Question

Suppose the president would like to stimulate the level of output in the economy, and he succeeds in introducing a tax cut. However, he also would like to keep a balanced budget. Assume a consumption function C = 100 + 0.8(Y-T), and let G=100, T=100, I=100.

a. First, suppose that both government spending and taxes are reduced from 100 to 90. i. Use the relevant Keynesian multipliers to compute the total change in output. ii. Compute the effect on government saving. iii. Will the president be satisfied (i.e. did he get an increase in output and a balanced government budget)?

Answer 1

a. Change in the government spending ($\Delta$G)=—10 , change in the tax ($\Delta$T)= —10

i. From the consumption function, C = 100+0.8(Y—T) MPC= 0.8, or MPS = 0.2 ( MPC+MPS=1) As government expenditures and tax both have been changed simultaneously, so two multipliers will operate together,

Government spending multiplier( $\Delta$ Y/$\Delta$G) = 1/(1—MPC) or, ($\Delta$Y/—10 )= 1/(1—0.8) , or $\Delta$ Y/(—10)=1/0.2 or, $\Delta$ Y= —10×5= —50

So a reduction in government spending by 10 reduces the output by 50

Tax multiplier ( $\Delta$ Y/$\Delta$T)= —MPC/(1‐MPC) or, $\Delta$ Y/—10 = — 0.8 /0.2 0r , $\Delta$ Y= —10×—4 = 40

So, a tax cut of 10 ,increases the output by 40

Thus as a joint effect of reducing government spending and tax by 10 reduces the output by (50 —40) 10.

ii. Previous government savings =T—G=100—100=0

Government savings after reducing government spending and tax = T—G =0

So ,there is not any effect on the government savings, as the budget remains balanced.

iii. No ,the government will not be satisfied, because this policy reduced output by 10 in the economy, which may decrease employment.