3.2 Spending and Tax Multipliers

The spending (expenditure) multiplier and the tax multiplier show how an initial change in spending or taxes leads to a larger total change in aggregate demand and real GDP. The expenditure multiplier equals 1/(1 - MPC), the tax multiplier equals -MPC/(1 - MPC), and both depend on the marginal propensity to consume.

Spending Multiplier Formula in AP Macroeconomics

The AP Macro spending multiplier formula is:

$\text{Spending multiplier} = \frac{1}{MPS} = \frac{1}{1 - MPC}$

Use it when autonomous spending changes, such as government spending, investment, consumption, or net exports. After you find the multiplier, multiply it by the initial spending change to get the total change in aggregate demand and real GDP. For tax changes, use the tax multiplier instead:

$\text{Tax multiplier} = \frac{-MPC}{MPS} = \frac{-MPC}{1 - MPC}$

That negative sign matters because a tax increase lowers disposable income and aggregate demand, while a tax cut raises them.

Multiplier skills carry directly into the fiscal policy questions later in the unit, where you apply these formulas to real policy decisions.

How MPC Sets the Size of Each Multiplier

• MPC is the share of each new dollar of disposable income that gets spent; MPS is the share that gets saved. They always add to 1.
• The expenditure (spending) multiplier is 1/(1 - MPC), which is the same as 1/MPS.
• The tax multiplier is -MPC/(1 - MPC), which is the same as -MPC/MPS.
• The spending multiplier is always larger in absolute value than the tax multiplier.
• To find the total change in real GDP, multiply the initial change in spending or taxes by the matching multiplier.
• A higher MPC means a larger multiplier, because more of each dollar keeps recirculating through the economy.

Core Vocabulary

• Multiplier effect: An initial change in spending sets off a chain of spending that produces a larger total change in the economy.
• Marginal propensity to consume (MPC): The portion of each new dollar of disposable income that consumers spend rather than save.
• Marginal propensity to save (MPS): The portion of each new dollar of disposable income that consumers save rather than spend.
• Autonomous expenditures: Spending such as investment, government spending, consumption, or net exports that changes independently of current income.

MPC and MPS

Marginal Propensity to Consume (MPC) is the change in consumption divided by the change in disposable income. It tells you how much more people spend when income rises. For example, if income rises from $50,000 to $60,000 (a $10,000 change) and consumption rises from $45,000 to $54,000 (a $9,000 change), then MPC is 0.9 ($9,000 / $10,000).

Marginal Propensity to Save (MPS) is the change in saving divided by the change in disposable income. It tells you how much more people save when income rises. Using the same $10,000 income change, if saving rises from $5,000 to $6,000 (a $1,000 change), then MPS is 0.1 ($1,000 / $10,000).

MPC and MPS always add up to 1, because every new dollar of disposable income is either spent or saved.

$MPC + MPS = 1$

So if you know one, you can always find the other: MPS = 1 - MPC.

Expenditure Multiplier

The expenditure multiplier (also called the spending multiplier) shows how much a $1 change in autonomous spending changes total aggregate demand and real GDP. Because one person's spending becomes another person's income, an initial change in autonomous expenditures leads to a larger overall change in output.

A change in autonomous expenditures causes further rounds of spending, so a $1 initial change leads to a larger total change in aggregate demand and real GDP.

How the Rounds of Spending Work

Suppose businesses increase investment by $10 and the MPC is 0.8:

• The $10 becomes income for some people. They spend $8 and save $2.
• That $8 becomes income for others. They spend $6.40 and save $1.60.
• That $6.40 becomes income for others. They spend $5.12 and save $1.28.

Each round is smaller than the one before because part of every new dollar is saved. After four rounds you already have $10 + $8 + $6.40 + $5.12 = $29.52 in added GDP. The rounds continue forever in smaller and smaller amounts, and the multiplier formula adds them all up for you.

The Formula

$\text{Expenditure multiplier} = \frac{1}{MPS} = \frac{1}{1 - MPC}$

Sometimes you are given MPC and need to find MPS first (MPS = 1 - MPC) before using the formula. The change in spending can be an increase or a decrease, and the multiplier works the same way in both directions.

