Question

Assume the following Keynesian model for the economy of Boogerland: AE = C + I + G + (X - M) C = 600 + .9Yd I = 200 G = 100 X = 200 M = 100 + .1Yd T = 100 a. Find the aggregate expenditure function and equilibrium level of GDP. b. Using a “Keynesian cross” (or 45-degree line) diagram, show graphically the equilibrium in part a). c. What is the spending multiplier in this model? Tax multiplier? d. At equilibrium, does the government have a budget surplus or a budget deficit? Of how much? e. Show that leakages = injections at equilibrium. f. If government spending increases by $100, find the new equilibrium level of GDP. Show graphically.

Answer 1

We have the following model

AE = C + I + G + (X - M)

C = 600 + .9Yd I = 200 G = 100 X = 200 M = 100 + .1Yd T = 100

a. Find the aggregate expenditure function and equilibrium level of GDP.

Use AE = Y

600 + 0.9*(Y - 100) + 200 + 100 + (200 - 100 - 0.1*(Y - 100)) = Y

920 + 0.8Y = Y

This is the required equation.

Equilibrium GDP is

Ye = 920/0.2 = 4600

b. Using a “Keynesian cross” (or 45-degree line) diagram, show graphically the equilibrium in part a).

The graph is shown below at point A.

c. What is the spending multiplier in this model? Tax multiplier?

Spending multiplier = 1/MPS + MPM = 1/(1 - 0.9 + 0.1) = 1/0.2 = 5.

Tax multiplier = -MPC/MPS + MPM = -0.9/0.2 = 4.5

d. At equilibrium, does the government have a budget surplus or a budget deficit? Of how much?

G = 100, T = 100. Hence Budget is balanced because G - T = 0.

e. Show that leakages = injections at equilibrium.

National savings = National investment

GDP - C - T + (T - G) = I + (X - M)

4600 - 600 - .9*(4600 - 100) - 100 + 100 - 100 = 200 + 200 - 100 - 0.1*(4600 - 100)

-150 = -150.

f. If government spending increases by $100, find the new equilibrium level of GDP. Show graphically.

Multiplier is 5 and so income is increased by 100*5 = 500. New equilibrium level of GDP = 4600 + 500 = 5100