Suppose the government reduces taxes by 20 billion that ther

Suppose the government reduces taxes by $20 billion, that there is no crowding out, and that the marginal propensity to consume is 3/4.

How does the total affect of this $20 billion tax cut compare to the total effect of a $20 billion increase in governmnet purchases?

Solution

Marginal propensity to consume (MPC) = 3/4 = 0.75

We know that MPC + MPS = 1 i.e. MPC = 1- MPS

Tax Multiplier = Marginal propensity to consume (MPC)/Marginal propensity to save (MPS) = MPC/(1-MPC) = 0.75/(1-0.75) = 0.75/0.25 = 3

Therefore, a $1 tax cut would increase real GDP by $3. So, a $20 billion tax cut would increase real GDP by $20 billion * 3 = $60 billion.

Spending multiplier = 1/MPS = 1/(1-MPC) = 1/(1-0.75) = 1/0.25 = 4

Therefore, a $1 increase spending would increase real GDP $4. So, a $20 billion increase in governmnet purchases would increase the real GDP $20 * 4 = $80 billion.

So, a $20 billion tax cut would increase the real GDP by $60 billion and a $20 billion increase in government purchases would increase the real GDP $80 billion.