Answer:
Planned Aggregate Expenditure equals 290 + 0.75Y and the short run equilibrium output equals 1,160.
Explanation:
Autonomous spending basically covers essential needs, e.g. housing expenses, food, clothing, etc., and is not affected by the marginal propensity to consume (MPC).
so consumption must equal: C = 100 + 0.75 (Y income - 40 taxes)
PAE = C + I + G + X = 100 + 0.75(Y - 40) + 50 + 150 + 20
PAE = 100 + 0.75Y - 30 + 50 + 150 + 20 = 290 + 0.75Y
Short run equilibrium exists when Y = PAE:
Y = 290 + 0.75Y
Y - 0.75Y = 290
0.25Y = 290
Y = 290 / 0.25 = 1,160