You are given the following information on the macroeconomy: Consumpt

You are given the following information on the macroeconomy:

Consumption: 200 + 0.75Y
Investment: 100 + 0.10Y
Government Spending 500
Exports 100
Imports 50 + 0.25Y

Compute the equilibrium level of income, the size of the multiplier, and the change in equilibrium income for an increase in autonomous consumption of $50 million.

ANSWER

Y = E
Y = C + I + G + X – M
Y = 200 + 0.75Y + 100 + 0.10Y + 500 + 100 – (50 + 0.25Y)
Y = 850 + 0.60Y
Y – 0.60Y = 850
(1 – 0.60)Y = 850
Y = 850/(1 – 0.60 )
Y = 2125

Multiplier: 1/(1 – 0.60 ) = 2.5
Change in Equilibrium Income: ΔY = ΔC × multiplier = 50 × 2.5 = 125