Question

6. Consider an economy described by the following equations:

Y = C + I + G
Y = 5,000 G = 1,000 T = 1,000
C = 250 + 0.75(Y − T) I = 1,000 − 50 r.
a. In this economy, compute private saving, public saving, and national saving.
b. Find the equilibrium interest rate.
c. Now suppose that G rises to 1,250. Compute private saving, public saving, and national saving.
d. Find the new equilibrium interest rate.

Answer 1

(a) Private saving = Y-T-C

Private saving = 5000-1000-250-0.75(5000-1000)

Private saving = 750

Public saving = T - G

Public saving = 1000-1000

Public saving = 0

National saving = S = private saving+ public saving

National saving = 750

(B) Equilibrium interest rate = S + I

750 = 1000 - 50r

-50r = 750 - 1000

-50r = -250

50r = 250

r = 250/50

r = 5%

(c) Private saving is unchanged

Public saving = 1000 - 1250

Public saving = - 250

(d) The new equilibrium interest rate

750 (-250) = 1000-50r

500 = 1000 - 50r

- 50r = 500 - 1000

- 50r = -500

-50r = 500

r = 500/50

r = 10%