We now consider how changes in taxes affect equilibrium income. A decrease in taxes ΔT\Delta T immediately raises disposable income YTY - T by ΔT\Delta T and, therefore, increases consumption by MPC×ΔTMPC \times \Delta T. For any level of income YY, planned expenditure is now higher and hence the planned expenditure schedule shift upward by MPC×ΔTMPC \times \Delta T:

ΔT\Delta T

0.00
012

Since the current MPCMPC is 0.30, a tax cut of 0.00 shifts the planned expenditure schedule by 0.00. The equilibrium of the economy moves from point A to point B, and income rises from YY to YY'.

Just as an increase in government purchases has a multiplied effect on income, so does the decrease in taxes. As before, the initial change in expenditure, now MPC×ΔTMPC \times \Delta T, is multiplied by 11MPC\frac{1}{1 - MPC}. The overall effect on income of the tax change is:

ΔYΔT=MPC1MPC\frac{\Delta Y}{\Delta T} = \frac{-MPC}{1 - MPC}

This expression is the tax multiplier, the amount income changes in response to a $1 change in taxes. (The negative sign indicates that income moves in the opposite direction from taxes). In this example, the MPCMPC is 0.30 and hence the tax multiplier is -0.30/(1 - 0.30) = -0.30/0.70 = -0.43 . A $1 cut in taxes raises equilibrium income by $0.43 . We can explore how this multiplier is affected by a change in the MPCMPC:

MPCMPC

0.30
01