Papers in the archieves

["Neri Salvadori" <nerisal@xxxxxxxxxxx>]

This is just to inform all pkters that I have inserted some more papers in the
archieves. The paper "Marshall, Sraffa, and the Problem of Returns" has been
written by Carlo Panico and myself, it is going to be published in the
_European_Journal_of_the_History_of_Economic_Thought_ (I will eliminate from the
archieves as soon as it will be published), and is connected to many debates
among pkters. The other two are more formal and maybe they are of interest for a
minority of pkters. One is on the Non Substitution Theorem, the other on Fixed
Capital. Here you will find the abstracts.

"Marshall, Sraffa, and the Problem of Returns" by Carlo Panico and Neri
Salvadori. The paper deals with some links between Sraffa's 1920s work on
Marshallian supply functions and his 1960 book. It argues that the content of
Sraffa's 1920s articles can justify the lack of reference in
_Production_of_Commodities_ to the analysis of the firm. Besides, it can clarify
Sraffa's position on the determinants of variable returns and some origins of
the method based on the assumption of "given quantities", which characterises
his later book. It also argues that some important aspects of the development of
_Production_of_Commodities_ find their origin in the Marshallian tradition as
well as in the "classical" one.

"The Non-Substitution Theorem: Making Good a Lacuna" by Heinz D. and Neri
Salvadori. An example shows that the Non-Substitution Theorem need not hold when
the rate of interest equals its maximum value. Then the Theorem is proved to
hold even in this case if a further assumption is met.

"Choice of Technique in a Model with Fixed Capital" by Heinz D. Kurz and Neri
Salvadori (This is the Introduction, not an abstract).
Ever since the inception of systematic economic analysis in the time of the
'classical' political economists, fixed capital was seen to introduce additional
complications into the theory of value and distribution, the most important of
which appear to be the following two. First, while the circulating part of the
capital advances contributes entirely to the annual output, i.e. 'disappears'
from the scene, so to speak, the contribution of the durable part is less
obvious and can only be imputed in correspondence with what may be considered
the 'wear and tear' of fixed capital items. Second, with fixed capital there is
always a choice of technique problem to be solved. This concerns both the choice
of the mode of utilization of a durable capital good and the choice of the
economic lifetime of such a good.
While the classical economists did not succeed in providing a general solution
to the problems mentioned, they deserve the credit for having pointed out an
analytical method by means of which fixed capital can be dealt with adequately.
This method, which can be traced back to Robert Torrens (cf. Sraffa, 1960, pp.
94-5), consists in treating what is left of a fixed capital good at the end of
the production period as an economically different good from the fixed capital
good which entered the production process at the beginning of that period. This
method seems to have fallen into oblivion in later times, but was reintroduced
in economic analysis by John von Neumann (1937, 1945) and explored in some
detail by Piero Sraffa (1960) in an explicit attempt to revive the 'classical'
approach to the theory of value and distribution.
As the literature following the publication of Sraffa's book shows, both
complications mentioned above can be tackled in terms of the joint-products
method. The more recent developments on the subject may be summarized as
follows. In Chapter X of his book Sraffa (1960) provided details for the
analysis of a single technique when no more than one old machine is used in each
sector and the efficiency of machines is constant over time. It was particularly
Schefold (1971, 1976, 1978, 1980b), Baldone (1974), and Varri (1974) who
analysed the case in which efficiency is not constant. They remarked that if
efficiency is decreasing, then the price of old machines may be negative even if
the rate of profits is greater than zero but smaller than the maximum rate of
growth. They argued also that if this is the case, then there is another
technique which at the same rate of profits pays a larger wage rate at prices
that are all positive. This further technique has been called a 'truncation' of
the original technique since it can be interpreted as utilizing the same 'type
of machine', but with a shorter economic life. Hence in these contributions the
problem of the choice of technique is reduced to the determination of the
optimal economic lifetime of machines, whereas the general problem of the choice
of technique is left unsolved. Woods (1984, 1990) dealt with some additional
problems concerning the choice of technique, but confined his investigation to
the two-sectoral case. An analysis of the choice of technique in a general model
that allows for the joint utilization of several machines was provided by
Salvadori (1988). In his paper Salvadori (1988) followed a complex procedure by
means of which the cost-minimizing technique can directly be determined without
studying techniques that are not cost-minimizing.
In this paper we consider once again the model in which no more than one used
machine is employed in the production of each commodity in each technique. We
shall prove: (i) the existence of a cost-minimizing technique; and (ii) the
uniqueness of the price vector if more than one cost-minimizing technique
exists. The procedure followed in this paper is similar to the traditional one
(we will in fact investigate in separate steps a single technique and the
determination of the cost-minimizing technique); it has the advantage of being
much simpler than that followed by Salvadori (1988). The uniqueness theorem
proved in this paper concerns the prices of all commodities (both finished goods
and old machines) that are produced with cost-minimizing techniques. Previous
uniqueness results were restricted to prices of finished goods only (cf.
Salvadori, 1988, Theorem 4; see also Stigliz, 1970, who uses a different
framework). However, the procedure followed here cannot deal with the case of
jointly utilized old machines, which was the main concern of Salvadori (1988).
The structure of the paper is as follows. Section 2 presents the assumptions
underlying the following analysis. In Section 3 the properties of a given
technique utilizing durable capital goods are studied. Section 4 introduces the
useful concept of the 'core processes'. Section 5 turns to a general discussion
of the choice of technique problem and the determination of the cost-minimizing
technique(s). Section 6 contains some remarks on new machines. Section 7 draws
some conclusions.


Neri Salvadori

Dipartimento di Scienze Economiche            TEL. (39)(50)549215
Universita' di Pisa                           FAX: (39)(50)598040
Via Ridolfi 10, i56100 PISA (Italy)           e-mail: nerisal@xxxxxxxxxxx