Prices, capital, and the one-commodity model in neoclassical and classical theories

 
,         History of Political Economy 21:2
                                                       0 1989 by Duke University Press
                                                       CCC 00 18-2702/89/$1.50

Prices, capital, and the one-commodity model in
neoclassical and classical theories

Avi J. Cohen

                         Such simple models or parables do, I think, have
                         considerable heuristic value in giving insights into
                         the fundamentals of interest theory in all its com-
                         plexities.
                                              -P. SAMUELSON      (1962, 193)

                              I. Ini‘roduction
There are two major price conceptions in the history of economic thought:
the neoclassical conception of price as a scarcity index and the classical
conception of price as an index of the difficulty of production. Each con-
ception is associated with robust results that hold without exception within
the respective one-commodity models that are the subject of this paper:
Samuelson’s surrogate production function and the neo-Ricardian corn
model. These one-commodity models are heuristically important because
in a wide range of more general models, capital-related exceptions arise
for each price conception. Neoclassicals face the exceptions of reswitching
and capital reversal. Modem descendents of classical political economy,
the neo-Ricardians, face exceptions to the inverse wage-rate of profits
relation.
   While numerous papers have debated the significance of these excep-
tions, this article does not attempt to judge whether the exceptions are
significant enough to invalidate the theories involved. The article focuses
instead on a simple prior question. For each price conception, why do
exceptions occur and what is it about the one-commodity model that elim-
Correspondence may be addressed to the author, Dept. of Economics, York University,
4700 Keele Street, Toronto, Ontario CANADA M3J 1P3.

    1. Stigler (1958) assesses the significance of the exceptions to Ricardo’s labour-theory-
of-value-version of the classical price conception while Cohen (1987b) provides a parallel
assessment of the neoclassical price conception. Major assessments of the Cambridge cap-
ital controversies, including the role of the neo-Ricardians, appear in Blaug (1975), Bur-
meister (1980), Hahn (1975, 1982), and Har-court (1972, 1975, 1982). See Cohen (1984a)
for a methodological assessment of why there-is no agreement on significance. On the
controversy over Sraffa’s standard commodity and the inverse wage-rate of profits relation,
see A. Levine (1974, 1975, 1977), Burmeister (1975, 1977), and Eatwell (1975, 1977).

                                                                                        231
232       History of Political Economy 21:2 (1989)

hates the exceptions? The answer to this question will establish the iden-
tical nature of the neoclassical reswitchingkapital reversal problem and
the classical wage-rate of profits problem. Both problems stem from an
incongruity between the endogenous nature of capital and the exogenous
basis of the price conceptions and underlying visions of neoclassical and
classical theories.
   The article is organized as follows: Section I1 traces the neoclassical
conception of price through increasing levels of complexity from the pure
exchange model to the one-commodity model to intertemporal general
equilibrium models. Section I11 similarly traces the classical conception
from the one-commodity model to Sraffa’s system. In Section IV, the prob-
lems caused by capital for each theory are compared and linked to the
respective visions of economics. Section V offers some conclusions.

                     11. The Neoclassical Price Conception
A.    Pure exchange and the one-commodity model
   For neoclassical theory, the fundamental economic problem is the opti-
mal allocation of scarce resources. The simplest illustration of the problem
is a model of pure exchange where preferences and resource endowments
(goods) are given exogenously. In a general qualitative sense, prices reflect
the utility and scarcity of goods.2 Malinvaud (1985, ch. 5 ) presents a typ-
ical pure exchange model exhibiting the basic quantitative propositions of
price determination: (1) If the utility of a good increases, its price in-
creases; (2) As a good becomes scarcer, its price increases. These two
propositions constitute the strong conception of price as an index of re-
source scarcity relative to consumption demand.
   In order to focus on the scarcity issue in what follows, utility/demand
conditions are assumed not to change. Thus the strong conception of price
as a scarcity index entails, ceteris paribus, a unique inverse relationship
between a good’s quantity and its price.
   The significance of the one-commodity model lies in its ability to extend
the results of the pure exchange model to a model with capital and pro-

   2. According to Walras (1954, 69): “Thus any value in exchange . . . partakes of the
character of a natural phenomenon. . . . If [goods] have any value at all, it is because they
are scarce, that is, useful and limited in quantity-both of these conditions being natural.”
(Emphasis in original.)
   3. Malinvaud’s propositions are simply modem restatements of the propositions in Wal-
ras’s (1954, 148) pure exchange model: “Given two commodities in a market in a state of
equilibrium, if, all other things being equal, the utility of one of these two commodities
increases or decreases for one or more parties, the value of this commodity in relation to
the value of the other commodity, i.e. its price, will increase or decrease.
   “If, all other things being equal, the quantity of one of the two commodities in the hands
of one or more holders increases or decreases, the price of this commodity will decrease or
increase .”
Cohen               Prices and one-commodity models                  233

duction, The legitimacy of this extension is not immediately obvious since
in what sense are goods scarce if they can be produced? The conception
of price as a scarcity index can be sustained, however, as long as goods
are produced from exogenously given resources under conditions of di-
minishing productivity. Production is seen as simply transforming one set
of scarce resources into a different set of consumption goods. As Solow
(1963, 14) notes “the theory of capital is after all just a part of the funda-
mentally microeconomic theory of the allocation of resources, necessary
to allow for the fact that commodities can be transformed into other com-
modities over time.”
   Samuelson’s (1 962) one-commodity model has a well-behaved produc-
tion function. In competitive equilibrium, the price of labour (the wage
rate) is determined by the relative scarcity and marginal productivity of
labour. The marginal product of labour, dYldL, is a ratio of two physical
magnitudes that are independent of prices. Analogously, the price of cap-
ital services (the rate of interest) is determined by the relative scarcity and
marginal productivity of aggregate capital. Since capital and output are
the same good, the marginal product of capital, dYldK, is a technological
datum also measurable in strictly physical quantities. The explanations of
the wage rate and interest rate do not depend on prices. Resources are
physical substances measurable independently of distribution that can ex-
plain distribution. Because the prodiuction function is well-behaved, as a
resource becomes scarcer, its price increases. There is a unique inverse
relation between factor intensity and relative factor price. Even with pro-
duction, (factor) prices in the one-cclmmodity model (in the form of phys-
ical returns to factors of production) reflect relative scarcities.5
   Samuelson attempts to extend these results to a model with heteroge-
neous capital goods. His parable assumes a variety of physically distinct
capital goods, each of which, when combined with labour, can be used to
produce either more of the capital good or a consumption good. A critical
further assumption is “that the same proportion of inputs is used in the
consumption-goods and [capitall-goods industries” (Samuelson 1962,
196-97). The significance of the equal factor proportions assumption is
that the relative prices of consumption and capital goods are independent
of changes in the distribution of income between wages and profits. As in
the one-commodity model, capital can be measured independently of dis-

