Euro. J. History of Economic Thought 8:3 363–390 Autumn 2001
Sraffa’s early contribution to competitive
price theory*
Giuseppe Freni
1. Introduction
As is well known, Sraffa’s 1926 Economic Journal article comprises two main
parts. The second part contains a seminal contribution to imperfect competition theor y. The paper, however, Ž rst summarizes the conclusions on
competitive price theor y that the author had drawn in a longer paper published in Italian the previous year (Sraffa 1925). There, Sraffa had questioned the soundness of the non-constant supply curves, a key element of
the Marshallian theory of competitive value that ‘is inspired by the fundamental symmetry existing between the forces of demand and those of
supply’ (Sraffa 1926: 180; see also Sraffa 1925: 325). His conclusion,
repeated in the 1926 EJ article, had been that ‘in normal cases the cost of
production of commodities produced competitively [. . .] must be regarded
as constant in respect of small variations in the quantity produced’ (Sraffa
1926: 186; see also Sraffa 1925: 363).
Together with the contribution to imperfect competition, it was this
thesis that after the publication of Sraffa’s 1926 article ‘generated a disproportionate amount of interest’ (Samuelson 1987: 458). The general
equilibrium reasoning on which Sraffa’s criticism rests had, on the contrary, no impact on the literature of that time (see Panico 1991: 558, 561;
and Samuelson 1967). In Samuelson’s words, it is ‘as a result of quite other
historical in uences and developments, [that] general equilibrium thinking has swept the Ž eld of analytical economics’ (Samuelson 1967: 116).
Moreover, Sraffa’s 1925 argument has been overlooked for nearly 50 years
afterward (for example, Garegnani 1984, contains no reference to Sraffa’s
Address for correspondence
Istituto di Studi Economici, Istituto Universitario Navale, Via Medina, 40, 80133
Napoli, Italy; e-mail: [email protected]
The European Journal of the History of Economic Thought
ISSN 0967-2567 print/ISSN 1469-5936 online © 2001 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/09672560110062979
Giuseppe Freni
1925/26 papers). In the last twenty years, however, the content of Sraffa’s
1925 and 1926 related papers has been the subject of a small literature
whose main aim is the reassessment of the links between Sraffa’s 1925 criticism and Production of Commodities (Sraffa 1960) (see e.g. Sylos Labini 1985;
Maneschi 1986; Samuelson 1987, 1990a, 1990b, 1991; Garegnani 1990;
Schefold 1990; Panico 1991; Panico and Salvadori 1994; Mongiovi 1996. For
an earlier treatment see Talamo 1976). In this literature, no consensus has
been achieved, so virtually ever y article contains a diffent interpretation –
often based on different evidence. In any case, the want of references to
the early work in Production of Commodities and Sraffa’s own statement that
his 1960 method of analysis is ‘that of the old classical economists from
Adam Smith to Ricardo’ (Sraffa 1960: v) give support to the prevalent view
that endorses the existence of a remarkable discontinuity between Sraffa’s
early competitive analysis and the method he employed in the 1960 book.
Contrar y to this view, the present article contains a reinterpretation of
Sraffa’s early work that emphasizes the elements of continuity with Production of Commodities in the method of analysis (see also Panico and Salvadori
1994). It also identiŽ es the sources of the major changes that intervened
during the short lapse of time separating the EJ paper from the Ž rst drafts
of Production of Commodities in the attempt to enhance the role of produced
means of productions and in the shift to a new subject of analysis.
The paper is organized as follows. In section 2, Sraffa’s Marshallian
framework of analysis underlying the 1925 and 1926 works is identiŽ ed.
Section 3 contains a description of the characteristic way in which mutual
interdependencies are treated in Sraffa’s 1925 contribution. The Ž rst part
of the section is dedicated to what Sraffa regarded in 1925 as ‘undiscarding’ interdependencies, i.e. the use of constant factors of production in
common by different industries and external economies generated in an
industr y, but not internal to the industr y itself. In the second part, the role
of produced means of production in the 1925 paper is scrutinized. A model
that rationalizes the main analytical points contained in Sraffa (1925) is
introduced in section 4. In section 5, the elements that mark the transition to
Production of Commodities are documented and what of the early Marshallian
analysis survived in Production of Commodities is detected. Section 6 contains
the concluding remarks.
2. Sraffa’s Marshallian framework of analysis
Commentaries on Sraffa’s contribution to the ‘cost controversy’ either do
not explicitly clarify Sraffa’s framework of analysis or specify different
models. This may suggest that most of the controversies are simply due to
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Sraffa’s early contribution to competitive price theory
the lack of a single analytical focus, and that the search for Sraffa’s own
framework may be worthwhile. It seems, in particular, that at least two
classes of models are described in the secondar y literature.1 In the former,
as in the usual Heckscher-Ohlin-Samuelson (HOS) model of trade, all
factors are supplied inelastically (in particular, leisure does not appear
among products). In the latter, as in Samuelson’s ‘Ricardo–Marshall’
speciŽ c factors model (Samuelson, 1971), the amounts of all factors, apart
from land, change with production (the models of this class involve a
generalized possibility production frontier in which leisure may be seen as
a produced good).
Of course, working within the Marshallian tradition does not necessarily
require a model belonging to the second class. Indeed, an alternative
version of the partial equilibrium speciŽ c-factors model in which labour is
supplied inelastically is quite common in the trade literature (see e.g.
Krugman and Obstfeld 1991, ch. 3) and the ‘external economies of scale’
counterpart of the same kind of model has been developed by Chipman
(1970). Moreover, an entire stream of literature suggests that Marshall’s
tenets refer to a single sector that constitutes an extremely small part of the
overall economy (or of the ‘group’). Accordingly, a proper Marshallian
model should take into account the effects of some ‘passing to the limit’
operations (see e.g. Vives 1987, that uses this procedure to derive decreasing demand curves). As regards the supply functions, a similar modelling
style is present in some passages of Sraffa’s 1925 paper (e.g. Sraffa
1925: 350). Moreover, Pigou (1927, see also Pigou 1928) embraced this view
and took the extreme position that partial equilibrium analysis can be
applied only to ‘commodities which individually employ so small a proportion of each of several factors of production that no practicable changes in
the scale of their output could sensibly affect the relative values of these
factors’ (Pigou 1927: 192). Therefore, ‘only the laws of constant or decreasing supply price, as so conceived, are admissible’ (Pigou 1928: 256).
Even with these qualiŽ cations, a model with elastically supplied factors
seems to be part of the Marshallian tradition. Joan Robinson’s 1941 paper
on rising supply price, for example, contains clear hints in this sense about
the structure of the Marshallian framework commonly employed before the
1930s.
The classical analysis, which gave rise to the Ricardian theor y of rent, dealt with the
question of what happens when the supplies of labour and capital increase, and land
remains Ž xed. This clearly has nothing to do with rising supply price for a particular
commodity. It belongs to the department of output as a whole. [. . .]
The problem of the long-period supply curve of a particular commodity belongs
to the department of the theory of value, which treats of relative prices of commodities. Marshall’s analysis appears to be a cross between the theory of value and
the theory of output as a whole. For he seems most often to be discussing the problem
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Giuseppe Freni
of the change in the supply of a particular commodity which occurs in response to a
net increase in demand. The demand for one commodity increases, but the demand
for the rest does not decline. The additional factors, apart from land, employed in
increasing the supply of the commodity are called into existence by the increase in
demand.
