Difficulty: Intermediate | Prerequisites: Sections 8.1 and 8.2 (consumption function, MPC/MPS, equilibrium output)
Source: Principles of Macroeconomics, Case/Fair, 8e – Chapter 8, Section 8.3
Tags: multiplier, spending multiplier, MPC, MPS, paradox of thrift, autonomous spending, Keynesian multiplier, multiplier effect, aggregate expenditure shifts
Sections 8.1 and 8.2 showed you how the economy reaches equilibrium. This section asks: what happens when something changes? If businesses decide to invest an extra $10 billion, does output rise by $10 billion? No, it rises by more. The multiplier captures this amplification effect. Each dollar of new spending becomes income for someone, who spends a fraction of it, creating income for someone else, and so on. The size of the multiplier depends entirely on the MPC (or equivalently the MPS). This concept is central to understanding why governments use fiscal policy to manage recessions and why small changes in spending can have outsized effects on the economy.
A change in autonomous spending (investment or autonomous consumption) causes a larger change in equilibrium output. The multiplier equals 1 / MPS, or equivalently 1 / (1 − MPC). With an MPC of 0.8, the multiplier is 5, meaning a $10 billion spending increase raises output by $50 billion.
Multiplier
The ratio of the change in equilibrium output to the initial change in autonomous spending that caused it. In simple terms, it tells you how much "bang for the buck" a spending change delivers.
Autonomous spending
Any component of aggregate expenditure that does not depend on current income. Autonomous consumption and planned investment are the two main examples in the simple model. A change in either one shifts the AE line up or down.
Paradox of thrift
The idea that if everyone in the economy tries to save more at the same time, the resulting drop in consumption reduces income so much that total saving in the economy may end up falling rather than rising. Individually rational behaviour (saving more) produces a collectively harmful outcome.
Suppose firms increase planned investment by $10 billion.
That $10 billion is new spending, which becomes $10 billion of income for the workers and suppliers who receive it.
Those recipients spend a fraction of their new income (determined by MPC). If MPC = 0.75, they spend $7.5 billion.
That $7.5 billion becomes income for another group, who spend 0.75 × $7.5 = $5.625 billion, and so on.
The total increase in output is the sum of this geometric series: $10b + $7.5b + $5.625b + ... = $10b × (1 / (1 − 0.75)) = $10b × 4 = $40 billion.
Multiplier = 1 / (1 − MPC) = 1 / MPS
This works in both directions: a decrease in autonomous spending reduces output by the multiplier times the decrease.
MPC = 0.5 → MPS = 0.5 → Multiplier = 2
MPC = 0.75 → MPS = 0.25 → Multiplier = 4
MPC = 0.8 → MPS = 0.2 → Multiplier = 5
MPC = 0.9 → MPS = 0.1 → Multiplier = 10
The higher the MPC (and thus the lower the MPS), the larger the multiplier. More of each round of spending recirculates rather than leaking into saving.
The multiplier depends on MPC (or MPS), not on the size of autonomous consumption or the level of planned investment. If autonomous consumption changes, the multiplier stays the same; only the equilibrium level of output shifts.
Increase in planned investment: AE line shifts up → equilibrium output rises by (multiplier × ΔI).
Decrease in planned investment: AE line shifts down → equilibrium output falls by (multiplier × ΔI).
Increase in autonomous consumption: AE line shifts up → same multiplier effect on output.
Decrease in autonomous consumption: AE line shifts down → output falls by (multiplier × Δa).
On the Keynesian cross diagram, a change in autonomous spending shifts the AE line vertically (parallel shift if MPC is unchanged).
The new equilibrium is where the shifted AE line crosses the 45-degree line.
The horizontal distance between the old and new equilibria is larger than the vertical shift, which visually shows the multiplier at work.
If every household tries to save more (autonomous consumption falls), the AE line shifts down.
Output and income decline by a multiplied amount.
As income falls, saving falls with it (since S depends on Y).
In the end, total saving in the economy does not increase, because the decline in income offsets the initial attempt to save more.
The lesson: what works for one household (saving more) can backfire if everyone does it simultaneously, because one person's spending is another person's income.
In practice, the multiplier is smaller than the simple formula suggests, roughly about 1.4.
Taxes, imports, and price-level changes all act as additional leakages that reduce the multiplier below its theoretical value.
The simple model gives you the intuition; the real economy layers in complications.
Formula | Meaning |
|---|---|
Multiplier = 1 / (1 − MPC) | The spending multiplier (simple model) |
Multiplier = 1 / MPS | Equivalent form |
ΔY = Multiplier × ΔI | Change in equilibrium output from a change in investment |
ΔY = Multiplier × Δa | Change in equilibrium output from a change in autonomous consumption |
Example 1 – Basic multiplier calculation: MPC = 0.8. Planned investment increases by $10 billion.
Multiplier = 1 / (1 − 0.8) = 1 / 0.2 = 5.
ΔY = 5 × $10b = $50 billion increase in equilibrium output.
