Question

1. Let j be 0. Suppose that the government increases expenditures by $100 × (1 + 0.01j) billion while increasing taxes by $100 × (1 − 0.01j) billion. Suppose that the MPC is 0.7 × (1 + 0.01j) and that there is no crowding out effect. What is the combined effects of these changes? Why is the combined change not equal to zero? 

Answer 1

Multipliers are used to measure the total economic effect of various policies. The government spending multiplier indicates the changes in aggregate demand from a given change in government spending. Tax multiplier gives the change in aggregate demand from the change in tax. The government spending multiplier and tax multiplier are calculated as,

Government spending multiplier$=\frac{1}{1-MPC}$

Tax multiplier$=\frac{-MPC}{1-MPC}$

where MPC is the marginal propensity to consume. Substituting the value of MPC will give the values of government expenditure multiplier and tax multiplier. Since the value of j is given as 0, the change in tax and government spending is $100 billion and the MPC is 0.7

Government spending multiplier$=\frac{1}{1-0.7}=3.33$

Tax multiplier$=\frac{-0.7}{1-0.7}=-2.33$

The change in aggregate demand due to an increase in government spending is the product of the government spending multiplier and the change in aggregate demand due to an increase in tax is the product of the tax multiplier and the increase in tax. The net change in the sum of the change in aggregate demand.

Change in aggregate demand due to change in government spending= government spending $\times$ change in spending

$=3.33\times\$100\space billion\\=\$333\space billion$

Change in aggregate demand due to change in tax= tax multiplier $\times$ change in tax

$=-2.33\times \$100\space billion\\=\$233 \space billion$

Net change$=\$333\space billion-\$233 \space billion=\$100\space billion$

Therefore the net change is $100 billion.

When the government spending and tax increase by the same amount, the output will increase by the same amount. This is because the balanced budget multiplier is equal to one. Adding government expenditure multiplier and tax multiplier will give a value of one irrespective of the value of MPC.

Tax multipler+ Government spending multiplier$=\frac{MPC}{1-MPC}+\frac{1}{1-MPC}$

$=\frac{1-MPC}{1-MPC}\\=1$