INPUT OUTPUT ANALYSIS.

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Input-Output Analysis. 1. According to the postulate of Leontieff, the value rij of goods shipped from the ith sector of the economy to the jth sector is proportional to the activity level a; of the latter: Cy = aye,. Also, the activity level of the ith sector is reckoned as the sum of (the values of ) the output, Tri, consumed within that sector, the goods, ri;j = 1, ... .n, shipped to other sectors, and the goods, y, consumed in final demand. Imagine a closed economy of three sectors which is characterised by the following activity levels and trade flows: 100 E11 E13 10 30 10 50 200 T23 30 50 20 1/2 100 100 E31 132 C33 10 20 20 50 Construct the complete input-output table including a row for the value added to each sector by factor services, and confirm that the various ac- counting identities have been observed in the construction of the table. Calculate the matrix A = [a;] of input-output coefficients. Use the method of Gaussian elimination and the method of back-substitution to solve the equation (I - A)x = y to find the vector * = [21, $2, x3]' of the activity levels in the three sectors when the levels of final demand are given by y = [31, 92, y3]' = [60, 120, 60]'