    4. Bliss (1975, 3-4) asks a similar question specifically about capital: “How can the
ownership of something which ultimately is not scarce, because augmentable by new pro-
.duction, command a rent?”
    5 . Pasinetti (1969, 519) states that in a one-commodity (corn) model the “inverse mon-
otonic relationship between physical rate of profit and existing stock of corn would permit
an extension to the rate of profit of the marginal theory of prices (which, as is well known,
interprets prices as indexes of scarcity). The smaller-i.e. the scarcer-the existing quan-
tity of corn, the higher the physical rate of return (and of profit).”
234      History of Political Economy 21 :2 (1989)

tribution and has an unambiguous physical marginal product that can ex-
plain the rate of interest.
   Samuelson ( 1976, 18) subsequently recognized that the parable turns
out to be nothing more than a special case of the one-commodity model.
“Thus, as Garegnani properly pointed out to me prior to the completion of
my 1962 paper . . . it is only when the same production function can be
written for the consumption good and the capital good sector, so that they
in effect collapse into one sector, that the [one-commodity results are
valid].” As is now widely recognized (Garegnani 1970; Ferguson and
Hooks 1971; Pasinetti 1969; Spaventa 1970), identical production tech-
niques cannot produce physically heterogeneous commodities. Samuel-
son’s parable collapses back into the one-commodity model.
B . Heterogeneous commodities and intertemporal general
      equilibrium
   The results of the one-commodity model do not necessarily hold in more
general heterogeneous commodity models. The unique inverse relation
between capital intensity and the rate of interest as well as the strong
conception of price as a scarcity index are both violated by the possibilities
of reswitching and capital reversing.
   In aggregate models with truly heterogeneous commodities, the interest
rate is no longer determined by a purely physically defined marginal prod-
uct of capital. Changes in the relative scarcity of a capital good no longer
affect just the technical productivity of capital but also the relative prices
of consumption and capital goods. Once the relative prices of consumption
and capital goods can vary, the marginal product of capital becomes dvalue
outputldvalue capital. Scarcity, the technical productivity of capital, and
prices now determine the interest rate. Distribution depends not only on
independent physical magnitudes, but also on prices which, in turn, de-
pend on distribution. The straightforward physical account of the inverse
relation between capital intensity and the rate of interest now becomes a
partially circular account with the addition of price changes.
   It is this complication of price changes, resulting from the differing
factor proportions underlying the production of heterogeneous commodi-
ties, that allows for the well-known possibilities of reswitching and capital
reversing (Harcourt 1972; Samuelson 1966). Reswitching-where the
same technique is preferred at two or more rates of interest while other
techniques are preferred at intermediate rates-violates the uniqueness of
the relation between capital intensity and the rate of interest. More impor-
tantly, the inverse nature of that relation is violated by capital reversing-
a positive relation between capital intensity and the interest rate.
   With capital reversing, a “lower capital/labour ratio” is associated with
a lower interest rate. In comparing two equilibrium positions, it is as
Cohen               Prices and one-commodity models                    235

though capital services have a lower price in the position where capital is
“more scarce.” The price of capital services need not reflect capital’s rel-
ative scarcity and the prices of other ,goods produced with capital need not
accurately reflect the scarcity of resource inputs. The universality of the
strong conception of price as a scarcity index is violated (Garegnani 1966,
 1970; Pasinetti 1969, 1970).
   Neoclassicals often argue that intertemporal general equilibrium models
avoid the problems of aggregate models (Hahn 1982; 373; Ferguson 1972,
 164) as well as provide the most general version of the optimal allocation
of scarce resources. What insight do general equilibrium models provide
into the relationship between the quantity of capital and the rate of interest
and into the conception of price as a scarcity index? Fortunately, Bliss
( 1975) provides an excellent treatment of these issues, the results of which
are briefly summarized here.
   A complication arises at the general equilibrium level regarding the
meaning of the rate of interest. Both in the neoclassical one-commodity
model and the equal factor proportioris model, the rate of interest ( r ) is the
price of capital services in that it measures the cost of capital services.
Since the price of capital (PJ never changes in these models, changes in
the rate of interest are uniquely and directly related to changes in the cost
of capital services. In general equilibrium models, the rate of interest is
not the cost of capital services. Since in general equilibrium models the
price of capital can vary, “the cost of using the capital good-the price
which will stand in the same relation to capital as the wage rate does to
labour-must include both the influence of the interest rate and the influ-
ence of the price of the capital good” (Bliss 1975, 83). Capital can no
longer be defined in physical terms as in the one-commodity model. In
general equilibrium models, as in the case of reswitchingkapital reversal,
price enters into the definition of the cost of using capital ( r - P k ) .
   Intertemporal general equilibrium results are generated from compara-
tive static exercises for pairs of economies along different semi-stationary
growth paths. Despite numerous simplifying assumptions necessary to
make the general equilibrium models; tractable,6 the simple results of the
one-commodity model are not sustained. Bliss demonstrates (1975, 82)
that there is no necessary inverse reladion between the rate of interest and
the quantity of capital. This result alone is not definitive since the rate of
interest is not the cost of using capital. However, he also demonstrates that
    6 . An economy in semi-stationary growth g,rows in scale over time while never changing
its structure ( i . e . , relative prices remain unchanged). The most important assumptions nec-
essary to make tractable comparisons of semi-stationary growth paths include: 1) every pair
of semi-stationary states have proportional capital vectors and proportional consumption
vectors, 2) constant returns to scale, 3) exogenously given rates of growth and rates of
interest, and 4) own-rates of interest are equal for all goods. See Bliss (1975) for the com-
plete set of assumptions.
236       History of Political Economy 21 :2 (1989)

