6) Consider a closed economy described by the following equations:

(1) Y = C + I + G

(2) Y = 5(K)0.5(L)0.5

(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?