their arithmetic mean, while the efficiency-gaining sector will be penalised by a loss in its terms of trade of an equal amount.
This result, in spite of the highly stylised form in which R has been obtained, may not be without interest, the more so since it applies to any two-fold division of the
economy, whether agriculture and industry, heavy and light industry, material production and services traditional and modern sector, or any of the divisions felt
to be structurally important to a given economy.
While smooth secular rises in the generators thus produce similarly smooth, but mitigated movements in relative value-prices, other types of movements may produce
aggravated, or even explosive movements in them. Suppose for instance the generators show movements of a sinusoidal type through time as instanced by
e
l
= cos t and e
2
= sin t, having values bounded above and below. The corresponding
value movements would then be sin tcos t=
tan t which increases without limit
as time approaches p2, leaving ample scope for disparities in value-prices that could produce opposing movements such as might engender scissor crises.
7. Specific instances of surplus-levelling value-prices
To give flesh and blood to formulae such as Eq. 2 or Eq. 4 we must of course define the nature of the generators on which they are based. This will depend on the
kind of ‘price rationality’ from which they are derived, which in the last analysis is a matter of philosophy or ideology, as will be made clear in the following sections.
These will be devoted to certain specific value-price models, and can now largely be confined to deriving the generators appropriate to them for subsequent application
of the formulae already established.
The instances dealt with here are given to illustrate the wide range covered by some of the better known concepts that have been examined or touched upon in the
literature without their functioning or mutual kinship being always recognised. Our justification for including them is above all that they obey the rules of behaviour in
the face of technological change derived in this article, but they are far from exhausting all the specimens of the large genus that may have been uncovered, or
even devised as yet.
8. ‘Sraffa prices’
The term is not in common use. I venture to introduce it here in deference to Piero Sraffa because of its evident close kinship with the ‘representative commodity’ or
‘standard commodity’ associated with that famous name.
5
5
Sraffa’s standard commodity is chiefly valued for its function as a composite numeraire. It was adopted by its author mainly to clarify the trade-off between the distributive shares of wages and the
rate of profit in a two-factor input-output model and produces a system closely resembling a dual of our ‘Sraffa prices’ in that its final demand vector is posited to be proportional to the sums of intermediate
inputs and therefore also to total value, which constrains these vectors to the right-hand dominant eigenvector of the coefficient matrix. The matter is introduced in Sraffa 1960 and exhaustively
discussed in Steenge 1997.
In the understanding of this author Sraffa rationality may be interpreted as implying a price system which ensures that the factors of production as a whole
earn the same reward per unit output in whichever sector they are employed, so that there is no tendency for them to move in search of better rewards. This implies
that the structure of total output at these prices must exactly correspond to the structure of value-added in the economy, and therefore also to the structure of
material input costs which are the residual when value-added is subtracted from total output. This requirement implies that wp = pA, where A stands for the
familiar Leontief matrix of direct input coefficients and represents the ‘generator’ a
1
b
1
, in this particular case. This we simplify by interpreting as output only those products which are sold by the producing sector outside itself, thus reducing the
generator matrix to
A =
b
1
a
1
which makes the model precisely conformable to that discussed in the previous section with Eq. 6a applicable as well as all the subsequent commentary. In
particular any time-path of the physical efficiencies e1t and e2t will be reflected in the timepath
e
2
te
1
t followed by the relative value-price of the first sector.
9. Marxian labour values and production prices
