Question #42837

question
consider a closed economy to which the keynesian-cross analysis applies.
consumption is given by the equation C =100+2/3(Y-T),where Y represents income and T represents taxes. planned investment is 200 a are government spending and taxes.
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)
b. what is the planned expenditure function? what is equilibrium level of income ?
show your results in diagram clearly indicating the intercepts and equilibrium values.
c. what are equilibrium consumption, private saving, public saving, and national saving?hint:private saving=Y-C-T
public saving=T-G
equilibrium saving=Y-C-T
d. how much does equilibrium income decrease when G is reduced to 50?
what is the multiplier for government spending?

Expert's answer

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.

equilibrium saving=Y-C-T

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.

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.

equilibrium saving=Y-C-T

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.

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