Question

Given the input - output table below:-

         P.     Q.        Final Demand. Total Output

P.      60.    140.          300.                 500
Q.    110.     90.           150.                 350

a) Find the technical coefficient matrix
b) Determine the total output hence distribute the results among the users,given that the final demand for output from industry p increased by 10% while that from Q went down by 5%

Answer 1

a)

The technical coefficient matrix will be:

$\begin{vmatrix} 60/500 & 140/350 \\ 110 /500& 90/350 \end{vmatrix}$`

$\begin{vmatrix} 0.12 & 0.4 \\ 0.22& 0.26 \end{vmatrix}$

b)

$I -A = \begin{vmatrix} 1 & 0 \\ 0& 1 \end{vmatrix} -\begin{vmatrix} 0.12 & 0.4\\ 0.22 & 0.26 \end{vmatrix} = \begin{vmatrix} 0.88 & -0.4\\ -0.22 & 0.74 \end{vmatrix}$

Determinant = (0.88 * 0.74) - (-0.4 * -0.22) = 0.6512 - 0.088 = 0.5632

Change in demand

P = 1.1 * 300 = 330

Q = 0.95 * 150 = 142.5

X = [I] - A^-1D

$X = 1/ 0.5632 \begin{vmatrix} 0.74 & 0.4\\ 0.22 & 0.88 \end{vmatrix} \begin{vmatrix} 330 \\ 142.5 \end{vmatrix}$

      $X = \begin{vmatrix} 534.8 \\ 351.5625 \end{vmatrix}$