The 'Balanced Budget Multiplier' suggests that an equal increase in government spending and taxes will:

Solution

• This is a classic theorem in Keynesian economics.
• Government Spending Multiplier = 1 / (1 - MPC)
• Tax Multiplier = -MPC / (1 - MPC)
  If the government increases spending ( Δ G) and taxes ( Δ T) by the  same amount  (so Δ G = Δ T), the net effect on national income ( Δ Y) is the sum of the two multipliers applied to that amount.
  Δ Y = (Spending Multiplier * Δ G) + (Tax Multiplier * Δ T)
  Δ Y = [1/(1-MPC)]* Δ G + [-MPC/(1-MPC)]* Δ T
  Since Δ G = Δ T, we can factor it out:
  Δ Y = Δ G * { [1/(1-MPC)] + [-MPC/(1-MPC)] }
  Δ Y = Δ G * { (1 - MPC) / (1 - MPC) }
  Δ Y = Δ G * 1 =  Δ G
  Hence, national income increases by exactly the amount of the increase in government spending. The multiplier is 1.