Question

The model with exogenous taxes (T=T̅) has a multiplier on investment of 1/(1-mpc). The model with proportional taxes (T=tY) has a multiplier on investment of 1/(1-mpc(1-t)). Explain in words why they differ.

Answer 1

When taxes are exogenous, there is only a lumpsum deduction of taxes from the income, therefore tax doesn't affect the multiplier, on the other hand, when taxes are proportional, the taxes are deducted for every extra rupee that is earned.

In case of exogenous tax, disposable income is Y-t while in case of proportional taxes, disposable income would be Y(1-t). This would imply that for every extra rupee that is earned due to increase in investment , a certain portion is taxed away, therefore the consumption will not increase as much as it would otherwise. Hence the process of income generation will slow down.

Hence, in case of exogenous taxation, the multiplier will be 1/(1-mpc) and whereas in case of proportional taxation, since income is taxed for every marginal increase , the multiplier is lesser than the previous case. Since disposable income rises by only (1 – t) times the increase in I and since b times the change in disposable income is respent on consumption, the proportion b(1 -t), instead of b will be respent on consumption, b being the mpc And therefore the multiplier will be 1/{1-mpc(1-t)}.