Use of the Symmetric matrices
Note: The following uses the Industry by Industry (IxI) matrix for the examples of use. However, the Commodity by Commodity matrix can be used in the same way.
The structure of the IxI matrix is very similar to the Use matrix and can be used for similar analyses but, as the rows have been converted from purchases of commodities to purchases from each industry, a number of additional analyses are readily available from the IxI matrix.
Destination of industry output
Where the Use matrix showed the destination of manufactured commodities, the IxI matrix shows the destination of manufacturing industry output - be it manufacturing commodities or other secondary commodities. From the Use matrix, the exports of manufactured commodities were estimated as £12,577 million (RUK) and £10,991 million (RoW), whereas the IxI matrix gives exports by the manufacturing industry (at basic prices) of £11,942 million (RUK) and £10,154 million (RoW).
Industry's contribution to GDP
The income measure of Gross Domestic Product at basic prices is defined as the sum of Taxes less subsidies on production, plus Compensation of employees and Gross operating surplus giving a total of £82,953 million for Scotland in 2004. This figure corresponds to the income measure of Gross Domestic Product - GDP(I).
It is possible to estimate each industry's contribution to GDP from the above table by dividing the Gross Value Added (GVA) at basic prices for each industry by the overall total GVA figure. For example, the Manufacturing industry contributes approximately 14% (£11,420m) to total Scottish GDP.
Industry linkages
The columns of the IxI matrix show purchases made by industries and final demand from each Scottish industry's output arising from both principal and secondary production. Column 3 of the IxI matrix shows that Manufacturing purchases the majority of its domestic inputs from other firms in the same industry, Finance & Business and Mining. If the output of the Manufacturing industry rose then more inputs would be required from its supplier industries.
The demand for Manufacturing industry outputs could in turn be influenced by the industries it supplies. Looking at row 3 of the IxI matrix, if demand for Construction rose we could expect to see an increase in the demand for Manufacturing industry outputs, as a supplier to Construction.
These industry linkages can be summarised as industry Multipliers and can be used to look at the knock-on effects throughout the Scottish economy of a change in final demand.