Find the aggregate expenditure function and equilibrium

Question

Assume the following Keynesian model:

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

C = 750 + .75Y_d

I = 800

G = 200

X = 400

M = 200 + .25Y_d

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. Show that leakages = injections at equilibrium.

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