(Robinson 1941: 233–4)
There is also some evidence that this model is what Sraffa used in his 1925
critique of Marshallian supply functions. First, consider the alternative
HOS-like model. The fact that the production possibility frontier was developed as an analytical tool after 1930 has been pointed out several times (see
Samuelson 1967: 29 and Newman 1987). So, even if an ante litteram use of
the frontier by Sraffa cannot be ruled out, it seems at least unlikely. Furthermore, in Sraffa’s 1925 paper there is nothing suggesting that the rising of
price in the ‘expanding’ industry may, in some way, depend on the structure of the presumed ‘contracting’ industries. Indeed, in cases of decreasing returns, Sraffa summarized his entire argument as follows:
[T]he increase in production of a commodity leads to an increase in cost that has equal
importance for that commodity and for the others of the group.
(Sraffa 1925: 361; emphasis added)
As regards the ‘small’ sector model, it is true, as remarked above, that Sraffa
made some references to it. However, it is equally true that the ‘small’ sector
case is always treated by Sraffa as a sub-case of a more general model (Sraffa
1925: 359–60, 362–3; see Panico 1991). This is especially clear in the treatment of increasing cost. Sraffa begins his argument with the case of a speciŽ c
factor:
These conditions reduce to a minimum the range over which hypothesis of increasing costs are applicable to the supply curve of a product. They are satisŽ ed only in
those exceptional cases where the totality of a factor is used in the production of a
single commodity.
(Sraffa 1925: 359)
Then, he examines two possibilities for the case of a factor used by a
number of industries, ‘the one appropriate to the case in which we are
dealing with a small number of commodities, and the other to a case
dealing with a large number of commodities’ (Sraffa 1925: 359–60). A substantially identical argumentation is developed for the decreasing supply
curve (Sraffa 1925: 362–3).
The last bit of evidence in favour of the ‘Ricardo–Marshall’ model is the
analysis of the intensive rent formation in §88 of Sraffa’s Production of Commodities (Sraffa 1960) – the only passage where changes in quantities are
admitted – which is built along the same lines J. Robinson attributed to
Marshall (see Panico and Salvadori 1994; infra section 5).
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Sraffa’s early contribution to competitive price theory
To summarize, the study of the conditions under which independent
supply functions can be constructed around an equilibrium point in a
‘Ricardo–Marshall’ framework appears to be Sraffa’s main analytical interest in 1925. In addition, there is no clear evidence that the scope of the
analysis was restricted to ‘small’ industries.
3. Interdependencies between industries
In Sraffa’s 1925 paper, the interdependencies that are most remarkable for
their absence are those arising from the presence of produced means of
production (see Steedman 1988). In view of Sraffa’s complete inversion of
emphasis in Production of Commodities (whose main propositions, it should
be remembered, had been already elaborated in 1928, Sraffa 1960: vi),
the following discussion is organized in two sub-sections entitled: ‘Pure
supply–demand interdependencies’ and ‘Produced means of productions
in Sraffa’s 1925 paper’.
3.1 Pure supply–demand interdependencies
In 1925 Sraffa overlooked the interdependence of the demand functions
though not as thoroughly as the capital-induced interdependence. As
regards income effects, he simply accepted their exclusion as a legitimate
approximation in the construction of demand functions (Sraffa 1925:
361). On the contrary, substitution effects were mentioned in considering the case of a factor used by a number of industries that produce
different commodities (Sraffa 1925: 359–60). However, since these effects
are not taken into account ‘in those exceptional cases where the totality
of a factor is used in the production of a single commodity’ (Sraffa
1925: 359; see also pp. 361–2 for decreasing costs), it is as if Sraffa’s
sought a role for substitution effects only if independent supply curves
cannot be assumed.
All demand-side interdependencies seem to belong, in summary, to the
set of cases in which ‘a slight degree of interdependence may be overlooked
without disadvantage’ (Sraffa 1926: 184). We are left, therefore, with
mutual interdependencies of the supply functions. And, indeed, the analysis of the conditions in which Marshallian non-constant supply schedules
can be constructed without violating the ceteris paribus assumption constitutes the core of Sraffa’s 1925 analysis and the basis for his criticism of the
Marshallian theor y.
Sraffa identiŽ ed the conditions which a supply curve must satisfy in the
following way:
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Giuseppe Freni
Since it represents only two variables, it is necessary to suppose that all the other conditions of the problem remain unchanged with the variation in the production of the
commodity. It is necessar y, in particular, that the demand of consumer, and the conditions in which other commodities are produced, should not change. That is to say
(1) the supply curve must be independent, both of the corresponding demand curve
and also of the supply curves of all the other commodities; (2) the supply curve is
valid only for slight variations in the quantity produced and, if we depart too far from
the initial equilibrium position, it may become necessary to construct an entirely new
curve, since a large variation would, in general, be incompatible with the condition
ceteris paribus.
(Sraffa 1925: 358–59)
Then, he found two situations in which these conditions are met in the construction of increasing and decreasing supply curves. The Ž rst occurs, as
already noted, when all factors in short supply are speciŽ c to a single industry (Sraffa 1925: 359). The second is the case when externalities generated
in one industr y do not spill over into other sectors (in Sraffa’s terminology
the increasing returns are in this case ‘external to the Ž rm and internal to
the industr y’) (Sraffa 1925: 361–2).
As noted above, in spite of the existence of these two consistent cases of
non-constant supply curves, Sraffa’s 1925 position was that Marshallian
rising or decreasing supply curves can be derived only in exceptional cases
(Sraffa 1925: 359 for decreasing returns, and pp. 361–2 for increasing
returns). This led him to the conclusion that, ‘in the study of the particular equilibrium of an industr y [. . .], we must concede that, in general, commodities are produced under conditions of constant costs’ (Sraffa 1925:
363).
The importance (in Sraffa’s work) and the soundness of this thesis have
given rise to some controversies in the secondar y literature that we can
usefully survey here. The various positions range from those of Eatwell
and Garegnani, who approve of Sraffa’s argument (Eatwell 1990: 281;
Garegnani 1990: 284), to that of Samuelson which is very critical about ‘the
fatal 1926 error’ (Samuelson 1990b: 320; 1991: 572–3). In between, we Ž nd
more cautious positions, as that of Schefold (Schefold 1990: 311, 313).
Since some aspects of this controversy have some bearings on the subjects of the next sections, we state about these aspects the following views:
(A) From a historical point of view, Sraffa’s 1925 and 1926 conclusion (as
opposed to his 1925 analysis) appears as an extraneous appendix in the
corpus of Sraffa’s critique of Marshallian supply functions. In addition, it is
almost irrelevant to Sraffa’s subsequent work.
Samuelson’s opposite view that Sraffa spent all his life in ‘the attempt to
emphasise the singular cases in which the theory of value happens to be
dependent only on technology and costs independently of the composition
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Sraffa’s early contribution to competitive price theory
of demand’ (Samuelson 1991: 570; see also Samuelson 1987: 459), is so
extreme an opinion as to be easy to reject. Indeed, when in chapter XI of
Production of Commodities Sraffa contemplated changes in quantities
(through a model that is no more than an elaboration of a model already
present in the 1925 paper, see Panico and Salvadori 1994; infra section 5),
changes in prices were explicitly involved (Sraffa 1960: 76 fn). Therefore,
it seems likely that Sraffa never advocated, apart from partial equilibrium
analysis, a quantity-independent theor y of competitive prices.