there is no necessary inverse relation between the cost of capital services
and the quantity of capital. For these exercises, the only exception occurs
in the stationary state. Only when there is no net production is there an
inverse relation between the cost of capital services and the quantity of
capital. In general though, the reswitchingkapital reversal results appear
at the general equilibrium level.
   In a critical passage, Bliss (1975, 8 1-82) addresses directly the counter-
intuitive nature (relative to the one-commodity model results) of the gen-
eral equilibrium results.
  If anyone has a feeling that capital should command a lower rental .in
  a state in which it is more abundant compared to alternative inputs he
  is probably giving his consideration only to the influence of the cost
  of the capital service on demand for it as an input. But in semi-
  stationary growth the more capital abundant path produces capital
  more abundantly, as well as using it more freely, and the price of the
  capital good . , . must be such [i.e., high] as to make it profitable to
  do so. There are then two forces . . . pulling in opposite directions.
  A large production of the capital good . . . makes for a high [price
  of capital] which in turn exerts an upwards influence on [the cost of
  capital services ( r - Pk)]. The use of a large volume of capital ser-
  vices relative to labour time makes for a low [price of capital goods
  and hence a downward influence on the cost of capital services].
  From these considerations it may be seen at once why the stationary
  state is a special case for which a strong result is obtainable: for the
  stationary state is not a net producer of the capital good so that the
  first influence is moribund.
As long as there is net production of capital goods, there is no necessary
inverse relation between the cost of capital services and the quantity of
capital.
  Thus while prices in general equilibrium models reflect the utility and
scarcity of goods in a general qualitative sense, Bliss (1975, 85) concludes
that the strong conception of price as a scarcity index is not necessarily
valid:7
  Even people who have made no study of economic theory are familiar
  with the idea that when something is more plentiful its price will be
  lower, and introductory courses on economic theory reinforce this
  common presumption with various examples. However, there is no
  support from the theory of general equilibrium for the proposition
  7. Hahn (1981, 128) also concludes that neoclassical general equilibrium theory “is not
committed to a relative scarcity theory of distribution.”
Cohen        *     Prices and one-commodity models                   237

  than an input to production will be cheaper in an economy where
  more of it is available.

                      111. The Classical Price Conception
A. Prices ofproduction and the one-commodity model
   For modern classicals who see Sraffa as the culmination of a classical
tradition with its most important roots in Ricardo, the fundamental eco-
nomic problem is the allocation of surplus output to ensure the reproduc-
tion and growth of the economy (Dobb 1973; Walsh and Gram 1980).
Analysis of this problem involves the classical conception of “prices of
production” which cover long-run costs of production plus !iuniform rate
of profits. For a given output, these prices (and the rate of profits) are
independent of demand and depend only on the exogenously given tech-
nical conditions of production and the real wage.8 Although the distribu-
tional determinant of price is not ignored, in a general qualitative sense
prices reflect “the objective ‘difficulty of production,’ be it represented by
a single magnitude (labor-contained) or the set of technical coefficients of
production” (Roncaglia 1982, 343) .9
   Within the classical tradition there is also a stronger conception of price
as an index of the difficulty of production. Under conditions discussed
below, the distributional and technical determinants of prices of production
collapse into a unidimensional quantity of physical inputs that is both pro-
portional to price and independent of changes in distribution. In other
words, the strong conception of price entails a unique positive relation,
independent of changes in distribution, between a good’s physical index
of difficulty of production and its price.
   The simplest conception of the classical problem (as well as an implicit
illustration of prices of production))is in the one-commodity corn model
which Sraffa claims provides the “rational foundation” for Ricardo’s Essay
on profits. l o Seed corn and labour produce more corn. The quantity of corn
output is determined exogenously by the levels of population and accu-
mulation, and the real wage is an exogenously determined quantity of

   8. The fixed wage model is the simplest model containing the essential features of the
classical tradition. See Walsh and Gram (1980) for other variations in classical models.
   9. According to Meek (1977, 160), classical authors “all explain prices and profits in
terms of . . . the ‘conditions of production’-meaning by this both the technological con-
ditions and the sociological conditions.” WaYsh and Gram (1980, 177) make a similar state-
ment. For Ricardo (I:217) “The natural price of commodities, which always ultimately
governs their market price, depends on the facility of production.” See also (I:273, 385),
(IV:375, 397) and ( 1 x 2 3 9 ) .
    10. Sraffa’s interpretation of Ricardo is simply accepted here. For an alternative inter-
pretation see Hollander ( 1979).
238       History of Political Economy 2 I :2 ( I 989)

