Calculate the open economy multiplier with proportional taxes, T = tY , instead of lump-sum taxes as assumed in the text.
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In the case of proportional tax, the equilibrium income would be, Y = C + c (1 − t) Y + I + G + X − M − mY Y − c (1 − t) Y + mY = C + I +G + X − M Y [1 − c (1 − t) + m] = C + I + G + X − M$\text{Y}=\frac{\text{C}+\text{I}+\text{G}+\text{X}-\text{M}}{1-\text{c}(1-\text{t})+\text{M}}$
Autonomous expenditure (A) = C + I + G + X − M Therefore, open economy multiplier with proportional taxes$\frac{\Delta\text{Y}}{\Delta\text{A}}=\frac{1}{1-\text{c}(1-\text{t})+\text{m}}$
Autonomous expenditure (A) = C + I + G + X − M Therefore, open economy multiplier with proportional taxes$\frac{\Delta\text{Y}}{\Delta\text{A}}=\frac{1}{1-\text{c}(1-\text{t})+\text{m}}$
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