Moreover, soon after 1926 (some time between 1927 and 1928), Sraffa
abandoned the Marshallian partial equilibrium approach and embraced
the intersectoral simultaneous approach to the analysis of value we Ž nd in
Production of Commodities. In particular, in the Preface of the 1960 book it is
stated that ‘the central propositions had taken shape in the late 1920s’
(Sraffa 1960: vi) and that ‘in 1928 Lord Keynes read a draft of the opening
proposition of this [book]’ (Sraffa 1960: vi). Therefore, the transition to a
‘general’ equilibrium analysis took place shortly after writing the 1926 EJ
article and, given this temporal contiguity, it is seen by part of the literature (see e.g. Talamo 1976; Panico 1991; cf. Mongiovi 1996) as stemming
from Sraffa’s lack of satisfaction with Marshall’s theor y.
Finally, regarding his own early contribution, the Preface of Production of
Commodities contains the somewhat critical statement:
The temptation to presuppose constant returns is not entirely fanciful. It was experienced by the author himself when he started on these studies many years ago – and
led him in 1925 into an attempt to argue that only the case of constant returns was
generally consistent with the premises of economic theory.
(Sraffa 1960: vi)
(B) From an analytical point of view, I agree with Samuelson (1990b: 320)
that Sraffa’s argument is weak. The irrelevance of non-constant supply
curves, and thus constancy of costs as a ‘generic’ property, require a comparison of the relative importance of constant and non-constant costs when
partial equilibrium analysis is valid. But this kind of analysis is not present in
Sraffa’s papers. What can be found instead is a reasoned discussion showing
how rarely the conditions for valid partial equilibrium analysis with nonconstant supply curve can be met in general (Sraffa 1925: 356–63,
1926: 180–7). Thus it seems that Sraffa sustained his conclusion by means
of an argument in which a wrong space of parameters was employed.
On the other hand, the ver y fact that various aspects of Sraffa analysis are
loosely speciŽ ed seems to weaken Samuelson’s other judgement (that
Sraffa’s conclusion is false, Samuelson 1991: 573). Since what is ‘generic’
may depend on what we choose to utilize as parameters, how can we
exclude that there is some competitive framework in which constant-cost
response is the ‘generic’ rule?
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The results of this sub-section can be summarized in the following way.
The incomplete framework in Sraffa’s 1925 article mainly encompasses
supply relations. Demand functions are loosely speciŽ ed and not integrated
with the other part of the structure. In conclusion, Sraffa’s framework
appears close to the supply side of a ‘Ricardian’ competitive model (i.e.
produced quantities are treated as parameters).
3.2 Produced means of production in Sraffa’s 1925 paper
Sraffa’s 1925 article contains some references to capital goods. The following are among the most signiŽ cant passages.
[L]et us call c the quantity of capital and labour that, on the same amount of land k,
gives the maximum average product per unit of capital and labour.
(Sraffa 1925: 331)
When, having spent an annual sum on the cultivation of a given land, and wishing to
spent another thousand lire, reference to the agricultural technology will indicate not
only one way but a whole series of different ways, A, B, C, D, . . . , in which it is technically possible to spent the additional 1,000 lire. It will be possible to buy additional
fertiliser, or make a deeper ploughing, or improve the quality of the seed, or one
hundred other possible expenditures, or any combination of these.
(Sraffa 1925: 333)
However, there is no evidence that produced means of production were
integrated in Sraffa’s scheme as they are in Production of Commodities (see
Steedman 1988). This is particularly clear if we consider the fact that all the
above passages refer to rising supply curves. And that, therefore, changes
in the prices of produced commodities should have been involved in the
process if, as in Production of Commodities, proportionality links between
input and output prices were present in Sraffa’s framework.
If we speculate on the reasons of the marginal role of produced inputs,
then at least two alternative explanations can be offered. It seems possible
either that Sraffa considered capital goods as ‘constant factors’ of which
‘marginal doses’ can be drawn from other industries without any increase
in costs (Sraffa 1925: 360, 1926: 185), or that, as suggested in Panico (1991),
he judged the interdependencies related to the common use of a given
factor and to external economies as the most important, and thought of
those related to produced inputs as being indirect. In any case, the fact
remains that Sraffa’s 1925 framework is analytically equivalent to a model
in which only primary factors are present.
Historically, therefore, it seems plausible that input–output interdependencies became central in Sraffa’s work between the end of 1926 and 1928
when Keynes read a draft of the opening propositions of Production of
Commodities (Sraffa 1960: vi). However, on the basis of the existing evidence,
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Sraffa’s early contribution to competitive price theory
how this change in perspective is connected with the development of
Sraffa’s interest in classical theor y is not clear (examples of antithetical
reconstruction are the two recent contributions by Panico and Salvadori
1994; Mongiovi 1996). In any case, the discussion contained in sub-section
3.1 suggests that the treatment of quantities as parameters is not too far
from the procedure that Sraffa had already adopted in 1925.
To sum up, the effects due to the existence of produced means of production, so central in Sraffa 1960 book, were ignored by Sraffa in 1925. The
elements of Sraffa’s 1925 analysis can now be assembled in a consistent
model. This is the task attempted in the next section.
4. A ‘Ricardian’ model of supply relationships
In this section, we present a model comprising the main features of Sraffa’s
1925 analysis as they were identiŽ ed in the previous sections. In particular,
demand functions and produced means of productions will not be included
in the model, given that Sraffa did not integrate the latter in the analysis and
did not specify the former (section 3). Moreover, as in Joan Robinson’s
Ricardo–Marshall framework (section 2), labour will be assumed to be available from the ‘leisure’ sector. The result is a model that in the decreasing
costs part has some features in common with Chipman’s (1970) treatment
of parametric external economies, while in the increasing cost part, it
resembles Samuelson’s (1959) Ricardian model and, signiŽ cantly, is consistent with Sraffa’s (1960) Ch. XI treatment of the intensive rent formation.
In 1925, Sraffa used two rather different procedures for reaching the
supply curves of increasing and decreasing costs industries. In the Ž rst case,
he well realized that a theory of Ž rm is vacuous under global constant
returns and that therefore, ‘[a]s far as the construction of this curve is concerned, we can consider the whole industry as a single Ž rm which employs
the whole of the “constant factor” ’ (Sraffa 1925: 341–2). In the second case,
he used the U-shaped cost curve of a representative Ž rm, probably in order
to stress that the quantity produced in the industry is a parameter from the
point of view of the single producer (Sraffa 1925: 348–55). Decreasing costs,
however, can be subsumed under the Ž rst approach provided we renounce
any functional role for the dimension of the representative Ž rm (this is consistent with Sraffa’s position. According to him, ‘[t]he point of maximum
economy could be moved in any direction’ (Sraffa 1925: 352). Furthermore, he judged the case in which the equilibrium production of the
representative Ž rm is indeterminate as perfectly possible (Sraffa
1925: 351). As is well known, this requires that the technical coefŽ cients be
explicitly treated as functions of the amounts of production. Dealing with
external economies, we will adopt this procedure in what follows.
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Now we study how the supply curve is linked to the ‘rent’ function when
labour and a land of given quality are employed in the production of a
single commodity. Assume that there are constant returns. Thus, a process
of production (at the unitary level) can be deŽ ned as the pair (l, k), where
l ³ 0 gives the quantity of labour needed per unit of output, and k ³ 0 gives
the corresponding land input. To begin with, assume that only a Ž nite
number m, m ³ 1, of processes are known, and call the Ž nite set T = {(li, ki),
i = 1, 2, . . . , m} the technology.