corn. Inputs and outputs are measured in the same physical unit (corn) and
profits are determined on marginal land as a residual: the surplus of output
over inputs necessary for production. The rate of profits (r)’ is defined as:
                quantity outputs (in corn) - quantity inputs (in corn)
         r =                                                                            (1)
                              quantity inputs (in corn)
   As the population grows and accumulation progresses, less-fertile land
is brought under cultivation requiring more labour (corn) input and yield-
ing less output. Rents rise, the surplus and profit rate in agriculture fall,
and the incentive slackens for further accumulation and growth. An ex-
ogenous increase in the real (corn) wage will also cause the profit rate to
fall.
   Within the corn model these inverse (rent-rate of profits and wage-rate
of profits) distributional relationships are clear and independent of changes
in relative prices because there are no relative prices to change. Surpris-
ingly, though, the corn model also illustrates the principle determining
relative prices of production.
   How can a one-commodity model illustrate the determination of relative
prices? Recall that Samuelson’s one-commodity model still determines
relative factor prices in the form of physical returns to factors of produc-
tion. That is not the case in the neo-Ricardian one-commodity model. The
wage is given exogenously, and the rate of profits is interpreted not as a
factor price but as a measure of the ability of the production system to
generate a surplus.
   Nonetheless, the corn model allows the construction of a unidimensional
quantitative index of the difficulty of producing corn. A relative price of
corn depends initially on the technical conditions of corn production and
the real wage. For a given corn output, the natural fertility of the soil sets
the technical conditions which consist of necessary seed corn and labour.
Because the real wage is defined in corn, the technical and distributional
determinants of the corn “price” collapse into a unidimensional quantity
of corn inputs. Although there are no true relative prices in the model,
there is a relative increase in the index of corn inputs as the cultivation of
less-fertile land increases the difficulty of producing a given corn output.
   To transform this rising index into a true rising relative price would
require comparison with other commodities. In the Essay, Ricardo (IV: 19)
moves beyond the one-commodity model to make just such a comparison.
“The exchangeable value of all commodities, rises as the difficulties of

   1 1 . The rate of interest and the rate of profits share the same dimension (a percentage
per time period) and are treated equivalently to facilitate comparison between neoclassical
and classical theories. However, these terms have conceptually different meanings within
their respective theories. See Harcourt (1986, 86-87), Walsh and Gram (1980, 236) and
below, Section I11 A.
Cohen        *      Prices and one-commodity models                   239

their production increase. If then new difficulties occur in the production
of corn, from more labour being necessary, whilst no more labour is re-
quired to produce gold, silver, cloth, linen, &c. the exchangeable value of
corn will necessarily rise, as compared with those things.” According to
Sraffa (Ricardo 1:xxxiii-xxxiv), this quotation foreshadows Ricardo’s la-
bour theory of value which will explain explicitly relative prices using the
strong conception of price as an index of the difficulty of production. But
the one-commodity model already contains the basic principle of this price
conception.
   The advantage of the one-commodity model, in Sraffa’s (Ricardo
1:xxxii) words, “is that at the cost of considerable simplification, it makes
possible an understanding of how the rate of profit is determined without
the need [to mention price] .” A second, previously ignored advantage of
the one-commodity model is that at the cost of considerable simplification,
it also makes possible an understanding of how prices of production (as
indexes of the difficulty of production) are determined without the need to
mention price.
   The one-commodity assumption bore the brunt of Malthus’s criticism of
the Essay. Malthus argued that corn production requires both corn and
manufactured inputs, and that the real wage includes both corn and man-
ufactured goods. l 3 Heterogeneous commodities call into question the corn
model’s theory of profits and its ability to collapse the technical and dis-
tributional determinants of price. In order to respond to Malthus, Ricardo
was forced to develop a theory of relative prices for expressing his theory
of profits.
    12. The one-commodity model’s illustration of the strong classical conception of price
must not be overstated. The model illustrates changes in distribution which are independent
of changes in relative prices only because there are no relative prices. It also illustrates the
collapse of the technical and distributional d.eterminants of price into an index of corn inputs
that increases with the increased difficulty of producing corn. The model cannot, however,
illustrate the independence of index-determined relative prices from changes in distribution.
Distributional changes between wages and profits, due to an increase in either the difficulty
of producing corn or the corn wage, increase the index of corn inputs. To sustain the strong
price conception these distributional changes must affect equally the physical indexes de-
termining the prices of all other commodities so that no relative prices change.
    While Ricardo does not demonstrate this result until he uses the labour theory of value
in a heterogenous commodity model, the Essay (IV:20) again foreshadows the result:
“Wherever competition can have its full effect, and the production of the commodity be not
limited by nature, as in the case with some wines, the difficulty or facility of their produc-
tion will ultimately regulate their exchangeable value. The sole effect then of the progress
of wealth on prices, independently of all improvements, either in agriculture or manufac-
tures, appears to be to raise the price of raw produce and of labour, leaving all other com-
odities at their original prices, and to lower general profits in consequence of the general
rise of wages.”
    13. In a letter to Homer, Malthus (Ricardo VI:187-88) writes: “On the supposition
which is generally allowed, that in a rich and progressive country, corn naturally rises
compared with manufactured and foreign commodities, will it not follow that, as the real
capital of the farmer which is advanced does not consist merely in raw produce, but in
240          History of Political Economy 2 I :2 ( I 989)

   In the Principles, Ricardo (I: 11) uses the labour theory of value to give
substance to the conception of relative prices that is only implicit in the
corn model and merely asserted in the Essay. “The value of a commodity,
or the quantity of any other commodity for which it will exchange, de-
pends on the relative quantity of labour which is necessary for its produc-
tion, and not on the greater or less compensation which is paid for that
labour.”
   Under certain conditions, the corn model results are sustained even
where outputs and inputs are heterogeneous commodities and must be
aggregated in value terms to calculate the profit rate in terms of a surplus
of value of outputs over value of inputs. With equal factor proportions (and
capitals of equal durability) in all sectors, prices are independent of
changes in distribution between wages and profits. The values of both
outputs and inputs, although no longer measurable in purely physical
quantities, remain unchanged as r and w change. An exogenously given
real wage uniquely determines the rate of profits. An increase in the real
wage will increase the value of the real wage bundle (inputs) without af-
fecting other prices (outputs) so r, now defined as
                  value outDuts - value inmts
         I    -

