Calculate the open economy multiplier with proportion of taxes, T = tY, instead of lump-sum taxes as assumed in the text.

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Solution

Y = C + c (1 - t) Y + l + G + X - M - mY

Y - c (1 - t) + mY = C + l + G + X - M

Y [1 - c (1 - t) + m] = C + l + G + X - M

Y = $\frac{C + l + G + X - M}{[1 - c (1 - t) + m]}$

Autonomous Expenditure (A) = C + l + G + X - M

$∴$ Open economy multiplier with proportional taxes:

$\frac{Δ Y}{Δ A} = \frac{1}{1 - c (1 - t) + m}$

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Calculate the open economy multiplier with proportional taxes, T = tY, instead of lump−sum taxes as assumed in the text.

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Calculate the open economy multiplier with proportion of taxes, T = tY, instead of lump-sum taxes as assumed in the text.

Y = C + c (1 - t) Y + l + G + X - M - mY Y - c (1 - t) + mY = C + l + G + X - M Y [1 - c (1 - t) + m] = C + l + G + X - M Y = C+l+G+X−M[1−c(1−t)+m] Autonomous Expenditure (A) = C + l + G + X - M ∴ Open economy multiplier with proportional taxes: ΔYΔA=11−c(1−t)+m