C =100+2/3(Y-T), I = 200.
a.if y is 1500, what are planned aggregate expenditures? what is inventory accumulation or deaccumulation? should equilibrium Y be higher or lower than 1500?(equilibrium; hint; planned expenditure=Y, and inventory =Y-planned expenditure)
If Y is 1500, planned spending equals:
PE = C+I+G = 200+ 2/3(Y-T)+300+300 = 800 + 2/3(1500 - 300) = 800+2/3(1200) = 800+800 = 1600
So, at Y=1500, planned spending is 1600.
Since at Y=1500, planned spending (1600) is higher than current output, there will be unplanned inventory decumulation.
The amount of inventory decumulation = (PE-Y) = (1600-1500) = 100.
At Y=1500, firms meet the excess demand by supplying goods from their inventories, resulting into an unplanned reduction in their stock of goods. Firms would respond to this decline in inventories by producing more goods. So, the equilibrium Y must be higher than 1500.
b. what is the planned expenditure function? what is equilibrium level of income?
The planned expenditure function PE = C+I+G =200+2/3(Y-T)+300+300 = 800 + 2/3(Y-300) = 800 +2/3Y -200 = 600 + 2/3Y
So, the planned expenditure function, PE, is 600 +2/3Y
If Y is 0, PE = 600. So, the vertical intercept (PE-intercept) of the expenditure function is 600.
The equilibrium condition:
Y = PE
Y = 600 +2/3Y
Y-2/3Y = 600
1/3Y = 600
Y = 1800
So, equilibrium level of income is 1800.
c. what are equilibrium consumption,private saving, public saving, and national saving? hint:private saving=Y-C-T, public saving=T-G
The equilibrium consumption, C = 200 + 2/3(Y-T) = 200 + 2/3 (1800-300) =200 + 2/3(1500) = 1200
So, the equilibrium consumption is 1200.
The equilibrium private saving, SP = Y-C-T = 1800-1200-300 = 300
So, the equilibrium private saving is 300.
The equilibrium public saving, SG = T-G = 300–300 = 0
So, the equilibrium public saving is 0.
The equilibrium national saving, S = Y-C-T = 1800-1200-300 = 300
So, the equilibrium national saving is 300.
d. how much does equilibrium income decrease when G is reduced to 50? what is the multiplier for government spending?
The government spending multiplier = 1/(1-MPC) = 1/(1-2/3) =1/(1/3) = 3
So, the government spending multiplier is 3. We can use this multiplier to find the change in the equilibrium income.
Change in equilibrium income = Government spending multiplier * Change in G = 3* (-100) =-300.
So, the equilibrium income decreases by 300 when G is reduced to 200.