                           value inputs
must fall.
   The equal factor proportions assumption makes prices not only indepen-
dent of distribution but also proportional to the exogenously given quantity
of (direct and indirect) labour embodied in each commodity. The technical
and distributional determinants of prices of production collapse into a
quantity of physical embodied labour that is proportional to price. These
features of the labour theory of value make it the prototypical example of
the strong classical conception of price as an index of the difficulty of
production that is independent of changes in distribution.
   Thus, the equal factor proportions model sustains and strengthens the
corn model results: 1) the inverse wage-rate of profits relation and 2) the
strong conception of price as an index of the difficulty of production.
Whereas in the corn model the price conception is only implicit and the

ploughs waggons threshing machines &c: and in the tea sugar clothes &c: &c: used by his
labourers, if with a less quantity of raw produce he can purchase the same quantity of these
commodities, a greater quantity of raw produce will remain for the farmer and landlord,
and afford a greater surplus from the land for the maintainance and encouragement of the
manufacturing and mercantile classes. . . .
   “The fault of Mr. Ricardo’s table which is curious, is that the advances of the farmer
instead of being calculated in corn, should be calculated either in the actual materials of
which the capital consists, or in money which is the best representative of a variety of
commodities. The view I have taken of the subject would greatly alter his conclusions.”
Cohen        -     Prices and one-commodity models                  241

difficulty of production is measured in corn inputs, in the equal factor
proportions model the conception is explicit and the difficulty of produc-
tion is measured in embodied labour inputs.
   Unlike Samuelson, Ricardo’s assumption of equal factor proportions
does not preclude the production of physically heterogeneous commodi-
ties. However, as in Samuelson’s parable and in the corn model, price
variations caused by changes in distribution are ruled out by assumption.
Ricardo’s equal factor proportions model goes no further than the corn
model in analyzing the price-distribution linkage that is crucial for both
the theory of profits and the strong classical price conception.
B . Heterogeneous commodities and SrafaS system
   An unrestricted analysis of heterogeneous commodites requires relaxing
the assumptions of equal factor proportions and equal durability of capital.
Without these assumptions the corn model results are “considerably mod-
ified” (Ricardo I:30-43).
   The strong conception of price as an index of the (labour-embodied)
difficulty of production is violated because changes in distribution between
wages and profits can affect a commodity’s relative price even when its
physical inputs remain unchanged. With prices dependent upon changes
in distribution, the technical and distributional determinants of price can
no longer be collapsed into a quantity of physical inputs with a necessary
unique positive relation to price.
   Once prices of outputs and inputs! depend on r, the determination of r
by equation (2) becomes a circular argument (Garegnani 1984, 301): “If
the value expression of either aggregate [output or input] were to depend
on r, the determination of profits as a surplus in accordance with [equation
(2)] is threatened by circular reasoning.” For example, if input industries
have “high capital/labour ratios” and output industries have “low capital/
labour ratios,” an increase in the real wage will increase the price of output
relative to inputs, making it uncertain whether r must fall.14 The inverse
wage-rate of profits relation is no longer guaranteed. “The constraint by
which one class cannot have more without the other class having less-so
evident if we could look at the product in physical terms-is no longer
apparent: might not the real wage rise without affecting the rate of profit,
or vice versa?” (Garegnani 1984, 301-302).
   According to Sraffa (Ricardo I:xlviii), this inability to guarantee an in-
   14. As the result of a rise in the value of labour: “All commodities which are produced
by very valuable machinery, or in very valuable buildings, or which require a great length
of time before they can be brought to market , would fall in relative value, while all those
which were chiefly produced by labour, or which would be speedily brought to market
would rise in relative value” (Ricardo I:35). Sraffa (1960, 14-15) points out that relative
price movements in fact depend not only on industries’ factor proportions but also on the
factor proportions of all input industries back through time.
242       History of Political Economy 21:2 (1989)

verse wage-rate of profits relation motivated Ricardo’s search for an in-
variable measure of value. “Thus the problem of value which interested
Ricardo was how to find a measure of value which would be invariant to
changes in the division of the product; for, if a rise or fall of wages by
itself brought about a change in the magnitude of the social product [out-
put], it would be hard to determine the effect on profits.”
   Modern classicals view Sraffa’s system as the solution to this problem
of an invariable measure of value as well as the most general version of
the problem of the allocation of surplus output for reproduction and
growth. In what sense does the Sraffa system sustain the corn model’s price
conception and theory of profits which are violated in the unrestricted
heterogeneous commodity model?
   In answering this qustion, Sraffa constructs a model where labour is the
only non-reproducible input in a general production system whose as-
sumptions includeI5 as exogenously determined: 1) the technical condi-
tions of production in the form of a fixed coefficient, input-output
production matrix, 2) the size and composition of output, and 3) either the
real wage bundle or the rate of profits.I6
   Relative prices are’ classical prices of production, determined by the
technical conditions of production and the rate of profits. In the special
case where the rate of profits is zero, each commodity’s vector of hetero-
geneous physical inputs can be collapsed to a scalar quantity of embodied
labour which equals relative price. But in general, the technical and dis-
tributional determinants of price cannot be collapsed into a unique un-
dimensional quantity of physical inputs. Sraffa’s general system does not
sustain the strong conception of price as an index of the difficulty of pro-
duction. I7
   Sraffa addresses the inverse wage-rate of profits relation by constructing
his solution to the invariable measure of value problem, the Standard sys-
tem. The Standard system is a unique, reduced-scale subset of the general
production system in which outputs are produced in the same proportions
as their reproducible non-labour inputs. The relationship between outputs
and inputs in the Standard system is determined solely by technical con-
ditions of production and is unaffected by changes in distribution between
wages and profits.
   Because of the invariance to distributional changes, the Standard system
yields a result similar to that of equation (I), where the profit rate depends
only on the conditions of production and the real wage. “Thus in the Stan-

