You are given the following information on the macroeconomy (in millions dollars):
Consumption: 250 + 0.50Y
Investment: 100 + 0.10Y
Government Spending 400
Exports 50
Imports 50 + 0.25Y
Compute the equilibrium level of income, the size of the multiplier, and the change in equilibrium income for a decrease in autonomous investment of $75 million.
Y = E
Y = C + I + G + X - M
Y = 250 + 0.50Y + 100 + 0.10Y + 400 + 50 - (50 + 0.25Y)
Y = 750 + 0.35Y
Y - 0.35Y = 750
(1 - 0.35 )Y = 750
Y = 750/(1 - 0.35 )
Y = 1155
Multiplier: 1/(1 - 0.35 ) = 1.54
Change in Equilibrium Income: ?Y = ?I × multiplier = -75 × 1.54 = -115.5
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