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

The open economy multiplier with proportional taxes will 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

Y = C + I + G + X – M / 1 - c (1 - t) +m

Autonomous expenditure (A) = C + I + G + X – M .Therefore, open economy multiplier with proportional taxes will be –

Y = A / 1 - c (1 - t) +m

∆Y/∆A = 1 / 1 - c (1 - t) +m

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