Vectors are also used in economics. One example of this is the use of vectors in predicting the consumption demand of a system. It uses an input-output matrix to show how goods from one industry are consumed in other industries.

The rows represent the producing sector of the economy and the columns represent the consuming sector of the economy. The total internal demand for the economy is equal to the sum of the entries per row in the input-output matrix and it can be represented as:

The image below shows an example and the result of the computation.

This shows the flow of goods between industries.

Now, if we get relative size of industries with respect to currency, we construct a diagonal matrix where the each entry is the price of the goods that the corresponding industry produces then multiply it to the input-output matrix we obtained before to have the value input-output matrix. We’ll then arrive at the internal demand vector with respect to currency when we get the sum of each rows.

Source:

http://kurser.math.su.se/pluginfile.php/30620/mod_resource/content/0/matrix-ex%20leontif.pdf

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