If competitive conditions prevail, then in equilibrium the following
relations hold:
wli + rki ³ p, 1 £ i £ m
[1]
xi (wli + rki) = xi p, 1 £ i £ m
[2]
m
x iki £ h
[3]
r
x iki = rh
[4]
i=1
m
i=1
xi ³ 0, 1 £ i £ m
[5]
w ³ 0, r ³ 0, p ³ 0
[6]
where w is the wage rate, r is the rent rate, p is the price of the commodity,
xi is the activity level of process i and h > 0 is the existing amount of land.
Inequalities [1] and equations [2] are the proŽ t maximization conditions,
while inequality [3] and equation [4] describe the outcome of the market
for land services.
Normalize the size of the available quantity of land to unity, h = 1, and
choose labour as numeraire (we therefore preclude the analysis of the case
w = 0). Then inequalities [1] and [6] deŽ ne the convex set illustrated in
Ž gure 1. Furthermore, since inequalities [3] and [5] and equation [4] can
be satisŽ ed if and only if a point on the frontier of the set is chosen, then
the equation of the frontier is linked to an overall solution of the system
[1]–[6]. We are, therefore, interested in Ž nding a way to represent analytically the frontier.
To obtain this result, note that each point on the frontier minimizes the
rent under the constraints [1] and [6]. Hence the equation we are looking
for is simply given by the solutions of the family of problems:
R(p) = min r
s.t. li + rki ³ p, 1 £ i £ n
p ³ 0, r ³ 0.
372
[P]
Sraffa’s early contribution to competitive price theory
Figure 1
Now suppose that the ‘rent’ function R(p) is known. Note that its (generalized) derivative gives the product per unit of land associated with the
equilibrium process. But, given the normalization above, this amounts to
the whole production. Therefore, the supply curve can be obtained from
the rent function by plotting its derivative against the price as in Ž gure 2.
External economies can be added to the frame by allowing the coefŽ cients l and k to var y with the level of production. To make things easy,
we assume the existence of a Ž nite number of technologies, each associated
to a threshold. Then we can plot all the supply curves together, selecting
for each interval the relevant one. It is clear that the use of thresholds can
induce discontinuities in the supply curve (Ž gure 3).
The value function of problem [P] (i.e. when external effects are absent)
can be smoothed by adding new viable processes to a given technology, and
in the limit it could become differentiable (this means that the associated
supply ‘function’ is univalued).2 In the rest of this section, indeed, safe for
the point where it reaches the price axis, the rent function will be assumed
to be smooth.3
At this point, the way the rent functions can be employed if different
qualities of land can be brought into cultivation should be clear. A rent
function can be constructed for each quality of land. Then, after the
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Giuseppe Freni
Figure 2
Figure 3
normalization of all lands sizes to 1, the supply curve can be obtained by
summing up the (generalized) derivatives of these functions. Lands can
also be classiŽ ed in order of fertility on the basis of the minimum price that
induces cultivation (Sraffa 1925: 339–40).
The rent functions can be easily used also in the ‘general’ equilibrium
framework that originates from the hypothesis that at least one piece of
land can be employed by a number of industries. Assume there are s, s ³ 1,
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Sraffa’s early contribution to competitive price theory
qualities of land and n, n ³ 2, commodities. Now the rent functions are to
be indexed both by the lands and the goods. Then let Rij(pi), i = 1, 2, . . . ,
n, j = 1, 2, . . . , s, indicate the rent function associated to commodity i and
to land j, where pi is the price of good i. Assume that, with the possible
exception of the root of Rij(pi) = 0, Rij(pi) is differentiable. At Rij(pi) = 0,
the left derivative will be zero, R9 ij(pi)2 = 0, while the right derivative will
be non-negative R9 ij(pi)+ ³ 0. If good i cannot be produced on land j, then
put Rij(pi) = 0 (i.e. in this case, using land of quality j in production of
commodity i amounts to allow land to go out of cultivation).
Now the competitive equilibrium relations, analogous with the above
conditions [1]–[6], are given by
Rij(pi) £ rj, 1 £ i £ n, 1 £ j £ s
[7]
sijRij(pi) = sijrj, 1 £ i £ n, 1 £ j £ s
[8]
s ij £ 1, 1 £ j £ s
i=1
n
rj s ij = rj, 1 £ j £ s
i=1
s
s ij R9 ij(pi)+ = qi, 1 £ i £ n
j=1
sij ³ 0, 1 £ i £ n, 1 £ j £ s
[9]
n
[10]
[11]
[12]
pi ³ 0, qi ³ 0, 1 £ i £ n
[13]
rj ³ 0, 1 £ j £ s
[14]
where rj is the rent (rate) on land of quality j, qi is the supply of commodity
i, and sij is the share of land j employed in the production of good i. As
before, inequalities [7] and equations [8] are the proŽ t maximization conditions, while inequalities [9] and equations [10] assert that the quantity of
each land used in production does not exceed the existing quantity and
that the rent (rate) is zero whenever a quality of land is in excess supply.
Finally equations [11] deŽ ne the supplied quantities.
Given a non-negative price vector, then the system [7]–[14] determines
a set of quantities that can be competitively produced at those prices.
Conversely, if for each commodity i a rent function, Rij(pi), exists such that
R9 ij(pi) ®¥ when pi ®¥, then, given a vector of quantities, the system determines a set of equilibrium supply price vectors.4
Assume an ‘equilibrium’ is reached. Then a relationship between pi and
qi can be constructed around the equilibrium point by maintaining the initial
values of all other quantities. Since a necessary and sufŽ cient condition for
valid partial equilibrium analysis is that the other markets are not to be disturbed by the new supply conditions, the key equilibrium relationships are
375
Giuseppe Freni
those given by equations [11] that link the uses of lands to the intensities
of cultivation. They Ž x the limits within which an increase of production
can be dealt with by means of a partial equilibrium analysis. First, if the
increase can be accommodated by changing only the weights sij. In this case
the costs are constant. Second, if the increase of production can be accommodated by a change of the price whose effects do not propagate to other
sectors. This requires that the weights of the lands on which the cultivation
of the isolated commodity will be intensiŽ ed are all 1. These lands, in other
words, are to be specialized in growing the single commodity at least in a
neighbourhood of the equilibrium.
Since interdependencies between sectors in the model arise only through
the use of common factors, the elements of the model are arranged in such
a way that linkages among sectors vanish whenever a one-to-one correspondence can be found between the set of commodities and a partition of
the set of lands. Rather obviously, this correspondence exists in the case
Samuelson analysed in 1971, where it is assumed that each land is a priori a
speciŽ c factor. And, as a matter of fact, the model boils down to the supply
side of Samuelson’s (1971) model under this assumption. In particular, as
regards the structure of relations [7]–[14], the speciŽ c-factors assumption
implies that for each j, 1 £ j £ s, only one of the weights sij can be positive.
In terms of the maximization problem mentioned in footnote 4, it implies,
instead, that the problem splits up into n independent problems, whose
solutions are n supply curves of the kind we introduced above.
