the multiplier.
The multiplier (k) tells us how much national income rises for each $1 of new autonomous spending.
k = 1 / (1 - MPCd) = 1 / MPW. Change in national income = k x change in autonomous spending.
With MPW = 0.4, k = 2.5: an extra $10 million of government spending would raise national income by $25 million.
The formula assumes spare capacity and fixed prices, and it takes time to work through. Singapore's high MPM and saving through CPF make its multiplier much smaller than those of large economies such as the US.
- Formula
- k = 1 / MPW = 1 / (1 - MPCd).
- Singapore
- High MPM and saving: small k.
| Round | Extra income | Running total |
|---|---|---|
| 1 | 10 | 10 |
| 2 | 6 | 16 |
| 3 | 3.6 | 19.6 |
| 4 | 2.16 | 21.76 |
| All rounds | - | 25 |
Worked example: Add up the rounds
Autonomous spending rises by 10 units. Each extra unit of income leads to 0.6 units of spending on domestic output.
- MPW = 1 - 0.6 = 0.4, so k = 1 / 0.4 = 2.5.
- Change in income = 2.5 x 10 = 25 units.
- Rounds: 10 + 6 + 3.6 + 2.16 + ... = 25.
- The 15 units beyond the first 10 come from induced spending.
Try it step by step
Problem 1
Autonomous spending rises by $10 million. Of each extra dollar of income, $0.60 is spent on domestic output.
Show the working
- MPW: MPW = 1 - MPCd = 1 - 0.6 = 0.4
- Multiplier k: k = 1 / MPW = 1 / 0.4 = 2.5
- Change in national income: Change in income = k x change in spending = 2.5 x $10 million = $25 million
Problem 2
Investment rises by $20 million. Of each extra dollar of income, $0.20 is saved, $0.15 is paid in tax and $0.15 is spent on imports.
Show the working
- MPW: MPW = MPS + MPT + MPM = 0.20 + 0.15 + 0.15 = 0.5
- Multiplier k: k = 1 / 0.5 = 2
- Change in national income: Change in income = 2 x $20 million = $40 million
Problem 3
Exports rise by $30 million. Of each extra dollar of income, $0.10 is saved, $0.20 is paid in tax and $0.45 is spent on imports.
Show the working
- MPW: MPW = 0.10 + 0.20 + 0.45 = 0.75
- Multiplier k: k = 1 / 0.75 = 1.33 (to 2 decimal places)
- Change in national income: Change in income = 1.33 x $30 million = $40 million (exactly 30 / 0.75)
Watch out for this
A bigger MPS makes the multiplier bigger.
Saving is a withdrawal. A bigger MPS means less is spent in each round, so the multiplier is smaller.
Check your understanding
MPW is 0.8. What is the multiplier?
- 0.8.
- 5, because 1 / (1 - 0.8) = 5.
- 1.25.
Show the answer
1.25.
Right. k = 1 / 0.8 = 1.25.