The information given below is relevant to an economy:

C = 20,000 + 0.8Yd

I^P = 15,000

G = 12,000

T = 1,250

X = 30,000

M = 16,000

Y*=250,000

Where C = consumption, Yd = disposable income, I^P = planned investment, G = government spending, T = lump sum tax, X = exports, M = imports, Y*= potential output

Required:

(i) Derive the equation for planned aggregate expenditure (PAE) and calculate the equilibrium level of output.

(ii) Calculate the size of the output gap that the economy faces and use the PAE diagram to illustrate this gap.

(iii) Calculate the spending multiplier of the economy.

(iv) Use your answer to part (ill) to calculate the change in government spending required to close the output gap.

(v) Calculate the tax multiplier of the economy.

(vi) Use your answer to part (v) to calculate the change in tax required to close the output gap.