Straightforward as it may be, this is not, however, the only way in which
the general equilibrium relations [7]–[14] can be used in connection with
partial equilibrium analysis. In the above discussion, for example, a different use was outlined. There, indeed, we suggested that the conditions
under which partial and general equilibrium responses to parametric
changes in quantities coincide locally can be found equally well through the
system [7]–[14]. In other words, the system can be used to Ž nd those parts
of a ‘general equilibrium supply curve’ along which a partial analysis is
appropriate. We are therefore led to the analysis of land specialization
associated with the growth of production (see Schefold 1990: 313).
The same kind of argument can be used if external effects are considered. If they are not (at least locally) speciŽ c to the isolated sector, then
‘[w]ith the increase in production of a commodity, if it utilises a large part
of the resources of a country, the prices of very many other commodities
will decrease, and thus the static system which is a necessary premise of the
supply curve is overturned’ (Sraffa 1925: 363).
We began this section with the aim of offering a model that rationalizes
the main analytical points contained in Sraffa (1925). A summar y of what
has been achieved can now be presented. The ‘Ricardo–Marshall’ system
376
Sraffa’s early contribution to competitive price theory
[7]–[14] is suitable for the analysis of the local effects of parametric
changes in quantities. And this analysis, that amounts to sift out Marshallian supply functions, was, as we argued in the previous sections (see also
Talamo 1976; Panico 1991; Panico and Salvadori 1994), the main aim of
the Sraffa 1925 critique. Specialization of lands and external effects that do
not spill over to other sectors, the conditions for valid partial equilibrium
analysis that Sraffa identiŽ ed in 1925, also emerge in the present model as
key elements for reaching sectors insulation. Only Sraffa’s (1925) conclusion that cases of constant costs are in some sense more frequent than
cases of land specialization does not seem to be supported by the model.
However, a deŽ nitive answer to this question requires a full speciŽ cation of
the functional space from which the rent functions are drawn, and is well
beyond the limits of the present analysis.
5. Echoes of the early Marshallian analysis in Production of Commodities
In sub-section 3.2, we suggested that paying full attention to the effects
associated with the existence of produced means of production made a
break in the developmental process leading Sraffa from his early Marshallian analysis to Production of Commodities. Had the above one been the only
change involved in the process, no doubt Production of Commodities would
have been replete with references to the feedbacks from the new elements
to the early system. In fact, ver y few things in the 1960 book are inherent
to the 1925 and 1926 articles. And of these, only two allude to the way the
early analysis should be amended in order to accommodate capital goods
(Sraffa 1960: 76fn, see this section below, and Sraffa 1960: 74, see point (C)
below). This lack of references suggests, therefore, that other major
changes took place during the few years that separate the EJ paper from the
Ž rst drafts of Production of Commodities.
Some information about the involved changes can be obtained from the
preface of Production of Commodities. There it is stated that in the book ‘[t]he
investigation is concerned exclusively with such properties of an economic
system as do not depend on changes in the scale of production or in the
proportion of “factors” ’ (Sraffa 1960: v). By itself this change of the subject
of the analysis would then be sufŽ cient to justify the lack of references to
the problems that were at the centre of the stage in the early work. It has
to be recognized, however, that Sraffa linked the above change to a shift in
the method of analysis from the ‘marginal’ one, in which change is fundamental, to ‘that of the old classical economists from Adam Smith to
Ricardo’ (Sraffa 1960: v), in which the produced quantities are given. It is
not surprising, therefore, that the prevalent view (see e.g. Garegnani 1984)
deduces from the above statement that the assumption of given quantities
377
Giuseppe Freni
and the focusing of attention on changes in distribution were the joint
products of the process through which Sraffa revived the classical approach.
In sections 2 and 3 we saw, however, that something akin to the method
of given quantities had already been adopted by Sraffa in 1925, although it
was not attributed to Ricardo, who was credited, at this stage, with a constant costs theory of value (Sraffa 1925: 354). But even if we are not ready
to accept that the frame of the 1925 article has a lot in common with the
schemes contained in Production of Commodities, the fact remains that in 1928
Sraffa had already avoided ‘the temptation to presuppose constant returns’,
and this occurred more than two years before his appointment as editor of
the Works and Correspondence of David Ricardo (see Panico and Salvadori
1994). In any case, therefore, a Marshallian origin of the assumption of
given quantities seems plausible.
The acceptance of the Marshallian derivation of the assumption of given
quantities, while leading to see more continuity in Sraffa’s analytical work
than is commonly believed, does not necessarily deny the classical in uence
(see also Panico and Salvadori 1994). The fact that part of this in uence
was mediated by Marshall does not constitute a problem if we accept that
Marshallian analysis is, as suggested by J. Robinson, ‘a cross between the
theory of value and the theory of output as a whole’ (Robinson 1941: 1).
In summar y, the fact that only echoes of the early analysis are perceptible
in Production of Commodities seems due more to the change of subject of
analysis, than to a new analytical method.
We can now look for the elements of the early Marshallian analysis that
survived in Production of Commodities. Before that, however, we temporarily
leave this essentially historical investigation by asking whether some
elements in the 1960 book have explicit bearing on the themes of Sraffa’s
early analysis. And, more generally, what the full integration of produced
means of production implies for the partial equilibrium conditions we mentioned in section 4.
In looking in Production of Commodities for what could directly refer to the
local comparative statics analysis of the 1925 paper, we can restrict the
search to the only section (§88) of the book in which a change in quantities is allowed. Section 88, in particular, describes the process of intensive
rent formation that follows a progressive increase of production of a single
agricultural commodity. Since Sraffa considered a Ž nite technology (see
Samuelson 1959; see also section 4 above) and Ž xed the processes of industrial commodities, then generically either one or two processes for the production of the agricultural good are operated in such a way that:
the existence side by side of two methods can be regarded as a phase in the course
of a progressive increase of production on the land. The increase takes place through
the gradual extension of the method that produces more corn at a higher unit cost,
378
Sraffa’s early contribution to competitive price theory
at the expense of the method that produces less. As soon as the former method has
extended to the whole area, the rent rises to the point where a third method which
produces still more corn at a still higher cost can be introduced to take the place of
the method that has just been superseded.
(Sraffa 1960: 76)
At a Ž rst look, the process described in this passage appears to be the same
that we had encountered in the analysis contained in section 4, if a ‘kinked’
rent function had been used there instead of a ‘smooth’ one. And, more
importantly, it seems remarkably similar to the process that Sraffa himself
in 1925 described in his critique of Wicksteed’s distinction between
‘genuine’ and ‘spurious’ margins (Sraffa 1925: 333–5; see Panico and
Salvadori 1994). A main difference between the early and the new analyses
is, however, clearly enunciated in a footnote appended to the word ‘superseded’, where it is stated: ‘The change in methods of production, if it concerns a basic product, involves of course a change of [the] Standard system’
(Sraffa 1960: 76fn). This implies that the prices of all basic commodities
change with a change in methods and that, therefore, land specialization
is no longer sufŽ cient for valid partial equilibrium analysis. Given the existence of produced means of production, something more is required.
No hints regarding these new conditions can be found in Production of
Commodities. We have to look elsewhere, in one of Samuelson’s 1971 articles
modelling speciŽ c-factors, in particular, in order to Ž nd something related
to what we are looking for. In footnote 12 of this paper it is stated:
One can admit capital goods in this model in the Von Neumann-Leontief fashion
provided all intermediate goods used in any industry are producible from labour and
the speciŽ c lands of those industries. (Of course, one must also specify the interest
rate in each country or the equations determining it.)
