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