Question

Equilibrium in the Classical model: Consider an economy described by the following equations:

Y = C + I + G

Y = 12,000

G = 2,000

T = 2,000

C = 500 + 0.75*(Y – T)

I = 2,400 – 80*r

a) In this economy, compute private saving, public saving, and national saving.

b) Find the equilibrium real interest rate r.

c) Now suppose that G rises to 1,200. Compute private saving, public saving, and national saving in this case.

d) Find the new equilibrium real interest rate.

Answer 1

a) In this economy, compute private saving, public saving, and national saving.

Private saving = Y - T - C = 12000 - 2000 - 500 - 0.75*(12000 – 2000) = 2000

Public saving = T - G = 2000 - 2000 = 0

National saving = Public saving + private saving = 2000

b) Find the equilibrium real interest rate r.

Y = C + I + G

12000 = 500 + 0.75*(12000 – 2000) + 2400 – 80*r + 2000

12000 - 12400 = -80r

Equilibrium interest rate = 400/80 = 5%

c) Now suppose that G rises to 1,200. Compute private saving, public saving, and national saving in this case.

When G is increased by 1200, income does no rise in Classical case so Y is 12000.

Private saving = Y - T - C = 12000 - 2000 - 500 - 0.75*(12000 – 2000) = 2000

Public saving = T - G = 2000 - 3200 = -1200

National saving = 2000 - 1200 = 800

d) Find the new equilibrium real interest rate.

12000 = 500 + 0.75*(12000 – 2000) + 2400 – 80*r + 3200

12000 - 13600 = 80r

Equilibrium interest rate rises to = 1600/80 = 20%