Question

Consider the following closed economy:

C=40+0.9 x Y^D.
I=1400
G=1500
TR=40
T=0.3 x Y

If there is a 90 increase in autonomous government expenditures, what is the change in government savings (assuming no change in the price level)?

The correct answer is -17.03. However, I am not getting that. The answer is not 243.23 and other work (that I tried):

Mpc=0.9[(1-0.3Y)+ Tr]

=0.63Y

1/ (1-0.63) = 2.7

2.7 X 0.63 = 1.7.  

Thanks

Answer 1

Equilibrium is given by

Y = C + I + G

Y = 40 + 0.9Yd + 1400 + 1500

Y = 2940 + 0.9(Y - T + TR)

Y = 2940 + 0.9(Y - 0.3Y + 40)  

Y = 2940 + 0.9(0.7Y + 40)

Y = 2940 + 0.63Y + 36

Y = 2976 + 0.63Y

Y - 0.63Y = 2976

0.37Y = 2976

Y = 8043.24

T = 0.3Y

T = 0.3(8043.24)

T = 2412.97

Government savings = T - G - TR

= 2412.97 - 1500 - 40

= 872.97

Now government expenditure increases by 90 so new level of G is 1500 + 90 = 1590

New equilibrium income

Y = C + I + G

Y = 40 + 0.9YD + 1400 + 1590

Y = 3030 + 0.9(Y - T + TR)

Y = 3030 + 0.9(Y - 0.3Y + 40)

Y = 3030 + 0.9(0.7Y + 40)

Y = 3030 + 0.63Y + 36

Y - 0.63Y = 3066

0.37Y = 3066

Y = 8286.48

T = 0.3Y

T = 0.3(8286.48)

T = 2485.94

Government savings = T - G - TR

= 2485.94 - 1590 - 40

= 855.94

Change in government savings = 855.94 - 872.97

= - 17.03