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OECD Culture and Local Development.pdf - PACA

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ANNEX 1<br />

consumption sales of each sector, <strong>and</strong> the lower right quadrant establishes the<br />

relationship between factor remuneration <strong>and</strong> final consumption.<br />

Table 3. The economy according to the input-output matrix<br />

Sectors<br />

Users<br />

Sectors<br />

Intermediate<br />

consumption<br />

Final<br />

consumption<br />

Total<br />

Primary<br />

factors<br />

Factor<br />

purchases<br />

Outlays<br />

Total<br />

Total<br />

Total<br />

More precisely, the matrix can be represented by the following system of equations:<br />

Where:<br />

X = A.X + Y<br />

• X represents the vector of final sales for each sector.<br />

• Y represents the vector of final dem<strong>and</strong>.<br />

• A represents the matrix of relationships between inputs <strong>and</strong> outputs.<br />

We may deduce successively:<br />

<strong>and</strong>:<br />

X - AX = Y<br />

(I - A). X = Y<br />

X = (I - A) -1 . Y<br />

X = (I - A) -1 . Y<br />

where I this time represents a unitary matrix equal to 1. Any variation in final dem<strong>and</strong><br />

(for example due to a shift in the dem<strong>and</strong> for cultural goods) will translate into a variation<br />

in activity levels, which can be analysed here sector by sector.<br />

In fact, this system is still oversimplified: a central element for underst<strong>and</strong>ing the<br />

local development impact will be the capacity to meet dem<strong>and</strong> from local output rather<br />

than imported products, which implies examining their relative competitiveness in<br />

terms of intermediate consumption <strong>and</strong> not only final consumption. To this end the<br />

formula:<br />

180 CULTURE AND LOCAL DEVELOPMENT - ISBN 92-64-00990-6 - © <strong>OECD</strong> 2005

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