Problem 3. (10 pts.) Input-Output (a) (4 pta.) Derive the formula for the production vector X from the relationship X - AX + D (show each step in isolating the matrix X). XSAYID X - Ax - D (I-A)X - D X- (I- A ) D (b) (2 pts.) Let A be the technology matrix A = 0.3 0.06 0.5 0.01 where sector ] is paper and sector 2 is wood. Then we know 10.06 units of wood are needed to produce one unit of paper. () units of paper are used in the production of one unit of paper. (c) (4 pta.) Suppose a recycling plant has three sectors: metal, paper, and glass. . 500 units of metal, 250 units of paper, and 1,000 units of glass are used to produce 2,000 units of metal. . 4 units of metal, 400 units of paper, and 80 units of glass are used to produce 1,600 units of paper. . 300 units from metal, 10 units from paper, and 1,800 units from glass are used to make 9,000 units of glass. Set up the input-output table for this economy. 410 m 9 M 500 360 P 250 10 1600 2050 900 0