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Question
We suppose that C = 70 + 0.70Y D, I = 90, G = 100, T = 0.10Y (a) Find the equilibrium income. (b) What are tax revenues at equilibrium Income? Does the government have a balanced budget?
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Solution
(a) C = 70 + 0.70 YD
I = 90
G = 100
T = 0.10Y
Y = C + I +G
Y = 70 + 0.70Y + 90 + 100
Y = 70 + 0.70YD + 190
Y = 70 + 0.70 (Y − T) + 190
Y = 70 + 0.70Y − 0.70 × 0.10 Y + 190
Y = 70 + 0.70Y − 0.07Y + 190
Y = 70 + 0.63Y + 190
Y = 260 + 0.63Y
Y − 0.634 = 260
0.37Y = 260
`Y = 260/0.37`
Y = 702.7
(b) T = 0.10Y
= 0.10 × 702.7
= 70.27
Government expenditure = 100
Tax revenue = 70.27
As, G > T, Government has a deficit budget, not a balanced budget.
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