Given the following macroeconomic equations that describe a certain economy:
C=100+0.8Y^d - Consumption function
I=10+10r - Investment function
G=10 - Government purchases
T=0.25 - Tax rate
L=Y-100r - Real money demand
M=295 - Real money supply
You are Required to Calculate the IS and LM equations.
Answers
Answer:
= C + I + G + X – M in equilibrium.
(a) C = Consumption function = 125 + 0.75(Y-T)
T = Net Taxes = 100
G = Government Spending = 100
I = Investment Spending = 120
Closed economy
Y = C + I + G + X – M in equilibrium
Y = 125 + 0.75(Y-100) + 120 + 100 = 345 + 0.75Y – 75
Y = 270 + 0.75Y
0.25Y = 270
Y = 1080
(b) C = Consumption function = 20 + 0.75(Y – T)
T = 0.2Y
G = Government Spending = 50
I = Investment Spending = 20
X = M + 10
Y = C + I + G + X – M in equilibrium
Y = 20 + 0.75(Y – 0.2Y) + 20 + 50 + 10 = 100 + 0.75(0.8Y)
Y = 100 + 0.6Y
0.4Y = 100
Y = 250
(c) S = Savings function w/ respect to output = -100 + 0.2Y
T = Net Taxes = 50
G = Government Spending = 100
I = Investment Spending = 175
M – X = 125
Solve for Y first, we know S = -100 + 0.2Y = -90 + 0.2(Y – 50) = -90 + 0.2(Y – T)
Using the relationship that MPS = 1 – MPC, we know MPC = 0.8 and autonomous consumption is
90.
C = 90 + 0.8(Y – T)
Y = C + I + G + X – M in equilibrium
Y = 90 + 0.8(Y – 50) + 175 + 100 – 125 = 240 + 0.8Y – 40