With lump-sum taxes, the government expenditure multiplier of an econ…

The correct answer is Option (4) → c = 0.6; tax multiplier = −1.5

The expenditure multiplier 1 ÷ (1 − c) gives c. The tax multiplier is −c ÷ (1 − c), which is always one less in absolute value.

Given:

Government expenditure multiplier = 2.5

    \( \displaystyle \frac{1}{1 - c} = 2.5 \;\Rightarrow\; 1 - c = 0.4 \;\Rightarrow\; c = 0.6 \)

    \( \displaystyle \text{Tax multiplier} = \frac{-c}{1 - c} = \frac{-0.6}{0.4} = -1.5 \)

So c = 0.6 and the tax multiplier is −1.5, one less than 2.5 in absolute value.

Option (1) c = 0.4; tax multiplier = −2.5 — Incorrect. 0.4 is 1 − c, the marginal propensity to save, and −2.5 gives the tax multiplier the same size as the expenditure multiplier.

Option (2) c = 0.6; tax multiplier = −2.5 — Incorrect. c is right, but the tax multiplier is one less in absolute value than 2.5.

Option (3) c = 0.4; tax multiplier = −1.5 — Incorrect. The tax multiplier is right, but 0.4 is 1 − c, the marginal propensity to save, not c.