Explain why the tax multiplier is smaller in absolute value than the government expenditure multiplier.

The tax multiplier is smaller in absolute value than the government expenditure multiplier, as the government expenditure affects the total expenditure and taxes through the multiplier. Tax multiplier also influences disposable income that affects the overall consumption level.
The reason is explained through the following example.
Let's assume MPC be to 0.80.
Then, the government expenditure multiplier = 1/1 - c

= 1/1 - 0.80

= 100/20

= 5

Tax multiplier = - c/(1 - c) = - 80/(1 - 0.80)

= - 0.80/0.20

= - 4

This shows that government expenditure multiplier is more than tax multiplier.

The tax multiplier is smaller in absolute value compared to the govt, expenditure multiplier. This is because, the govt, expenditure directly affect the total expenditure and taxes enter the multiplier, process and put impact on the disposable income. 

Disposable income influences the consumption expenditure of households. Therefore, the tax multiplier is always less in absolute value than the govt, expenditure multiplier.

For example, assume that MPC = 0.75, then Govt, expenditure multiplier = \(\frac{1}{1-c}\), C stands for MPC

= \(\frac{1}{1-0.75}\) = \(\frac{1}{0.25}\) = 4

Tax multiplier = \(\frac{-c}{1-c} = \frac{-0.75}{1-0.75} = \frac{-0.75}{0.25}\)

= -3 (absolute value is 3)

Thus, it is clear from the example, that tax multiplier is smaller than govt. expenditure multiplier.