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Multipliers - AP Macroeconomics

  1. Given the change in spending described, firms increase planned investment by $60 billion in the short run. The MPC is 0.75, and assume no additional leakages besides saving. What is the total change in real GDP predicted by the multiplier process?
    Answer: $240 billion The multiplier effect occurs because each dollar of new spending becomes income for someone else, who then spends part of it, creating more income in a continuing cycle. With MPC = 0.75, households spend 75% of additional income and save 25%, which is the only leakage here. The spending multiplier equals 1/(1-MPC) = 1/(1-0.75) = 1/0.25 = 4. When firms increase investment by $60 billion, this initial injection multiplies through the economy: $60 billion × 4 = $240 billion total change in GDP. Students often confuse the initial change with the total change—remember the initial spending gets magnified. The strategy is always: identify MPC, calculate multiplier as 1/(1-MPC), then scale the initial change.
  2. Two economies, X and Y, each increase government purchases by $20 billion in the short run. Economy X has an MPC of 0.90.9, while Economy Y has an MPC of 0.60.6. Given the change in spending described, which outcome is most consistent with the multiplier model when saving is the main leakage?
    Answer: Economy X has a larger total change in real GDP because less income leaks to saving each round. The multiplier, 1/(1−MPC)1/(1 - MPC), amplifies initial spending based on MPCMPC size, with higher MPCMPC meaning fewer saving leakages and larger effects. MPCMPC governs consumption from income, while saving leaks reduce ongoing spending. With 2020 billion spending in both, Economy X's MPC=0.9MPC = 0.9 yields larger GDP change than Y's 0.60.6 due to less leakage per round. Misconceiving equal effects from same initial spending ignores MPCMPC's role in leakage. Identify MPCMPC differences, compute multipliers, and scale initial changes to compare total GDP outcomes.
  3. A new investment tax credit leads firms to increase planned investment spending by 2020 billion. Households have an MPC of 0.750.75, and the economy is operating below full employment in the short run. Given the change in spending described, which statement best explains why the total change in real GDP is greater than the initial 2020 billion increase in investment?
    Answer: Each round of new income induces additional consumption spending until leakages reduce the process. The multiplier effect occurs when an initial spending change leads to further rounds of income and consumption, with the size determined by 1/(1−MPC)1/(1 - \text{MPC}). The MPC\text{MPC} dictates how much of new income is respent, while leakages such as saving diminish each round's impact. Here, the 2020 billion investment increase, with MPC=0.75\text{MPC} = 0.75, generates additional consumption in each cycle until saving leakages halt the process, making total GDP change exceed 2020 billion. One misconception is believing the multiplier is infinite if MPC\text{MPC} < 1, but it converges due to leakages. For any similar problem, spot the MPC\text{MPC} to derive the multiplier, then multiply it by the initial change to estimate total output effects.
  4. Given the change in spending described, the government increases purchases by $25 billion in the short run. The MPC is 0.80, and assume no additional leakages besides saving. Which value is the spending multiplier?
    Answer: 5 The spending multiplier formula is 1/(1-MPC), where MPC is the marginal propensity to consume. This formula captures how initial spending circulates through the economy in diminishing rounds. With MPC = 0.80, households spend 80% of additional income and save 20%. The multiplier equals 1/(1-0.80) = 1/0.20 = 5. This means each dollar of initial spending ultimately creates five dollars of total GDP change. A common error is using MPC directly as the multiplier or calculating 1/MPC instead of 1/(1-MPC). Remember the intuition: the multiplier must be greater than 1 because the initial spending itself counts, plus all the subsequent rounds of respending.
  5. In the short run, the government increases purchases by 4545 billion. Households have MPC = 0.60. Given the change in spending described, which value is closest to the implied government spending multiplier and the resulting total change in real GDP?
