Question

Suppose that instead of financing its spending by borrowing money, the government raised taxes to pay for the increase in spending. If the size of the recessionary gap is $200,000 and the MPC is .9, by how much would the government need to increase tax to have enough money to close the gap? Hint: you need to calculate the increase in government spending needed first and then keep in mind that the increase in tax decreases consumer spending. The goal is to increase GDP by $200,000.

Answer 1

Government should increase tax by 200000

When government purchases increase, the total income increases.

ΔY/ ΔG is the government-purchases multiplier, which measures how much the income changes ( ΔY) when government purchases change ( ΔG).

Equation: ΔY = ΔG*1/(1-MPC).

So, an increase in government purchases of ΔG increases the income by ΔG/(1-MPC).

There is a similar multiplier for taxes.

ΔY = -(MPC* ΔT)/(1-MPC)

The equation is different because taxes directly affect consumption, unlike government spending, which first increases income, which then increases consumption. Spending $1 on government purchases increases income by $1 before the multiplier effects. Raising taxes by $1 decreases income by less than $1 depending on how much consumers save before the multiplier effects. So, an equal increase in government spending and taxes actually raises income and thus aggregate demand increases.

Mathematically:

Add the two multiplier effects

ΔY = [ ΔG*1/(1 - MPC)] + [-(MPC* ΔT)*1/(1-MPC)]

Assume  ΔG = ΔT

ΔY = ΔG*[(1/(1-MPC)) - (MPC/(1-MPC))]

ΔY = ΔG

So income increases by amount of government purchases, which is positive, increasing aggregate demand.

So if the the government raised taxes to pay for the increase in spending. Government should increase G and taxes (T) both by $200,000