Introduction

Technical coefficients were defined in chapter 2 as the input requirements (amounts of commodities) per unit of output (for each commodity). The technical coefficients for output 1 were written in a column vector, (2.1), and placement of all the “recipes” next to each other yields the matrix of technical coefficients, (2.2). The matrix of technical coefficients is a function of the input and output data of the economy, which were presented in section 6.4. For every pair of a use and a make table, (U, V), we face the task of constructing the associated matrix of technical coefficients: A(U, V). It is important to distinguish a function, such as A, and a value it can take, A(U, V). A value is a matrix of technical coefficients that is associated with a given pair of data. The function itself represents the association or the rule by which the coefficients are constructed. The latter is the topic of this chapter.

If there are as many commodities as production units and the make table, V, is a diagonal matrix, the situation is simple. Every sector would use an input vector, a column of U, and make a single output.