Why tax multiplier is smaller than the multiplier for the sa

Why tax multiplier is smaller than the multiplier for the same amount of government spending? Please explain with the following data: $1 million tax cuts, $1 million increase in government spending, MPC=0.75.

Solution

Tax multiplier = 1 - Spending multiplier = 1 - [1 / (1 - MPC)] = [(1 - MPC) - 1] / [1 - MPC]

= - MPC / (1 - MPC)

Since 0 < MPC < 1, Tax multiplier is lower than spending multiplier [= 1 / (1 - MPC)].

To explain:

When MPC = 0.75, Spending multiplier = [1 / (1 - 0.75)] = 1 / 0.25 = 4

Tax multiplier = - 0.75 / (1 - 0.75) = - 0.75 / 0.25 = - 3

So, tax multiplier is lower than spending multiplier when government spending remains unchanged.

NOTE: To prove the statement, we only need the value of MPC and all other data are redundant.