Question

Part C The following equations characterize an open economy in billions of dollars. C = 100 + .6 (Y – T) T = 40 I = 48 G = 64 X = 76 M = 20 + .15Y (k) Suppose the full employment level of real GDP is $480. Does a recessionary gap or an inflationary gap exist? How can the government eliminate the gap by altering government expenditures? How can the government eliminate the gap by altering taxes? Note: State the amount and direction (increase or decrease) of taxes or government expenditure needed to eliminate the gap. 2½ marks

Answer 1

C = 100 + 0.6 (Y – T)

MPC= 0.6

T = 40

I = 48

G = 64

X = 76

M = 20 +0.15Y

MPM= 0.15

Full employment GDP=Y*= $480

K)

Current GDP:

Y= C+I+G+X-M

Y= 100+0.6(Y-40)+48+64+76-20-0.15Y

Y= 268+0.6Y-24-0.15Y

Y-0.6Y+0.15Y = 244

0.55Y = 244

Y= 244/0.55= 443.64 Current GDP

Here as Current GDP < Full employment GDP which means there is a recessionary gap exist.

To correct this situation, government should raise its expenditure.

Amount by which government should increase its expenditure depends on government spending multiplier.

Government spending multiplier= 1/(1-MPC+MPM)

Change in Y / Change in Government spending= 1/(1-0.6+0.15)

(480-443.64)/ Change in Government spending= 1/0.55

36.36/0.55= Change in Government spending

Change in Government spending= 66.11

Government should increase its expenditure by 66.11

To calculate the amount by which government should reduce the tax to increase the amount GDP depends on the tax multiplier.

Tax multiplier= -MPC/(1-MPC+MPM)

Change in Y/Change in T= -0.6/0.55

36.36/Change in T= -1.09

Change in T= 36.36/(-1.09)= 33.36

Government should reduce the tax by 33.36 to achieve full employment Y.