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?

Answer 1

(a) C = 70 + 0.70YD
I = 90
G = 100
T = 0.10Y
Y = C + I +G
Y = 70 + 0.70YD + 90 + 100
Y = 70 + 0.70YD + 190
Y = 70 + 0.70(Y - T) + 190
Y = 70 + 0.70Y - 0.70T + 190
Y = 70 + 0.70Y - 0.70 × 0.10Y + 190
Y = 70 + 0.70Y - 0.07Y + 190

Y = 70 + 0.63Y + 190
Y = 260 + 0.63Y
Y - 0.63Y = 260
0.37Y = 260

Y = 260/0.37

Y = 702.7

(b) T = 0.10Y

= 0.10 x 702.7

=70.27

Government expenditure = 100
Tax revenue = 70.27
As, G > T, Government has a deficit budget, not a balanced budget.