The parameter
m* is thus uniquely defined as the reciprocal of the maximum characteristic root, and the vector of prices
P_{0} as the characteristic vector of the matrix [I  (1+n*)A’]^{1}C’. It is thus possible to consider
m* as a function of
n*.
From the theory of nonnegative matrices it follows that dm*/dn* £ 0, and in cases of irreducibility, dm*/dn*
< 0.
Similarly, it can be shown that the choice of parameter
m*
from the interval [0; 1/l_{c}) uniquely defines
n*.
Value prices and
Nincome
prices are evidently limiting cases of Ntwochannel prices.
A certain ‘middle case’ is also of some interest. If we write
m*
= 1 + n*
we obtain the following price formula:
P_{0} = (1 +
n*)(A’
+ C’)P_{0}. (30)
These prices cover material and wage costs and profit proportional
to costs. We shall call them
cost
prices. Note that
n*
> 0, that is, there exists positive profit only if the maximum
characteristic root of matrix A’
+ C’ is less than unity. With cost prices
P_{0} is given by eq. (30),
