Question

An industrial system has two industries with the following input requirements.

(a) To produce $1.00 worth of output, Industry A requires $0.30 of its own product and $0.40 of Industry B's product.

(b) To produce $1.00 worth of output, Industry B requires $0.40 of its own product and $0.10 of Industry A's product.

An industrial system has two industries with the following input requirements. (a) To produce $1.00 worth of output, Industry A requires $0.30 of its own product and $0.40 of Industry B's product. (b) To produce $1.00 worth of output, Industry B requires $0.40 of its own product and $0.10 of Industry A's product. Find D, the input-output matrix for this system. A A D = B 10,000 Solve for the output matrix X in the equation X = DX + E, where is the external demand matrix E = (Round to the nearest whole number.) 20,000 x = B

Answer 1

O of A's B Given : To produce $1.00 worth of output, industry A requiree $0.30 product duct- & $0.40 of industry to los product. To produce $1.00 worth of output, industry requires $0.00 of B's product & a 10.10 of Ab product Approach for given inductries. Since there are 2 industries, We have to forum input-output materin matain will be 2x 2, A BAA DAB A Given by Da 1: DBA DBB j DAB A from given information DAA = 0.3 product red required to produce B's output worth $1.00 - 0.10 DBA = B's product required to produce A's output worth $1.00 . DBB = 0.40 0.40 B А 0.3 0.10 А D = Dom 0.40 0.40 B 3 X = ? Ez 10,000 20, ooo (6) X = DX + E Rearranging above equation I X- D X = E >> x (I-D) - E x = (1-D14E matrin Is identity 1 0.16 07 -0.1 은 ID 2 [603-10 [* 0.4 0.4 -0.4 0.6

[1-D342 0-6 0.1 ; ] 0.4 0.7 x = 0.6 8000 [os 10,000 20,ooo 0.4 0.7 1 lis 18000 А 8000 10000 B