If the tax rate is 0.1, and the marginal propensity to consume is 0.5, the multiplier is:

Question

BlackTom AI · Accepted Answer

We are given a macroeconomics question about the spending multiplier when a tax rate applies. The key formula for the multiplier with taxes is: Multiplier = 1 / [1 − c × (1 − t)], where c is the marginal propensity to consume and t is the tax rate.

Option 1: 2. This would imply a multiplier of 2, which would require c × (1 − t) to equal 0.5, since 1 / (1 − 0.5) = 2. With c = 0.5 and t = 0.1, we get c × (1 − t) = 0.5 × 0.9 = 0.45, so the resulting multiplier is 1 / (1 − 0.45) = 1 / 0.55 ≈ 1.818, not 2. Therefore this option is too large.

Option 2: 2.1. This would require the denominator to be 1 / 2.1 ≈ 0.476, meaning 1 − c × (1 − t) ≈ 0.476, or c × (1 − t) ≈ 0.524. Given c × (1 − t) = 0.45 from the provided values, this option does not align with the calculation, so it is incorrect.

Option 3: 1. This would occur if c × (1 − t) = 0, which would require either c = 0 or (1 − t) = 0 (i.e., t = 1). Since neither is true here (c = 0.5 and t = 0.1), this option is inconsistent with the data and is incorrect.

Option 4: 1.8. Applying the formula with c = 0.5 and t = 0.1 gives: c × (1 − t) = 0.5 × 0.9 = 0.45, and then 1 − 0.45 = 0.55, so the multiplier = 1 / 0.55 ≈ 1.818, which rounds to 1.8. This matches the computed value based on the given parameters, making it correct in the context of typical rounding.

In summary, the accurate computation yields a multiplier around 1.818, which aligns with option 1.8 when rounded to one decimal place, while the other options deviate from the calculation by misaligning with the effect of the tax rate on the spending multiplier.

If the tax rate is 0.1, and the marginal propensity to consume is 0.5, the multiplier is:

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