   15. See Sraffa (1960) or Pasinetti (1977, ch. 5) for a complete set of assumptions.
   16. For models where the wage is not fixed at subsistence, Sraffa (1960, 33) tends to fix
exogenously the rate of profits.
   17. Neo-Ricardians criticize the labour-theory-of-value-version of the strong classical
price conception. See Steedman ( 1977).
Cohen             Prices and one-commodity models                 243

dard system the ratio of the net product [outputs-inputs] to the means of
production [inputs] would remain the same whatever variations occurred
in the division of the net product between wages and profits” (Sraffa 1960,
21). The ratio to which Sraffa refers represents the maximum rate of profits
R (when wages = 0), since unlike the corn model, wages in the Standard
system are not treated as inputs but instead are paid out of the net product
post factum. When the real wage ( w ) is expressed as a fraction of the
Standard net product, (0 G w d l ) , the rate of profits is
        r = R(1-w)                                                                    (3)
The corn model theory of profits obtains since there is a linear inverse
relation between the rate of profits. and the real wage. The Standard sys-
tem, like the corn model, makes tra.nsparent the inverse wage-rate of prof-
its relation which in the general system may be obscured by relative price
changes (Sraffa 1960, 23).
   Despite this accomplishment, there is an important difference between
the inverse wage-rate of profits relation in the corn model and in Sraffa’s
model. The difference concerns the nature of wage goods. In the corn
model, labour is reproduced by consuming an exogenously determined
corn wage. Labour inputs are treated as a quantity of corn which enters a
production system “on the same footing as the fuel for the engines or the
feed for the cattle” (Sraffa 1960, 9). The real wage is part of the given
technical conditions of production.
   In contrast to the corn model, Sraffa’s general system does not restrict
the composition of the real wage. Once the rate of profits is given, the real
wage bundle can be any subsetI8 of the surplus output bundle equal in
value to the value of the appropriate fraction of the Standard net product. l 9
The composition of the real wage bundle can be interpreted as exogenously
determined. This interpretation is consistent with the exogenous determi-
nation of the real wage level and the composition of output in Sraffa’s
system. All three inter-related consumption parameters are determined by
the same exogenous conditions,
   This consistency breaks down in the analysis of changes in the real
wage. Consider, e.g., an exogenous decrease in the rate of profits that
yields an increase in the real wage level. A new real wage bundle can be
chosen from the surplus output bundle equal in value to the now larger
fraction of the Standard net product. To sustain the inverse wage-rate of
profits relation, however, the increase in the real wage level is assumed
nut to alter the composition of output even though it can alter the com-

   18. Subsistence can be guaranteed “by setting a limit below which the wage cannot fall”
(Sraffa 1960, 10).
   19. See Kurz and Salvadori (1987) for a correction of Burmeister’s (1984) mistaken
belief that Sraffa’s results depend on workers actually consuming the Standard commodity.
244      History of Political Economy 21:2 (1989)

position of the real wage bundle. This is inconsistent treatment of the
inter-related consumption parameters. Since workers’ consumption is a
significant component of total output, one would expect that a change in
exogenous conditions affecting the level and composition of workers’ con-
sumption would also affect the composition of total output.
   Thus while prices in Sraffa’s analysis reflect the difficulty of production
in a general qualitative sense, the strong conception of price as an index
of the difficulty of production is not necessarily valid. The only strong corn
model result Sraffa’s analysis sustains is the inverse wage-rate of profits
relation and that relation uses a questionable assumption eliminating the
impact of real wage changes on the composition of output. While it is
legitimate to determine exogenously all output parameters, it is not legit-
imate to allow changes in a subset of total output (the wage bundle) yet
hold total output constant.

                      IV    The Problems with Capital
A.      Capital and the conception of price
    For both neoclassical and classical theories, strong conceptions of price
and robust determinations of the rate of interest/profits are sustained under
the condition where prices are invariant to changes in distribution. This
condition holds in a one-commodity model and in an equal factor propor-
tions model that effectively reduces to a one-commodity model.
    For neoclassical theory, price invariance allows all resources, including
capital, to be defined in exogenously given physical quantities. In turn,
the rate of interest is determined by the physical marginal product of cap-
ital depending solely on the technology and the scarcity of capital relative
to consumption demand. All prices, including the price of capital services
( r ) ,reflect the relative scarcities of the exogenously given resources.
    For classical theory, price invariance allows the difficulty of production
of all goods to be defined in exogenously given unidimensional quantities
of physical inputs. Because prices reflect relative difficulties of production
and not changes in distribution, an increase in the real wage will not affect
the price of output but will cause the rate of profits to fall.
    In the more general heterogeneous commodity models of each theory
examined here, prices vary with changes in distribution. This causes crit-
ical exogenous conditions of each one-commodity model to become en-
dogenous.
    Instead of being determined by exogenously given physical magnitudes,
the rate of interest in neoclassical theory depends on prices, which in turn
depend on the rate of interest. The internalization of the measure of capital
is the source of the possibilities of reswitching and capital reversal. As a
result, the rate of interest (or, more generally, the cost of capital services)
Cohen      -    Prices and one-commodity models           245

will not necessarily reflect the relative scarcity of capital, and the strong
conception of price as a scarcity indlex need not obtain.
   Once prices vary with changes in distribution, the strong classical con-
ception of price as an index of the exogenous difficulty of production is
immediately violated. The rate of profits, which previously depended only
on exogenously given physical magnitudes of outputs and inputs, now
depends on the prices of outputs and inputs, which in turn depend on the
rate of profits. This internalization of the measure of inputs to production
eliminates the necessity of an inverse relation between the real wage and
the rate of profits.
   The reswitchingkapital reversal problem and the inverse wage-rate of
profits problem are identical in that both problems stem from the inability
to use exogenously defined physical magnitudes to determine prices in
heterogeneous commodity models. Eloth problems reflect exceptions to the
simple robust theories of the rate of interest/profits as well as to the strong
price conceptions of neoclassical and classical theories. It is not accidental
that these problems arise in conjunction with capital goods. There is a
basic incongruity between the existence of capital and both strong neo-
classical and classical conceptions of price.
   Prices in neoclassical theory reflect the scarcity of exogenously given
resources relative to consumption demand. As a produced resource, the
measure of the quantity of capital is not exogenously given, violating the
notion of scarcity based on a@ed quantity of resources. The incongruity
of production with the neoclassical conception of scarcity is reinforced by
findings of intertemporal general equilibrium models. In Bliss’s stationary
state general equilibrium model witlhout net production, the strong con-
ception of price as a scarcity index is sustained. But with net production
the strong conception is violated because the existence of capital makes
the measure of resources endogenous.
   Prices in classical theory reflect the difficulty of production, defined as
an exogenously given quantity of phlysical inputs (per unit of output). As
aproduced input, the measure of the quantity of capital is not exogenously
given. The strong classical conception of price is violated because the
existence of capital makes the measure of the difficulty of production en-
dogenous.
B.   Capital and visions of economic analysis
   The existence of capital is not only incongruous with the strong price
conceptions of neoclassical and classical theories, but also with the re-
spective visions (Schumpeter 1954) underlying the theories. All economic
theories recognize the mutual interdependence of production, consump-
tion, distribution, and exchange. A vision makes that complex interdepen-
dence analytically manageable by focusing more attention on some aspects
246       History of Political Economy 2 I :2 ( I 989)

