582 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28
All the individuals may then be considered as grouped in a
final sector, which may be called household — sector n —
which receives all productions for consumption and provides all
labour services for production.
All these flows may be framed in a usual input-output
table, which in our case becomes very simple. As is well
known, the table can be looked at from two different points of
view, and accordingly represented by two systems of identities.
From a physical point of view, the production of each com-
modity is identically equal to the sum of all quantities of that
commodity which are delivered as inputs to the other sectors.
(In our simple case this sum is reduced to one term: the amount
delivered to the household sector). Moreover, the sum of all
labour services is identically equal to labour employed. Si-
milarly, from a value point of view, the production of each
commodity must be equal in value to the sum of the values of
its total inputs, and the sum of the values of all commodities
must be equal to the total income which is distributed to the
factors of production (labour in our case).
We have therefore:
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