    Answer: Multiplier =2.5=2.5 and real GDP increases by $112.5 billion. The government spending multiplier formula is 1/(1−MPC)1/(1-\text{MPC}), which represents how much total GDP changes per dollar of government purchases. With MPC=0.60\text{MPC} = 0.60, the multiplier equals 1/(1−0.60)=1/0.40=2.51/(1-0.60) = 1/0.40 = 2.5. This means each dollar of government spending ultimately increases GDP by $2.50 through the circular flow of income and consumption. For a $45 billion increase in government purchases, the total GDP change equals $45 billion × 2.5 = $112.5 billion. Students sometimes confuse the multiplier with MPC itself (0.60) or calculate 1/MPC instead of 1/(1-MPC). Remember the strategy: the multiplier is always greater than 1 when MPC > 0, and equals 1/(1-MPC) for any autonomous spending change.
  6. Given the change in spending described, the government increases purchases by 30 billion30\text{ billion} in the short run. The MPC is 0.80.8. Alternatively, the government could cut lump-sum taxes by 30 billion30\text{ billion} with the same MPC. Ignoring other leakages, which comparison of total changes in real GDP is correct?
    Answer: The spending increase raises real GDP more than the tax cut. Government spending has a larger multiplier effect than tax cuts because spending directly increases GDP while tax cuts only affect GDP through induced consumption. With government spending of 30 billion30\text{ billion}, the full amount enters the income stream immediately, creating a total GDP change of 30 billion×11−0.8=30 billion×5=150 billion30\text{ billion} \times \frac{1}{1-0.8} = 30\text{ billion} \times 5 = 150\text{ billion}. With a 30 billion30\text{ billion} tax cut, only the consumed portion (30 billion×0.8=24 billion30\text{ billion} \times 0.8 = 24\text{ billion}) enters the spending stream initially, creating a total GDP change of 24 billion×5=120 billion24\text{ billion} \times 5 = 120\text{ billion}. The spending multiplier exceeds the tax multiplier by exactly 1. Students often assume equal-sized fiscal changes have equal effects, missing that tax cuts must first pass through the consumption decision.
  7. In the short run, the government cuts lump-sum taxes by $50 billion. Households have MPC =0.80=0.80. Given the change in spending described, what is the most likely total change in real GDP, assuming no other changes and that the tax cut affects consumption through disposable income?
    Answer: Real GDP increases by $200 billion. The tax multiplier differs from the spending multiplier because tax cuts first affect disposable income, and only the consumed portion (MPC × tax cut) enters the spending stream. The tax multiplier equals -MPC/(1-MPC), where the negative sign indicates that tax cuts increase GDP. With MPC = 0.80, the tax multiplier is -0.80/(1-0.80) = -0.80/0.20 = -4. A $50 billion tax cut increases GDP by $50 billion × 4 = $200 billion. Students often mistakenly use the spending multiplier (5) for tax changes, which would incorrectly yield $250 billion. Key strategy: remember that tax changes have a smaller multiplier than spending changes because only MPC × (tax change) is initially spent.
  8. In the short run, the government increases purchases by $30 billion. In a sequence of spending rounds, households spend 0.800.80 of each additional dollar of income and save the rest. Given the change in spending described, which statement best explains why the total change in real GDP is greater than $30 billion?
    Answer: Because each round of spending creates additional income that leads to further consumption spending. The multiplier effect occurs because each dollar of spending becomes income for someone else, who then spends a fraction (MPCMPC) of it, creating more income in a continuing cycle. With MPCMPC = 0.80, the initial $30 billion government purchase leads to $24 billion of induced consumption (0.80 × $30 billion), then $19.2 billion (0.80 × 2424 billion), and so on. This geometric series sums to $30 billion × [1/(1-0.80)] = $30 billion × 5 = $150 billion total. The key insight is that spending creates income, which creates more spending—a circular flow that amplifies the initial injection. Common misconceptions include thinking the multiplier equals MPCMPC or that saving prevents any multiplier effect. Strategy: visualize the spending rounds as a shrinking series that sums to initial change times 1/(1-MPCMPC).
  9. In the short run, a temporary tax cut increases households' disposable income by $40 billion. The MPC is 0.75, and assume no other leakages besides saving. Given the change in spending described, what is the total change in real GDP after the multiplier process is complete?