of the interdependence than others and by delineating exogenous parame-
ters and endogenously determined variables.2o
   Corresponding to the two major conceptions of price in the history of
economic thought are two major visions. The neoclassical vision is “con-
sumer exchange with nature” and the classical vision is “production by
nature.” The word “nature” has a two-fold meaning. The literal meaning
is nature-given conditions such as the fertility of the soil in the corn model.
The second meaning is exogenous conditions or parameters. Thus the vi-
sions can be re-stated as “consumer exchange with an exogenously given
set of conditions (resources)” and “production by an exogenously given
set of conditions (required inputs).”
   In the neoclassical vision, consumption and exchange are given primary
consideration. If the fundamental economic problem is the allocation of
given scarce resources for optimal satisfaction in consumption, the prob-
lem can be conceptualized without production in a pure exchange model.
The focus is on consumer exchange with nature.2i The problem can be
generalized to include production. But since production is not an integral
part of the neoclassical vision, when capital, production, and firms are
incorporated into the vision “the firm is a shadowy figure” (Hahn 1981,
131).22Production is conceived of as an indirect form of exchange for the
purpose of satisfying the goal of c o n ~ u m p t i o n . ~ ~
   Capital and production are problematic because of their incongruity with

    20. These characteristics of vision are not both obvious at the level of general equilib-
rium models. Although parameters and variables are obvious in such models, a set of si-
multaneous equations does not reveal any focus on some variables as more important than
others. Such a focus can be seen, however, at the level of vision and in the one-commodity
models. For an elaboration of the concept of focus or “priority of causation” in both eco-
nomic visions and general equilibrium models see Cohen and Cohen (1983).
    21. The predominant focus on exchange can be seen in Walras’s (1954, 143) claim that
the following proposition about exchange contains the gist of his entire model: “The ex-
change of two commodities f o r each other in a perfectly competitive market is an operation
by which all holders of either one, or of both, of the two commodities can obtain the
greatest possible satisfaction of their wants consistent with the condition that the two com-
modities are bought and sold at one and the same rate of exchange throughout the market.
    “The main object of the theory . . . is to generalize this proposition by showing, first,
that it applies to the exchange of several commodities for one another as well as to the
exchange of two commodities for each other, and secondly, that, under perfect competition,
it applies to production as well as to exchange. The main object of the theory of production
. . . is to show how the principle of organization of agriculture, industry and commerce can
be deduced as a logical consequence of the above proposition. We may say, therefore, that
this proposition embraces the whole of pure and applied economics” (Emphasis in original).
On the natural character of exchange in Walras see footnote 2.
    22. The insecure status of the firm is evident in Walras (1954, 225): “Assuming equilib-
rium, we may even go so far as to abstract from entrepreneurs [i.e., firms] and simply
consider the productive services as being . . . exchanged directly for one another, instead
of being exchanged first against products, and then against productive services. . . . Thus,
in a state of equilibrium in production, entrepreneurs make neither profit nor loss. They
make their living not as entrepreneurs, but as land-owners, labourers or capitalists.”
    23. “The great founders of the neo-classical school, Carl Menger, W. S. Jevons, and
Leon Walras, and their precursors, A. A. Cournot and H. H. Gossen, took as an expository
Cohen              Prices and one-commodity models                   247

the vision of consumer exchange with naturally given resources. The price
invariance of the one-commodity model avoids the incongruity by allow-
ing all resources (including capital) to be treated as though they are ex-
ogenously given (not produced). The neoclassical vision of consumer
exchange with nature is sustained.
   Production is the primary focus of the classical vision. If the fundamen-
tal economic problem is the allocation of surplus output to ensure repro-
duction and growth, the simplest conceptualization of the problem is as
production by nature in the corn             Production and growth are de-
termined by the fertility of the soil and the given real wage. Labourers
consume only corn so that all required inputs (including labour) collapse
into an exogenously given quantity of corn. The real wage in Sraffa’s
system is not restricted to corn. But all consumption-related terms-the
levels and compositions of both the real wage and output-are still deter-
mined exogenously, making the consumer a shadowy figure. Consumption
is conceived of as an indirect form of exchange for the purpose of satis-
fying the goal of production.
   Even after relegating consumption to the realm of exogenous parame-
ters, problems arise in incorporating capital into the vision of production
by exogenously given inputs. Because capital is produced, the required
inputs or difficulty of production cannot be defined exogenously. The price
invariance of the one-commodity model avoids these problems by allowing
all required inputs for production to be treated as though they are exoge-
nously given. The classical vision of production by nature is sustained.
                            V. Conclusions
   The problems associated with the theory of capital are not accidental or
due simply to the complexity of the subject matter. The existence of cap-
ital, as an endogenously produced commodity, creates exceptions to both

point of departure a model which was the polar opposite of the classical, the model of pure
exchange. They recognized the importance of production, but Menger and Jevons especially
put stress on the notion of exchange as expressing the essence of the economic system;
production to some extent appeared merely a:; an indirect way of exchanging initial hold-
ings’’ Arrow and Starrett (1973, 133). Hirshleifer (1970, 12) uses a natural metaphor similar
to the one used here in describing the neoclassical approach to production: “[production
involves] transformations of commodity-combinations effected through dealing with Nature
rather than through exchange with other economic agents. . . . Or to put it another way,
production is ‘exchange’ with Nature, while exchange proper represents redistribution of
the commodities already made available with the help of Nature.”
   24. D. Levine (1974) argues that Ricardo’s attempt to generalize the determining role of
production by nature in the corn model can be seen in the language of the Principles (Ri-
cardo 15). Although Ricardo’s book deals with heterogeneous commodities, he describes
them as “the produce of the earth.” Ricardo (K:85) also states that “The metals, like other
things, are obtained by labour. Nature, indeed, produces them; but it is the labour of man
which extracts them from the bowels of the earth, and prepare them for our service.” See
also St. Clair (1965, 278). The determining role of nature also appears in the neo-Ricardian
248       History of Political Economy 21 :2 ( I 989)

