Vectors
X,
Y
and matrices
A,
B,
C,
are defined so that the following equations hold

Matrices
A,
B,
C
are the three basic characteristics of the economic system from
which we shall derive our price systems. Note that these matrices
represent the requirements of productive factors per unit of
production in various branches: matrix
A
represents
requirements of intermediate products,
matrix
B
of the
stock of physical capital,
and matrix
C
requirements of
labor, expressed in subsistence
(real)
wages.
We shall assume that matrices
A,
B,
C
are nonnegative, that they have positive maximum characteristic
roots, and that the maximum characteristic root of matrix
A
is less than one. These are the only assumptions laid down. In a
normal economy, these assumptions are always fulfilled. 