Suppose real GDP is $200 billion, the government collects 20% of any increase in real GDP in the form of taxes, and the marginal propensity to consume is 0.7. If the government increases spending by $10 billion, real GDP will increase by $:

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BlackTom AI · Accepted Answer

We start by identifying the fiscal interaction in the question: a $10 billion increase in government spending (ΔG) plus taxes that rise with income, at a marginal propensity to consume (MPC) of 0.7 and a tax rate on income increases of 20% (t = 0.2).
Option-by-option evaluation helps reveal how the multiplier changes with distortionary taxes.
Option 1: 50 billion. This would be the simple spending multiplier without any tax effect, which would be ΔY = ΔG / (1 - MPC) = 10 / (1 - 0.7) = 10 / 0.3 ≈ 33.3 billion. Since taxes respond to income and reduce consumption, the actual multiplier should be smaller than the simple 1/(1−MPC) multiplier, not larger. Therefore 50 billion is clearly too large.
Option 2: 22.7 billion. This aligns with the correct distorted spending multiplier. When taxes rise with income, the effective marginal propensity to consume becomes MPC_eff = MPC × (1 − t) = 0.7 × (1 − 0.2) = 0.7 × 0.8 = 0.56. The fiscal multiplier with distortion is 1 / (1 − MPC_eff) = 1 / (1 − 0.56) = 1 / 0.44 ≈ 2.2727. Applying this to ΔG gives ΔY ≈ 2.2727 × 10 ≈ 22.727 billion, which matches 22.7 billion when rounded.
Option 3: 27.8 billion. This would correspond to a multiplier of about 2.78. That would require a higher effective MPC or a smaller tax drag than the given values. With MPC = 0.7 and t = 0.2, the tax drag reduces the multiplier, so 27.8 is too high for this setup.
Option 4: 10 billion. This would imply a zero or negligible multiplier, as if the increase in spending had no ripple effects on GDP, which contradicts the standard transmission mechanism where Gobierno spending induces additional income and consumption. The presence of a positive MPC ensures the total ΔY exceeds ΔG, so 10 is incorrect.
In summary, the correct reasoning structure shows that taxes on increases in GDP dampen the multiplier from the simple 1/(1−MPC) value. With MPC = 0.7 and t = 0.2, the effective MPC is 0.56, yielding a multiplier of 1/0.44 ≈ 2.2727, and hence ΔY ≈ 22.7 billion. The other options fail either by overstating the multiplier or by ignoring the tax-induced reduction in consumption, or by assuming no multiplier at all.

Suppose real GDP is $200 billion, the government collects 20% of any increase in real GDP in the form of taxes, and the marginal propensity to consume is 0.7. If the government increases spending by $10 billion, real GDP will increase by $:

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