(Samuelson 1971: 368fn)
Thus, if the requirement that the set of capital goods can be partitioned
among consumption goods is satisŽ ed, in addition to the earlier condition
that lands be speciŽ c, then we have a set of sufŽ cient conditions for valid
partial equilibrium analysis. Moreover, the rule applies besides the ‘Austrian’ framework suggested by Samuelson (that is only one of the possible
ways of introducing time-phasing in the system). And in particular in the
case in which produced commodities are encompassed by means of the
A commodity input matrix. Its use in this latter frame implies, however, that
all commodities are non-basics.
The conditions discussed above are global in nature. In section 4,
however, it was ventilated that linking partial equilibrium analysis with local
comparative statics may be a more appropriate procedure for mimicking
Sraffa’s analysis.5 In the labour-lands model of section 4, in particular, land
specialization, the local correlative of the notion of speciŽ c lands, was both
379
Giuseppe Freni
necessary and sufŽ cient for sound partial equilibrium analysis. We already
mentioned that, quite obviously, the condition is no longer sufŽ cient when
produced means of production are taken into account. What perhaps may
be more surprising is that neither is it necessar y. The following example
makes the point clear.
Example : Assume two Ž nal commodities (commodity 1 and commodity 2)
and an intermediate commodity (commodity 3) can be produced under
constant returns by means of the methods in table 1. Only 35 units of
land of quality [I] and 15 units of land of quality [II] are available. The
economy is stationar y and the rate of interest (proŽ t) is zero.
1
Assume the system is in a long-run equilibrium in which 10
units of the
1
Ž rst commodity and 10 units of the second commodity are consumed. It is
easily recognized that processes [1], [2], [3] and [4] are activated. Land of
quality [I] is in short supply and a positive rate of rent is paid on it. The
equilibrium price (in terms of labour) of commodity [1] is equal to 52 , while
the price of the other commodity is 25 .
18
If the quantity consumed of the second commodity ‘rises’ to 15 , land [II]
becomes scarce and process [5] has to be activated alongside the other four
processes. In the new equilibrium, the price of the second commodity
25
‘rises’ to 16
, but the price of the Ž rst commodity is unchanged. In a sense,
the market of commodity [1] is ‘not disturbed’ and a supply schedule,
based on ceteris paribus, can be used. This occurs despite the fact that land
(II), on which a positive rent arises, is not specialized in growing commodity
[2]. Indeed, a decrease in the rent rate paid on land [I] exactly compensates for the increase in produced inputs costs.6
Now we can search for the building blocks of Production of Commodities
that were already in place in 1925. In particular, the origin of the following
three structural features of Production of Commodities will be discussed:7 (A)
the absence of a theor y of the Ž rm; (B) the mentioning of only two factors
that can bring about variable returns; and (C) various concepts underlying
the analysis of the process of diminishing returns.
Table 1 Input-Output Patterns
Processes
[1]
[2]
[3]
[4]
[5]
380
Material inputs
Land inputs
[1] [2] [3]
[I]
[II]
.3
.5
0
.1
.2
4.5
1.5
0
0
0
0
0
1
1
0
0
0
.1
.1
.1
.3
.1
0
0
0
Labour inputs
Outputs
[1] [2] [3]
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
Sraffa’s early contribution to competitive price theory
(A) No analysis of the relationship between Ž rms and industr y is presented in Production of Commodities. In the book, indeed, price determination is discussed directly at the level of the industry, assuming a
Ž rm-independent process of cost minimization (Sraffa 1960: 81).
As mentioned in section 4, Sraffa had already in 1925 explicitly adopted
this procedure for the increasing costs industries (Sraffa 1925: 341–2).
Hence, at that time, he had appreciated the fact that under perceived constant returns to scale ‘it is immaterial where we draw the boundaries of
the Ž rm or whether we draw them at all’ (Samuelson 1967: 27).8 For the
decreasing costs industries, however, he had employed a different procedure that made use of the U-shaped curve of a ‘representative Ž rm’. This
discrepancy calls, therefore, for an explanation.
In 1925, Sraffa not only aimed at the construction of the supply curve,
but he was also interested in showing how ‘the general equilibrium is the
result of the series of individual equilibria which the competing Ž rms must
reach independently of one another’ (Sraffa 1925: 342). So he judged that
it was ‘necessar y to reconstruct the passage from the individual supply curve
to the collective curve’ (Sraffa 1925: 342).
It was with this end in view that he used the U-shaped cost curve of a ‘representative Ž rm’ (whose position was a function of the industry level of production) for the decreasing costs industries (Sraffa 1925: 350–1), while for
the increasing costs industries he had ‘recourse[d] to the stratagem’ that
consisted in ‘supposing that the number of producers is Ž xed, and that
each of them, with the increase in his production, cannot increase the
quantity used by him of the factor of which there exists a Ž xed quantity’
(Sraffa 1925: 343).
As a matter of fact, by the ‘recourse to the stratagem’ the two cases of
increasing and decreasing costs were made uniform in respect to the shape
of the individual costs curve, given that the attribution to each Ž rm of a
given quantity of a constant factor amounted to the introduction of a Ushaped cost curve, whose position was made dependent on the rent level
and therefore on the industry level of production (see Viner 1931). Thus
when the U-shaped cost curve was used with the horizontal Ž rm demand
curve in order to Ž nd the supply price (it was required that the two curves
were tangent), also the size of the ‘representative Ž rm’ was implicitly determined (Sraffa 1925: 350–1). Therefore, as a by-product of the attempt ‘to
reconstruct the passage from the individual supply curve to the collective
curve’ (Sraffa 1925: 342), a new notion: ‘the size of the representative Ž rm’
made its appearance in Sraffa 1925 analysis.
It can be safely concluded, however, that Sraffa in 1925 did not attribute
any meaning to this size. This follows from the statement that under increasing returns ‘[t]he point of maximum economy could be moved in any
381
Giuseppe Freni
direction because of the change [in the industr y output], corresponding to
larger or smaller individual outputs’ (Sraffa 1925: 352), and from the fact
that in the decreasing returns analysis the exact amount of each Ž rm’s share
of the constant factor was totally irrelevant. In summar y, in the 1925 article,
the Ž rm was introduced only to clarify how the aggregate supply curve can
be obtained from the individual curves. And the want of reference to the Ž rm
in the 1960 book can thus be explained by the absence of any interest in this
theme. Adapting Samuelson’s dictum to this situation, the process determined the euthanasia of the concept of Ž rm, but given its effective role in
1925, this ‘is actually an odd way of putting the matter since what need never
exist cannot very well be said to wither away’ (Samuelson 1967: 27).
(B) Both in the 1925 paper and in Production of Commodities non-constant
returns are due either to changes in output or to changes in the proportions of
factors of production. As regards Production of Commodities this is stated in the
Preface:
No change in output and (at any rate in Parts I and II) no changes in the proportions in which different means of production are used by an industr y are considered,
so that no question arises as to the variation or constancy of returns.
(Sraffa 1960: v)
In the 1925 paper, on the other side, a more speciŽ c statement is contained at the beginning of the section on increasing costs:
It is necessary to point out that the ‘supposed circumstances’, which give rise to the
variation of cost [. . .] are the same in the two cases. The circumstances are that, if we
consider, for simplicity’s sake, only two factors, one remains constant while the other
increases. This presupposes: (a) a modiŽ cation in the proportion between the quantities of the two factors; (b) an increase in the size of the industry.
