a. E = C + I + G = 200 + 2/3(1500 - 300) + 300 + 300 = 1600

E - Y = 1600 - 1500 = 100 = Inventory Decumulation

Equilibrium Y should be higher whenever there is Inventory Decumulation, i.e., whenever E > Y

b. Condition for Equilibrium is Y = E = C + I + G

Y = 200 + 2/3(Y - 300) + 300 + 300

Y = 200 + 2/3Y - 2/3(300) + 600

Y = 200 + 2/3Y - 200 + 600

Y - 2/3 Y = 600

1/3Y = 600

Y = 1800

c. Equilibrium C = 200 + 2/3(1800 - 300) = 200 + 2/3(1500) = 200 + 1000 = 1200

Private S = Y - T - C = 1800 - 300 - 1200 = 300

Public S = T - G = 300 - 300 = 0

National S = Private S + Public S = 300 + 0 = 300

d. Y = E = C + I + G = 200 + 2/3(Y - 300) + 300 + 200

Y = 200 + 2/3Y - 2/3(300) + 500

Y = 200 + 2/3Y - 200 + 500

Y - 2/3 Y = 500

1/3Y = 500

Y = 1500

So equilibrium Y decreases by 300 when G is reduced to 200.

Multiplier for government spending = change in Y / change in G = (1500 - 1800)/(200 - 300) = -300 / -100 = 3