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

$\Delta T$

0.00
012

Since the current $MPC$ 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 $Y$ to $Y'$.

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 $MPC \times \Delta T$, is multiplied by $\frac{1}{1 - MPC}$. The overall effect on income of the tax change is:

$\frac{\Delta Y}{\Delta T} = \frac{-MPC}{1 - MPC}$

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 $MPC$ 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 $MPC$:

$MPC$

0.30
01