Y = C+I+G
Y = 5000
G = 1000
T = 1000
C = 250+0.75(Y-T) = 250+0.75(5000-1000)
C = 3250
I = 1000-50r
a) Private savings = Y --T -- C = 5000-1000-3250 = 750
Public savings = T-G = 1000-1000= 0
National savings = 750+0=750
b) Y = C+I+G
5000= 3250+1000-50r+1000
50r = 5250-5000
50r = 250
r = 5%
d) If G = 1250
Private savings = Y-T-C = 5000-1000-3250 = 750
Public savings = T -G = 1000-1250 = -250
National savings = 750-250 = 500
e) Y = C+I+G
5000 = 3250+1000-50r+1250
5000 = 5500-50r
50r=500
r = 10%
SOLUTION
Y = C + I + G
C = 250 + 0.75(Y - T)
I = 1000 - 50 * r
=> Y = [ 250 + 0.75(Y - T) ] + [ 1000 - 50 * r ] + G
=> Y = 250 + 0.75Y - 0.75T + 1000 - 50 * r + G
=> (Y - 0.75Y) = 1250 - 0.75T - 50 * r + G
=> 0.25 Y = 1250 - 0.75T - 50 * r + G
=> 0.25 * 5000 = 1250 - 0.75 * 1000 - 50 * r + 1000
=> 50 * r = 250
=> r = 5
So,
C = 250 + 0.75(500 - 1000) = 3250
I = 1000 - 50 * 5 = 750
a.
Private saving = Y - C - T = 5000 - 3250 - 1000 = 750 (ANSWER)
Public saving = T - G = 1000 - 1000 = 0
National saving = Private saving + Public saving = 750 = 0 = 750 (ANSWER).
b.
Equilibrium interest rate = 5 % (ANSWER). (As calculated above).
d.
G = 1250.
Private saving = Y - C - T = 5000 - 3250 - 1000 = 750 (ANSWER)
Public saving = T - G = 1000 - 1250 = - 250 (ANSWER)
National saving = 750 + (- 250) = 500 (ANSWER).
e.
I = Y - C - G = 5000 - 3250 - 1250 = 500
I = 1000 - 50 * r
=> 500 = 1000 - 50 * r
=> r = 10 % (ANSWER).
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