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How does an initial change in spending produce a larger change in real GDP?

Topic 3.2 Multipliers: define the marginal propensities to consume and save, derive the spending and tax multipliers, and use them to calculate the total change in real GDP from a change in spending or taxes.

A focused answer to AP Macroeconomics Topic 3.2, covering the marginal propensity to consume and save, the spending multiplier, the tax multiplier, the balanced budget multiplier, and how to calculate the total change in real GDP, with full worked calculations.

Generated by Claude Opus 4.812 min answer

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  1. What this topic is asking
  2. The marginal propensities
  3. The spending multiplier
  4. The tax multiplier
  5. Try this

What this topic is asking

Topic 3.2 explains the multiplier effect: why an initial change in spending or taxes leads to a larger total change in real GDP. The College Board wants you to define the marginal propensities, calculate the spending and tax multipliers, and apply them. These are among the most heavily tested calculations on the exam.

The marginal propensities

The spending multiplier

When the government (or any spender) injects new spending into the economy, the recipients earn income and spend a fraction (the MPC) of it, which becomes someone else's income, and so on. The rounds form a geometric series that sums to:

spending multiplier=11−MPC=1MPS\text{spending multiplier} = \frac{1}{1 - MPC} = \frac{1}{MPS}

The total change in real GDP is:

ΔGDP=spending multiplier×Δspending\Delta GDP = \text{spending multiplier} \times \Delta \text{spending}

A larger MPC means more is re-spent each round, so the multiplier is larger.

The tax multiplier

A tax change works differently. A tax cut does not enter the economy directly as spending; it first raises households' disposable income, and they spend only the MPC fraction of it (saving the rest). So the first round is smaller, and:

tax multiplier=−MPC1−MPC\text{tax multiplier} = \frac{-MPC}{1 - MPC}

It is negative (a tax cut, a fall in taxes, raises GDP) and smaller in absolute value than the spending multiplier by exactly 1.

Try this

Q1. Write the formula for the spending multiplier in terms of the MPS. [1 point]

  • Cue. Spending multiplier =1MPS= \frac{1}{MPS} (equivalently 11−MPC\frac{1}{1 - MPC}).

Q2. If the MPC is 0.75, by how much does a 40 increase in government spending change real GDP? [2 points]

  • Cue. Multiplier =10.25=4= \frac{1}{0.25} = 4; ΔGDP=4×40=160\Delta GDP = 4 \times 40 = 160.

Exam-style practice questions

Practice questions written in the style of College Board exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

AP 2018 (style)1 marksMultiple choice. If the marginal propensity to consume is 0.8, an increase in government spending of 50 will, all else equal, increase real GDP by (A) 40. (B) 50. (C) 62.5. (D) 200. (E) 250.
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The answer is (E). The spending multiplier is 11−MPC=11−0.8=10.2=5\frac{1}{1 - MPC} = \frac{1}{1 - 0.8} = \frac{1}{0.2} = 5. The total change in real GDP is the multiplier times the initial change: 5×50=2505 \times 50 = 250.

(A) misuses the MPC as a multiplier. (B) ignores the multiplier entirely. (C) inverts the calculation. (D) uses a multiplier of 4 (which would come from an MPC of 0.75). The correct answer is 250.

AP 2022 (style)4 marksFree response. The marginal propensity to consume is 0.75. (a) Calculate the spending multiplier. (b) Calculate the tax multiplier. (c) Calculate the change in real GDP from a 100 increase in government spending. (d) Explain why the tax multiplier is smaller in absolute value than the spending multiplier.
Show worked answer →

A 4-point calculation FRQ.

(a) Spending multiplier (1 point): 11−MPC=11−0.75=10.25=4\frac{1}{1 - MPC} = \frac{1}{1 - 0.75} = \frac{1}{0.25} = 4.

(b) Tax multiplier (1 point): −MPC1−MPC=−0.750.25=−3\frac{-MPC}{1 - MPC} = \frac{-0.75}{0.25} = -3.

(c) Change in GDP (1 point): 4×100=4004 \times 100 = 400 (an increase of 400).

(d) Explanation (1 point): a change in government spending enters the economy entirely as new spending, but a tax cut first passes through households, who save a fraction (the MPS); only the consumed fraction (the MPC) is spent. So the first round of a tax change is smaller, making the tax multiplier smaller in absolute value.

Markers reward 4, −3-3, 400, and the saved-fraction reasoning.

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