    Answer: An increase of $120 billion Tax cuts affect GDP through the consumption they generate, not the full amount of the cut. With an MPC of 0.75, households consume 75% of the $40 billion tax cut ($30 billion) and save 25% ($10 billion). Only the consumed portion enters the spending stream and gets multiplied by the spending multiplier of 1/(1-0.75) = 4. The total GDP increase equals $30 billion × 4 = $120 billion, or equivalently, $40 billion × 0.75 × 4 = $120 billion. A common error is multiplying the entire tax cut by the spending multiplier, yielding $160 billion, without recognizing that part of the tax cut is immediately saved. The tax multiplier equals MPC × spending multiplier = 0.75 × 4 = 3, so $40 billion × 3 = $120 billion. The strategy for tax changes is to either apply the tax multiplier directly or calculate the initial consumption from the tax cut, then apply the spending multiplier.
  10. Given the change in spending described, the federal government increases purchases of goods and services by 50 billion50\text{ billion} in the short run. Households have a marginal propensity to consume (MPC) of 0.80.8, and each round of spending creates income that is partially spent again. Assuming no other leakages besides saving and that prices are sticky, what is the total short-run change in real GDP?
    Answer: 250 billion250\text{ billion} The spending multiplier shows how an initial change in spending creates a larger total change in GDP through successive rounds of spending. With an MPC of 0.8, households spend 80% of each new dollar of income they receive. The multiplier formula is 1/(1-MPC) = 1/(1-0.8) = 1/0.2 = 5. When the government increases purchases by $50 billion, this creates $50 billion in new income, of which $40 billion is spent (creating more income), then $32 billion, and so on. The total change in GDP equals the initial spending times the multiplier: $50 billion × 5 = $250 billion. A common mistake is forgetting that the initial spending itself counts as part of the total GDP change.
  11. In the short run, the government either (i) increases purchases by $40 billion or (ii) cuts lump-sum taxes by $40 billion. Households have MPC =0.75=0.75. Given the change in spending described, which policy is expected to cause the larger increase in real GDP, and why?
    Answer: The spending increase, because the spending multiplier exceeds the tax multiplier for the same dollar change. The spending multiplier and tax multiplier differ because government purchases directly inject the full amount into the spending stream, while tax cuts only inject MPC times the tax cut. With MPC = 0.75, the spending multiplier is 1/(1-0.75) = 4, while the tax multiplier is -0.75/(1-0.75) = -3. For a $40 billion change, government spending increases GDP by $40 billion × 4 = $160 billion, while tax cuts increase GDP by $40 billion × 3 = $120 billion. The spending increase has a larger effect because the entire $40 billion enters the circular flow immediately, whereas with tax cuts, only $30 billion (0.75 × $40 billion) is initially spent. Misconception alert: the multiplier effect applies to both policies, not just government spending. Strategy: compare multipliers before calculating total effects.
  12. In the short run, the government increases spending on road repairs by $50 billion. Households have a marginal propensity to consume (MPC) of 0.80.8, and the rest of any additional income is saved. Given the change in spending described, what is the total change in real GDP (output) predicted by the simple spending multiplier model, assuming no other leakages beyond saving?
    Answer: Real GDP increases by $250 billion. The spending multiplier represents the total change in real GDP resulting from an initial change in aggregate expenditures, defined as 1/(1 - MPC) in a simple model where saving is the only leakage. The marginal propensity to consume (MPC) shows the portion of additional income spent on consumption, driving successive rounds of spending, while leakages like saving diminish these rounds by diverting income away from further consumption. In this scenario, with an MPC of 0.8 and a $50 billion increase in government spending on road repairs, the multiplier is 5, resulting in a total real GDP increase of $250 billion as the initial spending circulates through the economy. A common misconception is assuming the GDP change equals only the initial $50 billion, ignoring the amplified effects from induced consumption. A transferable strategy is to first identify the MPC to calculate the multiplier, then scale the initial spending change by this multiplier to determine the overall impact on output.
