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Question
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
`Y = (C + I + G + X- M)/(1 -c(1-Y)+m)`
Autonomous expenditure (A) = C + I + G + X − M
Therefore, open economy multiplier with proportional taxes
`(DeltaY)/(DeltaA) = 1/(1 - c(1-t)+m)`
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