3. Consider the following information on a 4-sector ("private-public-open") economy, where Y stands for the GDP and Ca, lg, and Xn are respectively consumption after tax, autonomous investment and next exports. Ca = 40 +0.80 (Y-T) lg = 30 Xn= 10 T=20 G=20 DI-Y-T (a) Use the information above to solve for equilibrium value of GDP (Y), DI, Ca, Sa, and APC, and APS. Show all your calculations. (b) Show the 4-sector equilibrium GDP graphically. (c) What is autonomous consumption, MPC, MPS, and the multipliers for G and T in this economy? (d) If GDP =520, what would be AEa? Will there be unplanned inventory investment or disinvestment? Will GDP increase or decrease? Why? Explain. (e) At GDP-520, what would be planned investment? actual investment? A Go (1) GDP 100 200 300 400 500 600 700 (2) C 120 200 280 360 440 520 (3) Ig 30 30 30 30 30 30 600 30 (4) Xn 10 10 10 10 10 10 10 (5) G 100 100 100 (6) T 100 100 100 100 100 100 100 100 100 100 100 (7) Ca (8) AEa (4-Sector)