Question

The input-output matrix below represents a model of a certain economy with two industries: paper and plastic (in that order). [0.55 (0.45 0.601 0.40] Given the production matrix, [950] 750 what will be the output of plastic? Round to the nearest unit and do not include units in your answer.

Answer 1

Let us define the output of paper and plastic as X and Y. The vector of output are as follows: O

$\begin{bmatrix} X\\Y \end{bmatrix}$

The input output matrix I is :

$\begin{bmatrix} 0.55 &0.60 \\ 0.45& 0.40 \end{bmatrix}$

And production matrix P is:

$\begin{bmatrix} 950 \\ 750 \end{bmatrix}$

Now,

O = IP

Hence, we have:

$\begin{bmatrix} X\\Y \end{bmatrix} = \begin{bmatrix} 0.55 & 0.60\\ 0.45 & 0.40 \end{bmatrix} \begin{bmatrix} 950\\ 750 \end{bmatrix}$

or,

$\begin{bmatrix} X\\Y \end{bmatrix} = \begin{bmatrix} 0.55*950+0.60*750\\ 0.45*950+0.40*750 \end{bmatrix}$

or,

$\begin{bmatrix} X\\Y \end{bmatrix} = \begin{bmatrix} 522.50+450\\ 427.50+300 \end{bmatrix}$

or,

$\begin{bmatrix} X\\Y \end{bmatrix} = \begin{bmatrix} 972.50\\727.50 \end{bmatrix}$

Hence, as Y represents the output of plastic, Y =727.50

If I round it off to nearest units, Y = 728.