Consider an economy with the following characteristics (in $ billion):

C = 60 + 0.8Yd (where Yd = disposable income)
t = 0.2
I = 40
G = 30
X = 20
M = 10 + 0.14Y

(a) What is the aggregate expenditure function (AE)?
(b) Find the equilibrium GDP using algebra.
(c) Find the equilibrium GDP using graphical method. (If you write your answer, it is advisable to use a graph paper for this question.)
(d) Using the formula for the autonomous expenditure multiplier, compute the open economy multiplier for the above economy.
(e) Suppose that the government increases purchases of goods and services by $20 billion. Using your graph obtained in (c), draw the new AE line and determine the new equilibrium GDP. By how much is equilibrium GDP increased? Based on the result obtained in this part, calculate the value of the multiplier.

Q8.2 Multiplier in the Long Run
Explain why the government expenditure multiplier in the long run is zero.