Given the following model: Consumption: C = 500 + 0.5Yd Investment: I = 250 Government Expenditure: G = 100 Proportional Tax Rate: t = 0.1 Imports: M = 0.25Y Exports: X = 50 Yd: Disposal Income Y: Real GDP (Note: There is no lump-sum tax) Given the following model: Consumption: C = 500 + 0.5Yd Investment: I = 250 Government Expenditure: G = 100 Proportional Tax Rate: t = 0.1 Imports: M = 0.25Y Exports: X = 50 Yd: Disposal Income Y: Real GDP (Note: There is no lump-sum tax) a) If the current level of output is 1000, what is the level of actual investment?

This is the answer that I have been given - but where does the 50 come from for planned investment ?

AE = C + I + G + X - M

= 500 + 0.5(Y - 0.1Y) + 250 + 100 + 50 - 0.25Y [Since Yd = Y - T = Y - tY]

= 900 + 0.5 x 0.9Y - 0.25Y

= 900 + 0.45Y - 0.25Y

= 900 + 0.2Y

In equilibrium, Y = AE.

Y = 900 + 0.2Y

0.8Y = 900

Y = 1125

Explanation:

a)

AE = C + I + G + X - M

= 500 + 0.5(Y - 0.1Y) + 250 + 100 + 50 - 0.25Y [Since Yd = Y - T = Y - tY]

= 900 + 0.5 x 0.9Y - 0.25Y

= 900 + 0.45Y - 0.25Y

= 900 + 0.2Y

In equilibrium, Y = AE.

Y = 900 + 0.2Y

0.8Y = 900

Y = 1125

Since current output is less by 125 (= 1125 - 1000),

Actual investment = Planned investment - 125 = 50 - 125 = - 75

Therefore actual investment =-75