Question

Please, show work.

4. Solve for the equilibrium level of GDP if the same economy taxed the public for $35:
a = 100
b = .75
Ig= 50
G = 50
T = 35
EX = 20
IM = 30


5. Solve for the equilibrium level of GDP if government cuts taxes by $10 in the economy:
a = 100
b = .75
Ig= 50
G = 50
T = 35 - 10
EX = 20
IM = 30



6. What was the spending multiplier in the above economy (show the work)

Answer 1

4)

At equilibrium Aggregate Expenditure(AE) = Y(GDP)

AE = C + I_g + G + EX - IM

C = Consumption = a + b(Y - T) where b = MPC and a = Autonomous consumption.

AT equilibrium Y = AE

=> Y = C + I_g + G + EX - IM = a + b(Y - T) + I_g + G + EX - IM

=> Y = 100 + 0.75(Y - 35) + 50 + 50 +20 - 30

=> Y(1 - 0.75) = 163.75

=> Y = 655

hence Equilibrium level of GDP = 655

5)

At equilibrium Aggregate Expenditure(AE) = Y(GDP)

AE = C + I_g + G + EX - IM

C = Consumption = a + b(Y - T) where b = MPC and a = Autonomous consumption.

AT equilibrium Y = AE

=> Y = C + I_g + G + EX - IM = a + b(Y - T) + I_g + G + EX - IM

=> Y = 100 + 0.75(Y - 25) + 50 + 50 +20 - 30

=> Y(1 - 0.75) = 171.25

=> Y = 685

hence Equilibrium level of GDP = 685

(6)

Y = C + I_g + G + EX - IM = a + b(Y - T) + I_g + G + EX - IM

=> Y = [1/(1 - b)][ a - bT + I_g + G + EX - IM]

a - bT + I_g + G + EX - IM = Autonomous spending = A

=> Y = [1/(1 - b)][A]

Hence $1 increase in Autonomous spending will result in 1/(1 - b) increase in Real GDP

Hence Spending multiplier = 1/(1 - b) = 1/(1 - 0.75) = 4

Hence Spending multiplier = 4