Question

Solve for the short run equilibrium output using the Keynesian Model. Use the fact that Output = Y = 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.

(b) C = Consumption function = 20 + 0.75(Y – T)

T = 0.2Y

G = Government Spending = 50

I = Investment Spending = 20

X = M + 10

(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 

Answer 1

a) At equilibrium

Y = C + I + G + X – M 

Y = 125 + 0.75(Y-100) + 120 + 100

= 345 + 0.75Y – 75

Y = 270 + 0.75Y

0.25Y = 270

Y = 1080

b) At equilibrium

Y = C + I + G + X – M

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) 

Solve for Y first,

S = -100 + 0.2Y

= -90 + 0.2(Y – 50)

= -90 + 0.2(Y – T)

MPS = 1 – MPC,

but MPC = 0.8 and autonomous consumption is 90.

C = 90 + 0.8(Y – T)

At equilibrium, Y = C + I + G + X – M

Y = 90 + 0.8(Y – 50) + 175 + 100 – 125

= 240 + 0.8Y – 40

Y = 200 + 0.8Y

0.2Y = 200

Y = 1000  

Keynesian equilibrium is a balance between aggregate expenditures and aggregate production.