Application exercise suppose that the national income in a

Question

Question: Application exercise. Suppose that the national income in a three-sector economy is given by Y = C + I₀ + G₀, where C = C₀ + bY_d, Y_d = Y - T, T = T₀ + tY, C₀,I₀,G₀,T₀ > 0, 0 0, G₀, C₀, Y_d, T, T₀, b, and t denote national income, consumption expenditure, autonomous investment, autonomous government expenditure, autonomous consumption expenditure, disposable income, tax receipts, autonomous tax, MPC, and the fraction of national income collected as taxes, respectively. Assume that I0 = $50, G₀ = $500, C₀ = $100, T₀ = $300, b = 0.80, and t = 0.20.

(i) Find the equilibrium level of income in the economy.

(ii) What should be the change in autonomous investment so that the equilibrium level of income will be $1000?

(iii) What should be the change in autonomous government expenditure so that the equilibrium level of income will be $1100?

(iv) What should be the change in autonomous tax so that the equilibrium level of income will be $1200? All values are in billions.