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.
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: ?Y = ?C × multiplier = 50 × 2.5 = 125
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