ABSTRACT
Today, after Leontief and von Neumann, it has become easy to express Ricardo’s model of a closed economy without joint production mathematically. Suppose that there are n commodities j=1, …, n and that the industries of the country are divided accordingly into sectors i=1, …, n, each producing commodity i. The i’th industry uses the quantities of commodities 1, …, n as inputs and li hours of labour per period of production in order to produce one unit of commodity i; symbolically:
or, for all industries taken together:
The condition for reproduction for the economic system as a whole requires that for each single commodity at least as much be produced as is used in the production of all other commodities: if one unit of each commodity j is produced, we must have
We normalize In this perspective, the reproduction of commodities by means of commodities and
of labour appears as the fundamental reality from which economic reasoning starts. The methods of production of each industry are specified as technical relationships. It should be clear that the technology that they reflect depends on numerous social factors, as is particularly clear if we think of the inputs of labour. The character of the work process and the intensity of labour are clearly not simple matters of engineering requirements. Yet it is useful to start by treating the input-output structure of the economy as a technical datum, and to link the analysis only subsequently with the institutions governing the forms of work, the design of commodities, etc., as will be explained later (sections II.20a, b; Essay 5 in Part III).
