3.2 - Multipliers
The Multiplier Effect and Autonomous Spending
When someone spends money, it kicks off a chain reaction that ends up increasing total GDP by more than the original amount spent. This chain reaction is the multiplier effect. The initial spending that kicks it off is called autonomous spending, the first domino.
Disposable Income, MPC, and MPS
- Disposable income: the money someone can actually spend, calculated as Income + Transfers minus Taxes. It can only be spent or saved.
- Marginal Propensity to Consume (MPC): how much consumption rises when disposable income rises. Calculated as change in consumption divided by change in disposable income.
- Marginal Propensity to Save (MPS): how much savings rises when disposable income rises. Calculated as change in savings divided by change in disposable income.
- Key relationship: MPC + MPS always equals 1.
- Example: if disposable income rises by $1,000 and consumption rises by $750, MPC = $750 / $1,000 = 0.75. The other $250 is saved, so MPS = $250 / $1,000 = 0.25, and 0.75 + 0.25 = 1.
When we assign an economy-wide MPC, say 0.9, we’re assuming every extra dollar of disposable income gets spent according to that ratio.
The Expenditure Multiplier
The multiplier is just the reciprocal of the MPS. To find the maximum total increase in GDP, multiply the initial spending increase by this multiplier. For example, if MPS is 0.1, the multiplier is 10, so an initial $1,000 increase in spending could lead to a maximum GDP increase of $10,000. A smaller MPC (and bigger MPS) means a much smaller boost to GDP overall.
Since MPC + MPS = 1, the same multiplier can be written using the MPC:
This shows the multiplier depends on the MPC. The bigger the MPC, the more of each new dollar gets re-spent in every round, and the bigger the multiplier. With an MPC of 0.9 the multiplier is 10; with an MPC of 0.5 it's only 2. The tax multiplier below depends on the MPC too.
Where the multiplier comes from: every dollar of new spending becomes someone else's income. They spend part of it (the MPC) and save the rest, and the part they spend becomes the next person's income. Say the MPC is 0.8 and a business spends $100 million building a new factory (investment):
Round | New spending |
1 | $100 million (the factory) |
2 | $80 million (0.8 × $100 million) |
3 | $64 million (0.8 × $80 million) |
4 | $51.2 million (0.8 × $64 million) |
... | each round is 0.8 times the one before |
Total | $500 million ($100 million × 5) |
The expenditure multiplier works the same way for a change in any component of AD. A $100 million rise in consumption, investment, government spending, or net exports has the same multiplied effect. It also works in reverse: with an MPC of 0.8, a $100 million drop in spending can shrink real GDP by up to $500 million.
The Tax Multiplier
Tax cuts raise disposable income and consumption, increasing GDP; tax hikes do the opposite. The tax multiplier is always smaller than the expenditure multiplier, because an initial spending increase adds to GDP directly, while a tax change only adds to GDP indirectly, since only the consumption portion (MPC) of the tax cut kicks off the chain reaction.
Government transfers, like welfare or Social Security, use the tax multiplier formula too, since the transfer money only affects GDP indirectly once it’s spent.
Example: with an MPC of 0.8 and an MPS of 0.2, the expenditure multiplier is 1 / 0.2 = 5 and the tax multiplier is 0.8 / 0.2 = 4.
- A $100 billion increase in government spending can raise real GDP by up to $100 billion × 5 = $500 billion.
- A $100 billion tax cut can raise real GDP by up to only $100 billion × 4 = $400 billion. Households save $20 billion of the tax cut and spend just $80 billion in the first round, so the chain reaction starts smaller.
- A $100 billion tax increase can lower real GDP by up to $400 billion.
Some textbooks write the tax multiplier as . The minus sign just shows that taxes and real GDP move in opposite directions: a tax increase lowers GDP, and a tax cut raises it.
Takeaway
Initial spending triggers the multiplier effect, leading to a bigger eventual increase in GDP, calculated using the expenditure multiplier (). Changes in taxes or transfers use the smaller tax multiplier (), since the initial dollar change only indirectly affects GDP through consumption.