Assume that GDP (Y) is 6,000. Consumption (C). is given by the equation C = 600 + 0.6(Y - T) - 100r. Investment (I) is given by the equation I = 2,000 - 100r, where r is the real rate of interest in percent. Taxes (T) are 500 and government spending (G) is also 500.
a. Derive the equation for national saving. Is the saving schedule vertical or upward Sloping? What are the equilibrium values of C, I, and r?
b. What are the values of private saving, public saving, and national saving?
c. If government spending rises to 1,000, what are the new equilibrium values of C, I, and r?
d. Illustrate what happens to S, I, and r using the loanable funds framework.
This is the question. The only thing I need help with is part D to illustrate. Not really sure how to do that. below I am adding my answers for a, b and c
1. A. What are the equilibrium values of C, I, and r?
C = 600 + 0.6(Y - T) ⇒ C=600 + 0.6(6000 - 500⇒C=3900 I = 2,000 - 100r T=500 G=500 Y=6000 In Equilibrium: Y= C+I+G 6000 = [600 + 0.6(6000 - 500)]+[ 2,000 - 100r]+500 ⇒ r = 4 r = 4 ⇒ [I = 2,000 - 100r] ⇒ I=1600
b. What are the values of private saving, public saving, and national saving?
National account identity: Y= C+I+G⇒ Y- C - G = I⇒ add (-T +T) ⇒Y- C-T+T- G = I
Private Saving = Y- C-T ⇒ Private Saving =6000-3900-500=1600
Private Saving =1600
Public Saving = T-G ⇒ Public Saving = 500-500 =0
Public Saving = 0
National Saving = Private Saving + Public Saving ⇒ 1600 + 0 = 1600
National Saving= 1600
c. If government spending rises to 1,000, what are the new equilibrium values of C, I, and r?
G' = 1000⇒ C does not change since there is no G in consumption function ⇒ C=3900
In Equilibrium: Y= C+I+G
6000 = [600 + 0.6(6000 - 500)] + [2,000 - 100r] +1000 ⇒ r = 9
r = 9 ⇒ [I = 2,000 - 100r] ⇒ I=1100