  13. In an economy operating in the short run, the government increases purchases of goods and services by $50 billion. Households spend 0.800.80 of each additional dollar of disposable income (MPC = 0.800.80), and the rest is saved. Given the change in spending described, what is the most likely total change in real GDP, assuming prices are sticky and there are no other changes in policy?
    Answer: Real GDP increases by $250 billion. The spending multiplier measures how much total GDP changes when autonomous spending changes, calculated as 1/(1−MPC)1/(1 - \text{MPC}) or 1/MPS1/\text{MPS}. With MPC = 0.800.80, the multiplier equals 1/(1−0.80)=1/0.20=51/(1 - 0.80) = 1/0.20 = 5. When government purchases increase by 5050 billion, this initial injection circulates through the economy as households spend 80% of each round of new income, creating a chain reaction. The total change in GDP equals the initial change times the multiplier: 5050 billion × 55 = 250250 billion. A common misconception is forgetting to multiply the initial change by the multiplier, which would incorrectly yield only 5050 billion. To solve multiplier problems: first calculate the multiplier using 1/(1−MPC)1/(1 - \text{MPC}), then multiply by the initial spending change.
  14. In the short run, firms respond to higher demand by increasing production. Investment spending increases by $10 billion. The MPC is 0.90.9, but households also save 10%10\% of after-tax income and pay no additional taxes. Given the change in spending described, what is the predicted total change in real GDP according to the simple spending multiplier model, and what feature prevents the process from continuing indefinitely?
    Answer: Real GDP increases by $100 billion, and the process ends because saving is a leakage each round. The spending multiplier defines the overall GDP boost from new spending, equaling 1/(1 - MPC) when saving is the main leakage, allowing firms to ramp up output in the short run. The MPC propels additional consumption, extending the process, while leakages like saving prevent indefinite continuation by withdrawing funds each round. In this scenario, a $10 billion investment increase with MPC of 0.9 (MPS of 0.1) produces a multiplier of 10, totaling $100 billion in GDP growth, ending due to saving leakages. A misconception is believing the multiplier is always 1, missing how high MPC sustains rounds. The transferable strategy is to identify the MPC to compute the multiplier, then scale the initial change while noting leakages that limit the process.
  15. Given the change in spending described, the government increases purchases by $50 billion in the short run, and the MPC is 0.80 (assume no additional leakages besides saving). Alternatively, the government cuts lump-sum taxes by $50 billion with the same MPC. Which statement is most consistent with the spending multiplier versus the tax multiplier in the short run?
    Answer: The spending increase raises real GDP more because it is an initial injection not reduced by saving. The spending multiplier and tax multiplier differ because government purchases directly inject spending, while tax cuts only increase disposable income, of which households save a portion. With MPC = 0.80, the spending multiplier is 1/(1-0.80) = 5, so $50 billion in government purchases increases GDP by $250 billion. For tax cuts, households only spend 80% of the $50 billion tax cut initially ($40 billion), making the first-round injection smaller. The tax multiplier equals -MPC/(1-MPC) = -0.80/0.20 = -4 (negative because tax cuts have opposite sign). A $50 billion tax cut increases GDP by $200 billion. The key insight: government spending has a larger multiplier effect because the full amount enters the spending stream immediately, while tax cuts are partially saved.
  16. In the short run, the government increases spending by $15 billion. The MPC is 0.50.5. Given the change in spending described, which value is closest to the predicted total change in real GDP, and which comparison is correct about the multiplier size relative to the initial change?
    Answer: Real GDP increases by $30 billion, and the total change exceeds the initial change. The multiplier captures the magnified effect on real GDP from initial spending, computed as 1/(1 - MPC) in basic models with saving as the leakage. The MPC determines the strength of consumption responses, increasing the total change beyond the initial amount, while higher leakages shrink the multiplier. In this scenario, a $15 billion spending increase with MPC of 0.5 yields a multiplier of 2, totaling $30 billion in GDP growth, which exceeds the initial change due to induced spending. A misconception is expecting the total to be less than the initial if MPC is low, but it always exceeds it when MPC > 0. The transferable strategy is to identify the MPC for the multiplier, then scale the initial change to assess the total and compare it to the initial injection.
