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
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

ΔY/ΔA = 1/(1 - c(1 - t) + m)

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