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

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Solution

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

Autonomous expenditure (A) = C + I + G + X − M

Therefore, open economy multiplier with proportional taxes

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