Home > The Government and Fiscal Policy > Appendix A: Deriving the Fiscal Policy... >
The Government and Fiscal Policy
Appendix A: Deriving the Fiscal Policy Multipliers

To derive the government spending multiplier, we start with the consumption function:

C = a + bY

where b is the marginal propensity to consume.

In equilibrium,

Y = C + I + G


Y = a + b(Y – T) + I + G

Y = a + bY – bT + I + G

and rearranging terms yields

Y – bY = a + I + G - bT

Y (1 – b) = a + I + G – bT

solving for Y

Y = [1/(1 – b)] (a + I + G + bT)

and so [1/(1 – b)] is the government spending multiplier. Since b is the MPC, 1 – b is the MPS, and the multiplier is 1/MPS.

We can also derive the tax multiplier from the above; the equation tells us that if T increases by $1, income will decrease by b/(1 – b) dollars. Thus the tax multiplier is –b/(1 – b); recalling again that b is the MPC, it is - MPC/MPS.

The balanced budget multiplier can be shown to be equal to one of the following:

Because it is a balanced budget, G and T will increase by the same amount. The increase in T will reduce Y and reduce C by a fraction of the reduction in Y (that fraction being the MPC). Thus the net change in spending will be:

DG – DC = DG – DT(MPC) and since DG and DT are equal, this is DG –DG(MPC) or


but remember that 1- MPC is MPS, so this is


That is the net change in aggregate expenditures, but to find its impact on Y, we must apply the spending multiplier, which is (1/MPS).


DG(MPS) [1/MPS] = DY


So whatever the amount of the equal changes in G and T, the resulting change in Y will be in the same amount, and the multiplier is 1.

Copyright © 1995-2010, Pearson Education, Inc., publishing as Pearson Prentice Hall Legal and Privacy Terms