additionally needed to secure each unit of output. In this way the ‘augmented technology matrix’ F = A + E is formed, which enables us to establish the list of
prime costs for material and labour. The requirement that the surplus generated at these costs be a uniform proportion, say e
, of the wage payments can then be
put in the form 61 − F = e
6 E, or
6 1 − e
E1 − F
− 1
= 61 − e
E = 0
7
where E = El − F
− 1
will be recognised as the matrix of ‘total’ input coefficients which take account not merely of labour inputs carried by the material products
absorbed in production, but also of those inputs necessary to ‘feed’ or sustain the workers of the sector in question by means of subsistence- wage-financed con-
sumption, thus presenting a higher degree of ‘indirection’ than the ‘full’ coefficients 1 − A
− 1
. The Marxian labour values 6 are thus shown to be the left-hand
eigenvector of E , and their generators are the total labour input coefficients in the
sense just explained. It is to them that Eq. 6 has to be applied to calculate the changes in value prices in the wake of technological change.
In the Soviet price debates of the 1950s and 1960s one group of economists favoured a switch or transition from the chaotic operative price system to or
towards the labour values as given by Eq. 7 on the grounds that this would be the system ‘appropriate’ to a socialist economy which had overcome capitalism
with the ‘rate of exploitation’ aptly renamed ‘the rate of withholding’ or some such term. Another group, however, argued that this system would only be appropriate
to the ‘full communist’ stage which had not been reached yet, and that the system to be favoured was still a price structure which would equate the rate of profit on
prime costs material plus labour and therefore of the surplus to the prime cost, say f
, the system defined as ‘production prices’ in Marxian parlance, say u, where
uI − f F
= 0, with F = FI − F
− 1
8 The generators of these value-prices to which Eq. 6 applies are evidently the total
prime cost coefficients per unit output.
10. Eigenprices
6
Most of the value-prices proposed in the literature, notably the Marxian prices, of the previous section, are based exclusively on cost elements, neglecting the use
values or utilities of commodities and resources. This can be seen most clearly from an alternative definition of the labour values equivalent to Eq. 8 which explains
them as the ‘full’ labour coefficients
6 =
lI − A
− 1
9
6
Eigenprices are introduced in Seton 1985 and Seton 1992 and put to an empirical test in Dietzenbacher and Wagener 1999, among others.
where l stands for the direct labour-input coefficients. This can be paralleled by a definition of ‘full capital values’, say g = gI − A
− 1
or ‘full land values’, say
h = hI − A
− 1
, where g and h are the direct requirements of these factors per unit output, or any linear combination of these values weighted at the presumed
rental attached to the factors, say r
1
, r
2
, r
3
or rB, where B is the matrix of direct factor requirements per unit output. This yields ‘full costs’ equal to rC, where C is
the matrix BI − A
− 1
or, when provided with a uniform profit margin, 1f, the ‘full cost prices’ of commodities.
p = 1frC 10
We can now counterpose to the full-cost coefficients in which commodities are traced back to the primary level a set of ‘full use’ coefficients through which
commodity outputs are traced forward to some final use or combination of final uses weighted at their presumed use-values prices, say p. These are then trans-
ferred to the original factors in proportion to their roles in the production of commodities, thus deriving a second transformation formula. However, this time
the transformation is from commodity prices to factor ‘norms’ of the type
r = pN 11
where N is the ‘norm matrix’ derived from the same input-output table as A and B, though its elements are distribution output quotas rather than input coefficients.
The ‘norms’ n
kj
, more fully explained in the author’s The Economics of Cost, Use, and Value, measure the use-equivalent of factor k in terms of commodity i, or
equivalently, the output of commodity i that would be lost by withdrawing one unit of k from its production. It is then argued on both consistency and substantive
economic grounds that the only rational price system would be the one where the prices of commodities implied by factor rentals as per Eq. 11 would imply the
initially assumed commodity prices as per Eq. 10, and similarly in the opposite direction starting out from factor rentals, i.e.
p = 1fpNC or pfI − NC = 0 and r = 1frCN or rfI − CN = 0
12 These ‘rational’ prices, for which the author has suggested the name ‘eigenprices’
are thus the left-hand eigenvectors of the ‘norm-cost’ matrix in the case of commodities and of the ‘cost-norm’ matrix in the case of factor rentals.
Their ‘generators’ in the case of commodities are the ‘norm-costs’ which are composed of products n
rk
c
ks
, the full cost of commodity s in terms of factor k multiplied by the norm of factor k in terms of commodity r, products which must
be summed over all factors to give the generator S n
rk
c
ks
, a term which measures the cost of s incurred in terms of commodity r by shifting the necessary complement
of factors from r to s or more succinctly the ‘factor-diversion cost’ in commodity r per unit of s. As such the concept has all the characteristics of an ‘opportunity cost’
and is in stark contrast with the direct and indirect factor cost which figure in the other generators reviewed.
11. Summary and future outlook
