A certain firm has three main departments namely; steel, motor vehicles and construction. The three departments are interdependent. Each unit of output from the steel department requires 0.2, 0.3 and 0.4 units from steel, motor vehicles and construction departments respectively. Each unit of output from motor vehicles department requires 0.2, 0.4 and 0.2 units from steel, motor vehicles and construction departments respectively. A unit of output from the construction department requires 0.3, 0.4 and 0.1 units from steel, motor vehicles and construction departments respectively. The final demand of the firm comprises 20 million, 50 million and 30 million units of output from steel, motor vehicles and construction departments respectively.
Required:
(i) The technical coefficient matrix.
(ii) The total output of each department given that the Leontief's inverse matrix is as provided below:
\(\frac{1}{0.192}\)
\(\begin{bmatrix}
0.46 & 0.24 & 0.26 \\
0.43 & 0.60 & 0.41 \\
0.30 & 0.24 & 0.42 \\
\end{bmatrix}\)
(iii) The change in the total output of the construction department, given that the final demand of steel department decreases by 2 million units and that of motor vehicles department increases by 10 million units whereas that of the construction department does not change.
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