Question

Given a hypothetical consumption function of the form
Y = C + I0 + G0 ,C = α + β Yd Where: Yd = Y – T, Y = Income, T = Taxes
Government spending and investment are exogenously determined at G and I respectively. Assuming this model represent a three sectors economy, determine Investment multiplier, Government spending multiplier and Tax multiplier. If there is an increase in marginal propensity to consumer, how will this affect the national income?

Answer 1

Y = C + I0 + G0, C = α + β Yd, where: Yd = Y – T, Y = Income, T = Taxes
Investment multiplier mi = 1/(1 - MPC) = 1/(1 - β).
Government spending multiplier in this case is the same as investment multiplier, so mg = 1/(1 - MPC) = 1/(1 - β).
Tax multiplier mt = MPC/(1 - MPC) = β/(1 - β).
If there is an increase in marginal propensity to consume, then the national income will decrease.