To find the total change in real GDP, multiply the initial change in autonomous spending by the multiplier:

$\Delta \text{Real GDP} = \text{initial change in spending} \times \frac{1}{1 - MPC}$

For AP Macroeconomics, focus on using the expenditure multiplier to calculate the total change in output from an initial change in autonomous spending in any component of aggregate demand: consumption, investment, government spending, or net exports.

Tax Multiplier

The tax multiplier measures the total change in aggregate demand and real GDP caused by a change in taxes. It works in the opposite direction of the expenditure multiplier: a tax increase reduces disposable income, so people cut back on spending, while a tax cut raises disposable income and increases spending.

The Formula

$\text{Tax multiplier} = \frac{-MPC}{MPS} = \frac{-MPC}{1 - MPC}$

The tax multiplier is always smaller in absolute value than the expenditure multiplier. When the government spends, the full amount enters the economy right away. When taxes change, the effect first passes through disposable income, and people do not spend all of that change. For example, if a tax cut gives people more disposable income, there is no guarantee they spend all of it; part of it gets saved.

Worked Example

If MPC is 0.8 and the government raises taxes by $50, find the tax multiplier and the change in GDP.

$\text{Tax multiplier} = \frac{-MPC}{MPS} = \frac{-0.8}{0.2} = -4$

$\Delta \text{Real GDP} = -4 \times \text{\textdollar}50 = -\text{\textdollar}200$

A $50 tax increase lowers real GDP by $200. Notice the negative sign: a tax increase shrinks aggregate demand, while a tax cut would raise it.

Choosing the Right Multiplier and Showing Your Work

Problem Solving:

• Start by writing down MPC and MPS. If you are given one, find the other with MPS = 1 - MPC.
• Pick the right multiplier. Use 1/(1 - MPC) for spending changes and -MPC/(1 - MPC) for tax changes.
• Multiply the multiplier by the initial change to get the total change in real GDP. Keep the sign so you know the direction.

Free Response:

• If asked why government spending changes aggregate demand more than an equal tax change, explain that spending enters the economy in full immediately, while a tax change first runs through disposable income and part of it is saved.
• If asked to close an output gap, work backward: divide the size of the gap by the multiplier to find the required change in spending or taxes.
• Show your formula and your arithmetic. Correct setup with clear steps earns credit even on a calculation question.

Common Trap:

• Mixing up the formulas. The spending multiplier uses 1/(1 - MPC); the tax multiplier puts -MPC on top.
• Dropping the negative sign on the tax multiplier and reporting the wrong direction for GDP.

Common Misconceptions

• Misconception: The spending and tax multipliers are the same size.
  Actually: The spending and tax multipliers are not the same size. The spending multiplier is always larger in absolute value because the full amount of new spending circulates immediately, while a tax change only affects spending after it passes through disposable income.
• Misconception: A higher MPC makes the multiplier smaller.
  Actually: A higher MPC makes the multiplier bigger, not smaller. More spending out of each dollar means more recirculation, so the multiplier grows as MPC rises.
• Misconception: MPC and MPS are about totals, not changes.
  Actually: MPC and MPS are about changes, not totals. They measure how much of each additional dollar of disposable income is spent or saved, not your overall spending or savings.
• Misconception: The tax multiplier's negative sign has no meaning.
  Actually: The tax multiplier is negative for a reason. A tax increase reduces aggregate demand and a tax cut raises it, so the sign tells you the direction of the effect.
• Misconception: Saving is a boost, not a leakage.
  Actually: Saving is a leakage, not a boost. The part of each dollar that gets saved is exactly why the multiplier is finite instead of infinite.

Related AP Macroeconomics Guides

• 3.1 Aggregate Demand
• 3.3 Short-Run Aggregate Supply (SRAS)
• 3.4 Long-Run Aggregate Supply (LRAS)
• 3.8 Fiscal Policy
• 3.5 Equilibrium in Aggregate Demand-Aggregate Supply (AD-AS) Model
• 3.6 Changes in the AD-AS Model in the Short Run