Question #46601

you are provided with the following:
Marginal propensity to save (MPS) =0.2
Tax rate (t) =0.2
Autonomous saving=-50
investment spending (I) =100
Government expenditure (G) =150
exports(X) =120
autonomous imports=30
marginal propensity to import (m)= 0.15
Answer the following question:
(a) derive the consumption equation from the information given.
(b) calculate the equilibrium level of income using the AD=AS approach.
(c) calculate the equilibrium level of income using the injection = withdrawals (J=W) approach.
(d) calculate the fiscal surplus (or deficit) at the equilibrium level of income.
(e) calculate the value of net export at the equilibrium level of income.
(f) what would the level of income have to be net exports are zero?
(g) what is the value of the multiplier in an economy:
i. consisting only of households and businesses (no government or foreign sectors)
ii. consisting of households, businesses and the government (but no foreign sector)
iii consisting of both C,I,G and foreign sector

Expert's answer

Marginal propensity to save (MPS) =0.2

Tax rate (t) =0.2

Autonomous saving=-50

investment spending (I) =100

Government expenditure (G) =150

exports(X) =120

autonomous imports=30

marginal propensity to import (im)= 0.15

(a) Consumption equation will be: C = autonomous consumption + c*Y = autonomous consumption + (1 - 0.2)*Y = autonomous consumption + 0.8Y

(b) The equilibrium level of income using the AD=AS approach is in the point, where S = I, so:

-50 + 0.2Y = 100

Y = 750, S = 100

(c) The equilibrium level of income using the injection = withdrawals (J=W) approach will be:

I + G + X = S + T + M

100 + 150 + 120 = (-50 + 0.2Y) + 0.2Y + (30 + 0.15Y)

370 = 0.55Y - 20

Y = 709

(d) fiscal surplus (deficit) = T - G = 0.2*709 - 150 = -8.2, so there is a deficit.

(e) net export at the equilibrium level of income will be NX = X - M = 120 - (30 + 0.15*709) = -16.35

(f) The level of income should be:

120 - (30 + 0.15Y) = 0

0.15Y = 90

Y = 600

(g) what is the value of the multiplier in an economy:

i. consisting only of households and businesses (no government or foreign sectors)

m = 1/(1 - c) = 1/s = 1/0.2 = 5

ii. consisting of households, businesses and the government (but no foreign sector)

m = 1/(1 - (1-t)(1-s)) = 1/(1 - 0.8*0.8) = 2.78

iii consisting of both C,I,G and foreign sector

m = 1/(1 - (1-t)(1-s - im)) = 1/(1 - 0.8*0.65) = 2.08

Tax rate (t) =0.2

Autonomous saving=-50

investment spending (I) =100

Government expenditure (G) =150

exports(X) =120

autonomous imports=30

marginal propensity to import (im)= 0.15

(a) Consumption equation will be: C = autonomous consumption + c*Y = autonomous consumption + (1 - 0.2)*Y = autonomous consumption + 0.8Y

(b) The equilibrium level of income using the AD=AS approach is in the point, where S = I, so:

-50 + 0.2Y = 100

Y = 750, S = 100

(c) The equilibrium level of income using the injection = withdrawals (J=W) approach will be:

I + G + X = S + T + M

100 + 150 + 120 = (-50 + 0.2Y) + 0.2Y + (30 + 0.15Y)

370 = 0.55Y - 20

Y = 709

(d) fiscal surplus (deficit) = T - G = 0.2*709 - 150 = -8.2, so there is a deficit.

(e) net export at the equilibrium level of income will be NX = X - M = 120 - (30 + 0.15*709) = -16.35

(f) The level of income should be:

120 - (30 + 0.15Y) = 0

0.15Y = 90

Y = 600

(g) what is the value of the multiplier in an economy:

i. consisting only of households and businesses (no government or foreign sectors)

m = 1/(1 - c) = 1/s = 1/0.2 = 5

ii. consisting of households, businesses and the government (but no foreign sector)

m = 1/(1 - (1-t)(1-s)) = 1/(1 - 0.8*0.8) = 2.78

iii consisting of both C,I,G and foreign sector

m = 1/(1 - (1-t)(1-s - im)) = 1/(1 - 0.8*0.65) = 2.08

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