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 =

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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