3.2 Multipliers

AP Macroeconomics · AP (Advanced Placement) · 4 min read · Updated: 7 Sept 2026

Unit 3.2: Multipliers

Welcome to one of the most important "aha!" moments in Macroeconomics! In the previous chapter (3.1), we looked at Aggregate Demand (AD). Now, we are going to explore a fascinating phenomenon: how a small initial change in spending can lead to a much larger change in the total Real GDP. This "chain reaction" is known as the Multiplier Effect.

Think of it like a pebble dropped into a still pond. The pebble is the initial spending, but the ripples it creates spread far across the water. By the end of this chapter, you’ll be able to calculate exactly how big those ripples will be!

The Building Blocks: MPC and MPS

Before we can calculate multipliers, we need to understand what people do when they receive an extra dollar of income. In the world of AP Macroeconomics, there are only two options: you either spend it or you save it.

1. Marginal Propensity to Consume (MPC): This is the fraction of any change in income that is spent on consumption.
Formula: $MPC = \frac{\Delta \text{Consumption}}{\Delta \text{Income}}$

2. Marginal Propensity to Save (MPS): This is the fraction of any change in income that is saved.
Formula: $MPS = \frac{\Delta \text{Saving}}{\Delta \text{Income}}$

The Golden Rule: Since every extra dollar is either spent or saved, these two fractions must always add up to $1$.
$MPC + MPS = 1$

Example: If you receive a \$100 bonus and you spend \$80 of it, your $MPC$ is $0.8$ and your $MPS$ is $0.2$.

Key Takeaway

If you know one, you know the other! If the exam tells you the $MPC$ is $0.9$, you automatically know the $MPS$ is $0.1$.

The Expenditure Multiplier

The Expenditure Multiplier (also called the Spending Multiplier) tells us how much Total Spending (AD) will increase following an initial increase in spending by consumers, businesses, or the government.

Why does this happen?
Imagine the government spends \$100 to hire a worker. That worker now has \$100 of new income. If their $MPC$ is $0.8$, they will spend \$80 at a local grocery store. That \$80 becomes new income for the grocer, who then spends $80\%$ of it (\$64) somewhere else. This cycle continues, adding more and more to the total GDP.

The Formulas:
You can calculate the multiplier in two ways:
1. $\text{Multiplier} = \frac{1}{1 - MPC}$
2. $\text{Multiplier} = \frac{1}{MPS}$

Calculating the Total Change in GDP:
$\Delta \text{Real GDP} = \text{Initial Change in Spending} \times \text{Multiplier}$

Quick Example: If the $MPC$ is $0.75$ and the government increases spending by \$10 billion, what is the total change in GDP?
1. Find the $MPS$: $1 - 0.75 = 0.25$.
2. Find the Multiplier: $\frac{1}{0.25} = 4$.
3. Calculate the total change: $\$10 \text{ billion} \times 4 = \$40 \text{ billion}$.

The Tax Multiplier

The government can also influence the economy by changing taxes. However, the Tax Multiplier works a little differently—and it's always less powerful than the spending multiplier.

Why is it smaller?
When the government spends \$100, that full \$100 goes directly into the economy immediately. When the government gives you a \$100 tax cut, you don't spend all of it. You save a portion (the $MPS$) first, and only spend the rest. Because a portion "leaks" into savings right away, the overall impact is smaller.

The Formulas:
1. $\text{Tax Multiplier} = \frac{-MPC}{1 - MPC}$
2. $\text{Tax Multiplier} = \frac{-MPC}{MPS}$

Note: The tax multiplier is negative because a tax increase leads to a decrease in GDP, and a tax cut (negative change) leads to an increase in GDP.

Relationship between the Multipliers:
The Tax Multiplier is always one less than the Spending Multiplier. If the spending multiplier is $5$, the tax multiplier is $-4$. If the spending multiplier is $10$, the tax multiplier is $-9$.

Did You Know?

The "Simple Multiplier" assumes there are no "leakages" other than savings (like taxes on income or spending on imports). In the AP Macro curriculum, we focus on this simplified version to understand the core concept.

Step-by-Step: Solving Multiplier Problems

Don't worry if this seems tricky! Follow these steps every time:

Step 1: Identify the initial change. Is it spending ($G$, $I$, or $C$) or is it taxes ($T$)?
Step 2: Identify the $MPC$ or $MPS$.
Step 3: Calculate the correct multiplier. Use $\frac{1}{MPS}$ for spending or $\frac{-MPC}{MPS}$ for taxes.
Step 4: Multiply. Multiply the initial change by your multiplier to find the total change in Real GDP.

Common Mistake to Avoid:
Students often use the spending multiplier for tax questions. Remember: Taxes involve saving first! Always use the $MPC$ in the numerator for the tax multiplier formula.

Summary and Key Review

1. Marginal Propensities:
$MPC + MPS = 1$. This is the foundation for everything else.

2. Spending Multiplier:
$\frac{1}{MPS}$. Use this for changes in Government Spending ($G$), Investment ($I$), or Consumption ($C$).

3. Tax Multiplier:
$\frac{-MPC}{MPS}$. Use this for changes in Taxes ($T$). It is always smaller than the spending multiplier.

4. The "Inverse" Relationship:
The smaller the $MPS$ (or the larger the $MPC$), the larger the multiplier will be. If people spend almost everything they earn, the ripples in the pond will travel much further!

Ready for the next step? In Chapter 3.3, we will see how these changes in Aggregate Demand interact with the Short-Run Aggregate Supply (SRAS) to determine the price level and output of the whole economy.

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

What is the Marginal Propensity to Consume (MPC)?

The fraction of any change in income that is spent on consumption, calculated as $MPC = \frac{\Delta \text{Consumption}}{\Delta \text{Income}}$.

What is the Marginal Propensity to Save (MPS)?

The fraction of any change in income that is saved rather than spent, calculated as $MPS = \frac{\Delta \text{Saving}}{\Delta \text{Income}}$.

What is the Expenditure Multiplier (Spending Multiplier)?

A number representing how much total spending (AD) will increase following an initial change in spending, calculated as $\frac{1}{MPS}$ or $\frac{1}{1 - MPC}$.

How do you calculate the total change in Real GDP resulting from a change in spending?

$\Delta \text{Real GDP} = \text{Initial Change in Spending} \times \text{Multiplier}$

What is the Tax Multiplier, and how is it calculated?

The factor by which a change in taxes affects Real GDP, calculated as $\frac{-MPC}{MPS}$.

Why is the Tax Multiplier less powerful than the Spending Multiplier?

Because a portion of a tax change is immediately saved by consumers (the "leakage"), whereas government spending is injected directly into the economy in full.

What is the relationship between the size of the MPS and the size of the multiplier?

There is an inverse relationship: the smaller the MPS (or larger the MPC), the larger the multiplier will be.

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