We suppose that C = 70 + 0.70Y, 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?
Equilibrium income Y 703
Tax revenues at equilibrium income = ₹70.27 (approximately). No, the government does not have a balanced budget. Since Government expenditure (G = 100) exceeds Tax revenue (T 70.27), the government has a budget deficit.
Explanation
The question involves proportional taxes (T = 0.10Y) rather than lump-sum taxes. The consumption function C = 70 + 0.70Y should be interpreted as C = 70 + 0.70YD where YD is disposable income. Since T = 0.10Y, disposable income YD = Y - T = Y - 0.10Y = 0.90Y. Therefore, C = 70 + 0.70(0.90Y) = 70 + 0.63Y. Using the equilibrium condition Y = C + I + G, we solve for Y. The context provides the formula for lump-sum taxes, but for proportional taxes, we must adjust the approach as shown in the solution.