  17. Given the change in spending described, the government increases purchases by 20 billion20\text{ billion} in the short run. The MPC is 0.750.75, and households save the remainder each round. Which statement best explains why the spending multiplier is greater than 1 in this scenario?​
    Answer: Because each round of spending creates new income that is partly spent again. The spending multiplier exceeds 1 because initial spending creates income that gets partially re-spent in successive rounds, creating a chain reaction. With an MPC of 0.75, when the government spends $20 billion, recipients spend $15 billion of this new income, which becomes income for others who spend $11.25 billion, and so on. Each round adds to total GDP, making the final impact larger than the initial spending. The multiplier equals 1/(1-0.75) = 4, so total GDP rises by $80 billion. Option A correctly identifies this circular flow mechanism. Common misconceptions include thinking the initial amount gets counted multiple times (it doesn't—each round represents new transactions) or that saving increases faster than income (saving is a constant fraction of income).
  18. Given the change in spending described, the government increases purchases by $15 billion in the short run. The MPC is 0.60, and assume no additional leakages besides saving. If a student calculates the total change in real GDP as $15 \div 0.60 = $25 billion, which statement best identifies the error?
    Answer: The student used 1/MPC1/\text{MPC} instead of 1/(1−MPC)1/(1-\text{MPC}) for the spending multiplier. The student's error reveals a common misunderstanding of the multiplier formula. They used 1/MPC instead of the correct formula 1/(1-MPC) for the spending multiplier. With MPC = 0.60, the correct multiplier is 1/(1-0.60) = 1/0.40 = 2.5, not 1/0.60 = 1.67. The total GDP change should be $15 billion × 2.5 = $37.5 billion, not $25 billion. This mistake often occurs because students confuse the fraction saved (1-MPC) with the fraction consumed (MPC). The denominator must be the fraction that leaks out (saving), not the fraction that continues circulating. Remember: the multiplier formula uses 1 minus MPC because we need to account for what doesn't get respent in each round.
  19. Assume the economy is in the short run and firms have unused capacity. The government increases purchases of goods and services by $20 billion. The MPC is 0.750.75, and there is also a proportional income tax of 20%20\% on each additional dollar of income; the remainder of any after-tax income is split between consumption and saving according to the MPC. Given the change in spending described, what is the total change in real GDP predicted by the multiplier process when taxes create an additional leakage?
    Answer: Real GDP increases by $50 billion. The multiplier effect describes the amplified impact on real GDP from an initial spending change, adjusted for leakages like taxes and saving, with the formula 1 / (1 - MPC × (1 - t)) where t is the tax rate. The MPC determines the share of after-tax income consumed, propagating spending rounds, while leakages from taxes and saving weaken the multiplier by reducing disposable income available for consumption. In this scenario, with MPC of 0.75, a 20% tax rate, and $20 billion government spending increase, the effective MPC is 0.6, giving a multiplier of 2.5 and total GDP rise of $50 billion. A misconception is overlooking how taxes reduce the effective MPC, mistakenly using the simple multiplier without adjustment. The transferable strategy is to identify the MPC and adjust for leakages like taxes, then scale the initial change by the computed multiplier for the total output change.
  20. In the short run, planned investment rises by $20 billion due to improved business expectations. Households have MPC =0.60=0.60. Given the change in spending described, what is the most likely total change in real GDP, assuming no other changes?
    Answer: Real GDP increases by $50 billion. The investment multiplier works identically to the government spending multiplier because both represent direct injections into the spending stream. With MPC = 0.60, the multiplier equals 1/(1-0.60) = 1/0.40 = 2.5. When planned investment rises by $20 billion, this autonomous spending increase circulates through the economy as households spend 60% of each round of new income. The total GDP change equals $20 billion × 2.5 = $50 billion. A common error is thinking investment has a different multiplier than government purchases—it doesn't. The key insight: any autonomous spending component (C, I, G, or NX) uses the same multiplier formula 1/(1-MPC) when it changes independently.

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