(Sraffa 1925: 327)
That the change in the proportions of factors (with one of the factors
maintained constant) recurring in the above passage, which is generated
by the process that has been analysed in section 4, is the source of decreasing returns also in 1960, is already clear from the analysis of the emergence
of intensive rent (see above). Furthermore, this interpretation is strengthened by the observation that the various concepts used in 1925 for the
analysis of the process were again employed in Production of Commodities (see
point (C) below).
Besides the mentioning in the Preface, nothing is said in Production of
Commodities about decreasing costs. However, if in Production of Commodities
the uniformity of the rate of proŽ ts is due, as it seems likely, to competitive
markets, then, as in 1925, internal economies are to be excluded from the
determinants of decreasing costs (Sraffa 1925: 344–5). Again external
effects remain then the only admissible source of decreasing costs (see
Panico and Salvadori 1994).
382
Sraffa’s early contribution to competitive price theory
(C) In sections 86–9 of Production of Commodities, the plurality of lands
under cultivation is described as the result of ‘extensive’ diminishing
returns and the coexistence of two methods on the same quality of land as
the result of a process of ‘intensive’ diminishing returns (Sraffa 1960: 76).
The processes take place because land is scarce and are shaped by the costminimizing activity of the economic agents. It is this activity that in turn
generates ‘spurious margins’ (Sraffa 1960: 76, vi). The order in which lands
of different qualities are put into cultivation when agricultural output grows
is called the order of fertility. This order, Sraffa adds, is dependent on
proŽ t-wage distribution (Sraffa 1960: 75). Apart from the last remark about
the order of fertility, both the tools and the conclusions of the analysis were
already present in the 1925 pages.
The conditions under which decreasing returns occur and the cause
that produces this effect were carefully speciŽ ed by Sraffa in the 1925
paper at the beginning of the section on increasing costs. Decreasing
returns, he stated, take place when different doses of variable factors are
combined with a ‘constant’ factor, whose quantity cannot be increased,
although it can be typically reduced ‘at the wish of the person using it’
(Sraffa 1925: 327fn 11). Hence it is only because a larger quantity of the
‘constant’ factor would be demanded, if it existed, that the phenomenon
occurs. Furthermore, given the appropriate technical conditions (some
possibility of substitution between factors) and applying the principle of
substitution:
diminishing returns must of necessity occur because it will be the producer himself
who, for his own beneŽ t, will arrange the doses of the factors and the methods of use
in a descending order, going from the most favourable ones to the most ineffective,
and he will start production with the best combinations, resorting little by little, as
these are exhausted, to the worst ones.
(Sraffa 1925: 332)
In connection with the problem of the cause of diminishing returns, Sraffa
then contrasted his own ‘Ricardian’ position with the position he attributed
to neoclassical authors, and in particular to Wicksteed, that made decreasing returns descend from a physical law (Sraffa 1925: 335). In both the conceptions, he said, downward sloping curves are constructed and the
concept of marginal dose is used, but it is only the second kind of margin
that Wicksteed accepted as the foundation of the theor y of distribution
(Sraffa 1925: 336). This distinction, he concluded, is however groundless
since ‘any decreasing curve with a general and not merely an accidental
character, must be a “descriptive curve” ’ (Sraffa 1925: 337). The main
elements of the 1960 analysis are in summary the same ones described in
the initial part of the section on increasing costs of the 1925 article.
As regards the order of fertility, in 1925 its independence from the
383
Giuseppe Freni
intensity of cultivation was examined after the just mentioned criticism of
the distinction between ‘functional’ and ‘descriptive’ curves:
Having examined the objection that the decreasing order of fertility in which the
various pieces of land are arranged is arbitrar y, let us go on to consider another
objection – the denial of the possibility of classifying the pieces of land according to
their fertility, such that the ordering does not change with the increase in the intensity
of cultivation. It is clear that if this were true, the construction of the static curve of
diminishing returns, based on the order of fertility of the pieces of land, would no
longer be conceivable.
(Sraffa 1925: 338)
Then, having rejected the deŽ nitions adopted by Marshall, Malthus and
J. S. Mill, the following notion of order of fertility was given:9
[I]t is best to cultivate Ž rst of all – and must therefore be considered the most ‘fertile’
– that piece of land which, at the point at which its marginal productivity is equal to
the average productivity, has a productivity greater than all other pieces of land.
(Sraffa 1925: 339–40)
And it was remarked:
The order of fertility thus determined does not change with the intensiŽ cation of cultivation since the form of the two productivity curves [. . .] does not change with a
change in the [number of doses employed].
(Sraffa 1925: 340)
In Production of Commodities, mutatis mutandis, the same chain of reasoning
was employed, so that with regards to a given ordering of lands it is stated:
Note that the sufŽ xes are arbitrary and do not represent the order of fertility, which
is not deŽned independently of the rents.
(Sraffa 1960: 75, latter italics added)
In conclusion, the old model elaborated in 1925 was used for the treatment of decreasing returns in the 1960 book. Of course, the aim of the
analysis was different and produced means of production were integrated
in the framework. The old skeleton, however, remained unchanged and is
clearly discernible in what appear to be one of the oldest parts of Production of Commodities .
This point can be further strengthened by arguing that the integration of
produced means of production in the diminishing returns schemes contained in Production of Commodities §§85–90 is incomplete. In particular, two
circumstances point to this incompleteness. The Ž rst reduces to the following fact: (1) an unwarranted relationship between the rent rate and gross agricultural product is postulated in the treatment of intensive rent contained in
§87 of the 1960 book. The second, strictly linked to fact (1), is the following:
(2) The treatment of multiple agricultural commodities is oversimpliŽ ed.
(1) Section §87 of Production of Commodities opens with the following
paragraph:
384
Sraffa’s early contribution to competitive price theory
If land is all of the same quality and is in short supply, this by itself makes it possible
for two different processes or methods of cultivation to be used consistently side by
side on similar lands determining a uniform rent per acre. While any two methods
would in these circumstances be formally consistent, they must satisfy the economic
condition of not giving rise to a negative rent: Which implies that the method that
produces more corn per acre should show a higher cost per unit of product, the cost
being calculated at the ruling levels of the rate of proŽ ts, wages and prices.
(Sraffa 1960: 75)
Hence this statement contains the following postulate: the fact that a
method producing a higher quantity of corn per unit of land does incur
extra costs at the prices, wages and proŽ t rate that are associated with a
method producing a lower quantity of corn per unit of land is necessar y for
economic compatibility of the two methods. This is certainly true for the
model in section 4 (see Ž gure 1), but, as we will see, it does not hold in
general if produced means of production are involved in the framework.
To evaluate the role of produced means of production in the simplest way,
we now contrast the land–labour economy of section 4 with a simple land–
labour–capital economy (in which all commodities are self-reproducing nonbasics). To this end the following straightforward generalization of the rent
functions can be employed. If each commodity enters its own reproduction
together with labour and lands, then section 2 deŽ nition of a process has
to be enlarged to encompass the new technological conditions. Process i is
therefore the triplet
ai, li, ki,
where 1 > ai > 0 is the commodity input per unit of production.
Assume that capital decays at the rate µi, µi ³ 010, and indicate with r, r ³ 0,
the rate of proŽ t. Then the rent function can be updated by solving the
following family of problems:
R(p) = min r
s.t. li + rki ³ [1 2
[P1]
ai(µi + r)]p, 1 £ i £ n
p ³ 0, r ³ 0.
