Question

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. In this economy, compute private savings, public savings, and national savings.

Solution

National Savings = Y – C – G = 5000 – (250 + .75(5000-1000)) – 1000 = 750

Private Savings = Y – T – C = 5000 –1000 – (250 + .75(5000-1000)) = 750

Public Savings = T – G = 1000 – 1000 = 0.

b. Find the equilibrium interest rate (r).

Solution

750 = 1000 – 50r thus 50r = 250 and r =5.

c. Now suppose that G rises to 1,250. Compute private, public, and national savings.

Solution

National Savings = Y – C – G = 5000 – (250 + .75(5000-1000)) – 1250 = 500

Private Savings = Y – T – C = 5000 –1000 – (250 + .75(5000-1000)) = 750

Public Savings = T – G = 1000 – 1250 = -250.

d. What is the new equilibrium interest rate?

Solution

500 = 1000 – 50r thus r = 10.