Example 2 – Working backwards from the multiplier: The multiplier is 4. What is the MPC?
4 = 1 / (1 − MPC), so 1 − MPC = 0.25, MPC = 0.75.
Example 3 – Decrease in investment: MPS = 0.2. Planned investment decreases by $20 billion.
Multiplier = 1 / 0.2 = 5.
ΔY = 5 × (−$20b) = −$100 billion. Output falls by $100 billion.
Example 4 – From Figure 8.10 in the textbook: AE₀ = 50 + 0.75Y. Equilibrium = 200. Multiplier = 1 / (1 − 0.75) = 4.
A $10 million increase in investment → new equilibrium = 200 + (4 × 10) = 240.
A $20 million decrease in autonomous consumption → new equilibrium = 200 + (4 × (−20)) = 120.
Example 5 – Effect of changing MPC on equilibrium: AE₀ = 50 + 0.75Y gives equilibrium at 200. If MPC rises to 0.8:
New equilibrium = 50 / (1 − 0.8) = 50 / 0.2 = 250.
(Note: autonomous spending remains 50, but the higher MPC means more recirculation, so equilibrium output is higher.)
Governments use the multiplier to estimate the impact of stimulus packages. If the government injects spending into the economy during a downturn, the total effect on GDP is a multiple of the injection. This was the logic behind fiscal stimulus programmes after the 2008 financial crisis and during the 2020 pandemic. The debate among economists is often about the actual size of the multiplier, not whether the effect exists.
Students often think the multiplier applies only to investment. It applies to any change in autonomous spending, including autonomous consumption.
The multiplier works in both directions. A spending cut is multiplied downward just as a spending increase is multiplied upward.
A change in MPC changes the multiplier itself. A change in autonomous consumption or investment does not change the multiplier; it changes the level of output via the multiplier.
The paradox of thrift does not mean saving is always bad. It means that in the short run, a sudden collective increase in saving reduces aggregate demand. In the long run, saving funds investment, but that is a different model.
Multiplier calculations are among the most commonly tested items in this chapter. Be confident computing 1 / (1 − MPC) and 1 / MPS.
Know how to go from multiplier to MPC and back.
Graph questions may ask you to identify the new equilibrium after an AE shift. The horizontal gap between old and new equilibria = multiplier × vertical shift.
The paradox of thrift is a favourite exam topic for short-answer and true/false questions. Be ready to explain the logic in two to three sentences.
In practice, the real-world multiplier is about 1.4. This fact has come up in past exams as a standalone question.
If MPC = 0.75, the multiplier is ________. (4)
True or false: If autonomous consumption increases, the multiplier decreases. (False, the multiplier stays the same)
If the multiplier is 5 and investment rises by $20 billion, output rises by ________. ($100 billion)
True or false: The paradox of thrift says that increased efforts to save can lead to lower total saving. (True)
The formula for the multiplier (no government, no foreign sector) is ________. (1 / (1 − MPC) or 1 / MPS)
Q: What is the multiplier if the MPS is 0.2?
A: Multiplier = 1 / MPS = 1 / 0.2 = 5.
Q: If the multiplier is 5, a $10 billion increase in planned investment causes aggregate output to increase by how much?
A: $10 billion × 5 = $50 billion.
Q: As the MPS decreases, what happens to the multiplier?
A: The multiplier increases. A smaller MPS means more of each dollar recirculates as spending, amplifying the total effect.
Q: According to the paradox of thrift, what happens when everyone tries to save more?
A: Income falls because reduced consumption lowers aggregate demand. The decline in income leads to an overall decrease in saving, despite each individual's intention to save more.
Q: If MPC = 0.8, what is the multiplier, and what happens to equilibrium output if planned investment drops by $20 billion?
A: Multiplier = 1 / (1 − 0.8) = 5. Output falls by 5 × $20b = $100 billion.
Q: Why is the real-world multiplier smaller than the simple model predicts?
A: Because the simple model ignores taxes, imports, and price-level effects, all of which act as additional leakages that reduce the amount of spending recirculated in each round.
Q: If autonomous consumption increases, does the size of the multiplier change?
A: No. The multiplier depends on MPC (or MPS), not on the level of autonomous spending. The equilibrium shifts, but the multiplier itself remains the same.
The multiplier is the mechanism through which fiscal policy works (Chapter 9). When the government increases spending or cuts taxes, the effect on GDP is amplified by the multiplier. Understanding the simple spending multiplier here prepares you for the government spending multiplier and the tax multiplier, both of which are modifications of this formula. The paradox of thrift connects to broader debates in macroeconomics about whether austerity helps or harms an economy in recession.
multiplier, spending multiplier, Keynesian multiplier, multiplier effect, 1/MPS, 1/(1-MPC), paradox of thrift, autonomous spending, autonomous consumption, planned investment change, AE shift, equilibrium shift, fiscal policy multiplier, government spending multiplier, tax multiplier, Case Fair Chapter 8, ECO 2013, principles of macroeconomics