Now the (generalized) derivative of the function is neither the gross output
per unit of land, nor the net output per unit of land. It is instead the hypothetical net output that would result if the depreciation rate were µi + r. It
is therefore a lower bound of gross and net product that is constrained to
grow with the price (and the rent rate). And, in principle, nothing can be
said with regard to the behaviour of the above two variables. Therefore, two
methods can be economically compatible even if the one that is ‘more
costly’ produces a lower quantity of corn per unit of land.
385
Giuseppe Freni
The above facts cannot of course prove our point. The circumstance that
the statement opening section 87 is true when produced means of production are absent, while not holding in general, could however be more
than a coincidence.
(2) A similar argument can be advanced with reference to the treatment
of the multiplicity of agricultural products. In section 89, after some
remarks on cases in which multiple agricultural products are grown on
lands of different qualities, Sraffa stated that ‘in the case of a single quality
of land, the multiplicity of agricultural products would not give rise to any
complications’ (Sraffa 1960: 77).
As before, it is simple to rationalize this statement within the bounds of
a land–labour model, but it seems untenable in more general models.
Indeed, if for simplicity’s sake only two products, q1 and q2, are considered,
then a linear frontier can be obtained from system [7]–[14] for each positive level of the rent rate (see Samuelson’s 1959 ‘land theory of value’,
Samuelson 1959: 12). Moreover, the frontier shifts outwards whenever
rent increases. The above discussion of the properties of rent functions in
land–labour–capital models, however, immediately implies that this comparative statics property evaporates as soon as capital goods are taken
into account. Again, Sraffa’s treatment of decreasing returns Ž ts better an
‘atemporal’ production model than a ‘time-phased’ one.
6. Concluding remarks
Sraffa’s 1925 critique of Marshallian analysis calls for a general equilibrium
treatment of competitive markets and this route was taken by Sraffa in 1960.
However, many elements of the early analysis survived in the new framework. In a sense, the main change was in the subject of analysis. While in
1925 Sraffa focused his attention on the conditions that grant the coincidence of Marshallian supply curves with ‘general equilibrium supply
curves’, in 1960 he mainly concentrated on a single point of the latter curve
in order to examine the problems of distribution. In this perspective
Samuelson’s works on Ricardian economics appear as the natural complements to Sraffa’s analysis. Our Ž nal suggestion is therefore: read Sraffa’s
1925 ‘Sulle relazioni fra costo e quantità prodotta’ with Samuelson’s 1959
‘A Modern Treatment of the Ricardian Theory’ and 1971 ‘An Exact
Hume–Ricardo–Marshall Model of International Trade’ as guides, and
have a look to Samuelson’s 1975 ‘Trade Pattern Reversals in Time-Phased
Ricardian Systems and Intertemporal EfŽ ciency’ in rereading Production of
Commodities.
Istituto di Studi Economici, IUN, Napoli
386
Sraffa’s early contribution to competitive price theory
Notes
* I am grateful to Carlo Panico and Neri Salvadori for helpful discussions at all stages
of the research. I also thank Heinz Kurz and a referee for many useful comments.
1 A sample from some recent articles can help to make clear the point. Consider the
following passages:
As soon as two competitive goods involve different land/labour proportions, the
production possibility frontier is curved and not straight in the fashion Sraffa needs.
(Samuelson 1990a: 268–9)
I here present an impeccable Marshallian model in which (a) each of n goods is
produced by transferable labour and a specialised land speciŽ c to itself, (b) every
person’s demand function for each of the n goods is strictly independent of every
other good’s price or quantity (strongly additive independent utilities), (c) for
every person the marginal disutility of labour is a strict constant (‘objectively’
identiŽ able from market data). The example glaringly contradicts Sraffa’s
constancy of costs and obeys all partial equilibrium requirements (at the same time
that it is a full general equilibrium model, a congruence Alfred Marshall never
quite achieved).
(Samuelson 1990a: 268–9)
Where a large difference exists between the proportions in which the factors are
employed in the industry expanding its output and the proportions in which the
same factors are employed in the industries that will correspondingly have to
contract their output [. . .], the increase in costs cannot be ignored in the
expanding industr y, but for the same reason it will not be possible to ignore it
either in those other industries in which the factors are used in a proportion close
to that of the expanding industry [. . .] [W]here the proportions of factors in the
expanding industr y are almost the same as in the contracting industries. Here, the
effect on the costs of other industries using proportions of factors close to those
of the expanding industry will be small, and so will the effect on the costs of the
industr y in question.
(Garegnani 1990: 285)
2 For each Ž nite set of methods, if ki > 0 for each i, then the rent function is deŽ ned on
the interval [0, ¥). We assume that the application of the operator ‘limnumber of processes®¥’
is not associated with a discontinuity of the set on which the rent function is deŽ ned.
3 This assumption has a purely historical justiŽ cation. In 1925 Sraffa approached the
construction of increasing supply curves by means of the productivity curves (Sraffa
1925: 327–32). Within this framework, the equivalent of the differentiability of the
rent function is the fact that the marginal productivity curve decreases ever ywhere.
Except for the Ž rst part of the curve, it seems that Sraffa took this fact for granted
(however, cf. Sraffa 1925: 333–5, where the technology is a Ž nite set). But he considered as normal the existence of a constant initial part of the curve. The corresponding rent function would, therefore, be ever ywhere differentiable only in ‘the
extreme case in which productivity is decreasing right from the start’ (Sraffa 1925:
340fn. 42).
4 Since it can be shown that there is equivalence between equilibria and solutions
of the maximization problem reported below, a proof of this result, non provided
here, amounts to showing that, under the conditions in the text, a solution of the
problem
387
Giuseppe Freni
max (
n
piqi 2
i=1
s
j=1
rj)
s.t. Rij(pi) £ rj, 1 £ i £ n, 1 £ j £ s
pi³ 0, 1 £ i £ n
rj ³ 0, 1 £ j £ s,
exists for each non negative vector [qi], 1 £ i £ n.
5 Sraffa attributed this position to Marshall (see Sraffa 1925: 358–9).
6 Note that locally commodity [1] is the only basic commodity.
7 We closely follow the analysis presented in Panico and Salvadori (1994) and reach in
part their conclusions.
8 It is true that, in dealing with the case in which the size of the ‘representative Ž rm’
is indeterminate, Sraffa followed his contemporaries ‘in supposing that with ever y
Ž rm in neutral equilibrium, there would be no penalty to having one expand indefinitely until it “monopolized” the industry’ (Samuelson 1967: 29), see Sraffa (1925:
351). Sraffa’s statement was, however, appended to a secondar y passage in which the
Pigouvian notion of ‘simple competition’ was discussed.
9 Remember that, in terms of the rent functions used in section 4, the order of fertility
is obtained by ordering the functions according to the level of price that corresponds
to a zero rent rate.
10 If the production process is discrete, then µi £ 1.
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Abstract
In this paper, Sraffa’s 1925 contribution to competitive price theor y is
reconsidered. It is argued that Sraffa’s 1925 framework of analysis is a
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Giuseppe Freni
‘general’ equilibrium model of the supply side of the economy with many
Ricardian features. It is suggested that Samuelson’s 1959 Ricardian model
and 1971 Marshallian speciŽ c-factors model may help re-analyse Sraffa’s
1925 work along the lines outlined above. It is also contended that the
elements of continuity between Sraffa’s early work and Production of Commodities are more pronounced than commonly believed.
Keywords
Sraffa, partial vs. general equilibrium, supply curves, speciŽ c-factors models
390