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The Multiplier
Effect

Discover how a single dollar of spending ripples through the economy, amplifying output by a predictable factor tied to the marginal propensity to consume.

AP Macroeconomics

What Is a Multiplier?

In macroeconomics, a multiplier measures how much total output (real GDP) changes in response to an initial change in spending. A small injection of spending doesn't just add to GDP once: it cascades through the economy as each recipient spends part of what they receive.

MPC and MPS: The Building Blocks

MPC
Marginal Propensity to Consume: the fraction of each additional dollar that is spent. $$MPC = \frac{\Delta C}{\Delta Y}$$
MPS
Marginal Propensity to Save: the fraction of each additional dollar that is saved. $$MPS = \frac{\Delta S}{\Delta Y}$$

How Spending Ripples Through the Economy

Round 1 Round 2 Round 3 Round 4
\($100\)
\($80\)
\($64\)
\($51.20\)
 ...
Save \($20\)
Save \($16\)
Save \($12.80\)
Save \($10.24\)
\(\times 0.8\)
\(\times 0.8\)
\(\times 0.8\)
\(\text{Total} = \$100 + \$80 + \$64 + \$51.20 + \cdots = \$500\)
Multiplier \(= \frac{1}{1 - 0.8} = \frac{1}{0.2} = 5\)

The Spending Multiplier Formula

The simple spending multiplier tells you the total change in GDP for a given change in autonomous spending:

This applies to changes in government spending (\(G\)), investment (\(I\)), exports (\(X\)), or autonomous consumption. Any initial injection is multiplied through consumption rounds.

The Tax Multiplier

A tax cut doesn't inject spending directly: consumers first decide how much of the cut to spend vs. save. That makes the tax multiplier smaller than the spending multiplier.

Why the negative sign?
A tax increase reduces GDP, and a tax cut increases GDP. The sign captures this inverse relationship.
Why smaller?
The first round is only \(MPC \times \Delta T\), not the full amount. Part of the tax cut leaks immediately into saving.

The Balanced-Budget Multiplier

What happens when the government increases spending and raises taxes by the same amount? The two multipliers combine:

Spending vs. Tax Multiplier

Spending Multiplier Tax Multiplier
Formula \(\frac{1}{1 - MPC}\) \(\frac{-MPC}{1 - MPC}\)
If MPC = 0.8 5 −4
First-round effect Full amount spent Only MPC fraction spent
Absolute size Larger Smaller by 1
Policy example Build a highway Cut income taxes

How to Apply the Multiplier

1
Identify the MPC (or MPS). Remember: \(MPC + MPS = 1\).
2
Choose the correct multiplier. Spending change → use \(\frac{1}{MPS}\). Tax change → use \(\frac{-MPC}{MPS}\).
3
Calculate the multiplier value. Plug in MPC or MPS.
4
Multiply: \(\Delta GDP = \text{Multiplier} \times \Delta\text{(G or T)}\).
5
Check the sign. Spending increase → GDP rises. Tax increase → GDP falls. Tax cut → GDP rises.

Example 1: Government Spending Increase

The government increases spending by \($20\) billion. The MPC is 0.75. What is the total change in GDP?

1
Find MPS: \(MPS = 1 - 0.75 = 0.25\)
2
Spending multiplier: \(\frac{1}{0.25} = 4\)
3
Calculate: \(\Delta GDP = 4 \times \$20\text{B} = \$80\text{ billion}\)

Example 2: A Tax Cut

Congress cuts taxes by \($30\) billion. The MPC is 0.9. How much does GDP change?

1
Find MPS: \(MPS = 1 - 0.9 = 0.1\)
2
Tax multiplier: \(\frac{-MPC}{MPS} = \frac{-0.9}{0.1} = -9\)
3
Calculate: \(\Delta GDP = -9 \times (-\$30\text{B}) = +\$270\text{ billion}\)

Example 3: Closing a Recessionary Gap

The economy has a recessionary gap of \($600\) billion. The MPC is 0.8. How much must the government increase spending to close the gap?

1
Spending multiplier: \(\frac{1}{1 - 0.8} = 5\)
2
Rearrange: \(\Delta G = \frac{\Delta GDP}{\text{Multiplier}} = \frac{\$600\text{B}}{5} = \$120\text{ billion}\)

Multiplier and Aggregate Demand

Real GDP Price Level SRAS
\(AD_1\)
\(AD_2\)
\(Y_1\)
\(Y_2\)
\(\Delta G \times\) Mult.
\(\Delta GDP\)

Why the Multiplier Matters for Fiscal Policy

Expansionary Policy
To close a recessionary gap, increase \(G\) or cut \(T\). The multiplier means you need less new spending than the gap size.
Contractionary Policy
To close an inflationary gap, decrease \(G\) or raise \(T\). The multiplier means a small cut has an amplified cooling effect.

Common Mistakes with Multipliers

✕ Confusing MPC and MPS
Using \(MPC\) in the denominator instead of \(MPS\). The spending multiplier is \(\frac{1}{MPS}\), not \(\frac{1}{MPC}\).
✕ Forgetting the Sign
The tax multiplier is negative. A tax cut (negative \(\Delta T\)) times a negative multiplier yields a positive GDP change.
✕ Using Spending Mult. for Taxes
Applying \(\frac{1}{MPS}\) to a tax change. Tax changes use \(\frac{-MPC}{MPS}\) because the first round is reduced by saving.

Multiplier Summary

Multiplier Type Formula If MPC = 0.8
Spending \(\frac{1}{1 - MPC}\) 5
Tax \(\frac{-MPC}{1 - MPC}\) −4
Balanced-Budget Always \(= 1\) 1

Question 1 of 5

If the MPC is 0.75, what is the value of the spending multiplier?

Question 2 of 5

If the MPC is 0.8, what is the tax multiplier?

Question 3 of 5

The government increases spending by \($50\) billion and raises taxes by \($50\) billion. GDP will:

Question 4 of 5

An economy has a recessionary gap of \($200\) billion and an MPC of 0.5. How much must the government increase spending to close the gap?

Question 5 of 5

Which statement best explains why the spending multiplier is larger than the absolute value of the tax multiplier?