Question

All else equal, how would an increase in the tax rate affect the government purchases multiplier?

A. It increases the multiplier only if the marginal propensity to consume if the MPC is greater than the tax rate.

B. It has no effect.

C. It increases the multiplier only if the marginal propensity to consume (MPC) is less than the tax rate.

D. It increases the government purchases multiplier.

E. It decreases the government purchases multiplier.

Answer 1

Government spending multiplier = 1 / (1 - MPC (1-t))

Where t is the tax rate.

Example: Now suppose MPC = 0.5 and t = 0.6

Government spending multiplier = 1 / (1 -0.5 (1-0.6))

Government spending multiplier = 1 / (1 - 0.5(0.4))

Government spending multiplier = 1 / (1 -0.2)

Government spending multiplier = 1 / 0.8

Governmnet spending multiplier = 1.25

Now assume tax rate increases to 0.7

Government spending multiplier = 1 / (1 -0.5 (1-0.7))

Government spending multiplier = 1 / (1 - 0.5(0.3)

Government spending multiplier = 1 / (1 -0.15)

Government spending multiplier = 1 / 0.85

Governmnet spending multiplier = 1.17

We can see that increase in tax rate from 0.6 to 0.7 leads to a decrease in government spending multiplier from 1.25 to 1.17.

Note: It doesn't matter whether MPC is higher than or lower than the tax rate. An increase in tax rate will decrease the government spending multiplier in both cases.

Answer: Option (E) i.e. it decreases the government spending multiplier.