Question

In this country, for each additional $1 of income earned, 4 cents ($0.04) is saved, 15 cents ($0.15) is taken as tax and 6 cents ($0.06) is spent on imported goods and services. Calculate the value of the multiplier.

Answer 1

Answer

Y = C + I + G + X - M

C = Co + c(Y - tY)

=> Y = Co + c(Y - tY) + I + G + X - (Mo + mY)

where c = MPC = 1 - MPS and Imports(M) = Mo + mY

where m = Marginal propensity to import = 0.06

t = tax rate = 0.15 and MPS = 1 - c = 0.15 => c = 0.96

=> Y - cY(1 - t) + m = (Co + I + G + X - (Mo))

=> Y = [1/(1 - c(1 - t)) + m)][Co + I + G + X - (Mo)]

Hence Increase in autonomous expenditure(i.e. Co + I + G + X - (Mo)) will increase equilibrium output by [1/(1 - c(1 - t)) + m)] unit.

Hence Multiplier = [1/(1 - c(1 - t)) + m)] = [1/(1 - 0.96(1 - 0.15) + 0.06)] = 4.1

Hence, multiplier = 4.1