Question

6) Consider a closed economy described by the following equations: (1) Y=C+I+G (2) Y = 5(K)S(L)05 (3) K = 1600 (4) L = 1600 (5) G = 2500 (6) T = 2000 (7) C = 1000 + 2/3 (Y-T) (8) I= 1200 - 100r, where r is the real interest rate. a) What is the equilibrium level of income? Show your work. b) Solve for the equilibrium interest rate (r) and the level of investment (I). The interest rate will be a whole number. c) Suppose G increases by 500 to 3000. i.) What happens to Y? And, why? ii.) Solve for the new equilibrium interest rate. iii.) What happens to I? And, why?

Answer 1

(a)

Y = 5 x (1600)^0.5 x (1600)^0.5 = 5 x 1600 = 8000

(b)

In equilibrium, Y = C + I + G

8000 = 1000 + (2/3 x (8000 - 2000) + 1200 - 100r + 2500

8000 = 4700 + (2/3) x 6000 - 100r

3300 = 4000 - 100r

100r = 700

r = 7

I = 1200 - 100 x 7 = 1200 - 700 = 500

(c)

(i) Y depends only on L and K and not on G, so Y remains unchanged.

(ii) When G = 3000,

8000 = 1000 + (2/3 x (8000 - 2000) + 1200 - 100r + 3000

8000 = 5200 + (2/3) x 6000 - 100r

2800 = 4000 - 100r

100r = 1200

r = 12

(iii) When r = 12,

I = 1200 - 100 x 12 = 1200 - 1200 = 0

It means that the increase in interest rate due to increase in G completely crowded out private investment.