the strong neoclassical conception of price as an index of the scarcity of
exogenously given resources relative to consumption demand, and the
strong classical conception of price as an index of the exogenously given
difficulty of production. Capital is also incongruous with the visions under-
lying the price conceptions: the neoclassical vision of consumer exchange
with exogenously given resources, and the classical vision of production
by exogenously given inputs.
   Each vision focuses on a limited aspect of the mutual interdependence
of economic analysis: consumption or production. Each vision is sustained
in a one-commodity model, even with the existence of capital, because
price invariance suppresses that mutual interdependence. A change in any
of the interdependent elements of production, consumption, distribution,
and exchange normally causes a change in prices. The price invariance of
the one-commodity model neutralizes that interdependence, allowing a
theory to focus on one element while downplaying the others.
   In addition to supplying a focus, each vision also specifies a set of
parameters. For theories of capital, the most important such parameters
are resources or the technical conditions of production. Even with the
existence of capital, the price invariance of the one-commodity model
allows each theory to sustain its strong price conception and robust theory
of interest/profits because the measures of its parameters remain exoge-
nously determined.
   While there is an extensive literature on the limited focus of different
economic visions,25there has been no discussion of the incongruities be-
tween the endogenous nature of capital and theories constructed on the
basis of exogenous parameters. The power of capital lies in its ability to
liberate the economic system from its dependence on nature; to transcend
the limitations of any temporarily fixed set of circumstances such as re-
sources or technology. That power is also the source of the problems cap-
ital poses for economic theory.
   The results of this article suggest that problems will arise from attempts
to integrate capital into theories that explain economic phenomena by re-
ducing them to an exogenous set of conditions. Is there a form of economic
explanation more congruous with the endogenous nature of capital? There
is another tradition in the history of economic thought that does not root
explanations in exogenous conditions. This tradition, which begins with
classical growth theory, views economic activity as an endogenously gen-
erated process of development. Historical conditions at a moment in time

language of price. The terms “natural prices” and “prices of production” are used inter-
changeably. Equating the terms yields “natural production .”
   25. There is an extensive literature on the distinction between visions of consumer ex-
change (neoclassical) and production (classical). See Schumpeter (1954), Myint ( 1 9 6 3 ,
Nell(1967), Meek (1977), D. Levine (1977), Blaug (1978), and Walsh and Gram (1980).
Cohen               Prices and one-commodity models                  249

generate outcomes which transform those conditions, and the process con-
tinues spiraling on an expanded scale.26This endogenous process analysis
can be seen in the works of Smith,*’ Marx,28Young (1928), Schumpeter
( 1934), Kaldor ( 1972, 1985),29 and others. 30 Previous calls for attention
to this tradition have been made on the grounds that it addresses more
“significant” issues or that the focus of its vision is more “relevant.” More
importantly, the tradition of endogenous process analysis deserves atten-
tion for developing the theory of capital because at least, a priori, its form
of explanation is not incongruous with the endogenous nature of capital.

Michael Bernstein’s (1985) comments on an earlier paper (see Cohen 1984a, 1985) sparked
the idea for this paper. Two anonymous referees posed particularly helpful questions which
considerably sharpened the arguments. Suggestions from Brian Bixley, Meyer Burstein,
Sam Hollander, David Levine, Andrea Maneschi, David Weiman, and especially Jon Cohen
are also gratefully acknowledged. Remaining errors are mine alone.

                                       Re$,91-ences
Arrow, K. J . , and D. A. Starrett 1973. ‘Cost- and demand-theoretic approaches
  to the theory of price determination.’ In J. R. Hicks and W. Weber, eds., Carl
  Menger and the Austrian school of economics. Oxford.
Bernstein, M. A. 1985. ‘The methodological resolution of the Cambridge contro-
  versies: a comment.’ Journal of Post Keynesian Economics 7:607-1 l .
Blaug, M. 1975. The Cambridge revolution: success or failure, rev. ed. London.
        1978. Economic theory in retrospect, 3rd ed. Cambridge.

   26. See Lowe (1954) and Machlup (1959).
   27. Smith’s dictum that “the division of labour is limited by the extent of the market”
provides a clear example of endogenous process analysis. An increase in the extent of the
market creates the incentive for increased specialization or an increase in the division of
labour. The resulting increase in productivity allows for lower prices which, in turn, create
new consumer needs that increase the extent of the market. The process continues spiraling
on an expanding scale. The extent of the market, like every component of the analysis, is
alternatively a parameter and then a variable:as the process of development moves through
time. There is no reference to parameters outside the scope of the variables to be explained.
   28. Schumpeter (1947, 43) describes this same form of endogenous process analysis in
Marx: “there is one truly great achievement to be set against Marx’s theoretical misdemean-
ors. . . . the idea of a theory, not merely of an indefinite number of disjointed individual
patterns or the logic of economic quantities in general, but of the actual sequence of those
patterns or of the economic process as it goes on, under its own steam, in historic time,
producing at every instant that state which will of itself determine the next one.”
   29. According to Kaldor (1972, 1244), it is illegitimate “to assume that the operation of
economic forces is constrained by a set of exogenous variables which are ‘given’ from the
outside and stable over time.” Instead, he believes that “the forces making for continuous
changes are endogenous . . . and the actual state of the economy during any one ‘period’
cannot be predicted except as a result of the sequence of events in previous periods which
led up to it.”
   30. For a modem attempt to develop a systematic theory using endogenous process anal-
ysis see Levine (1978, 1981). Cohen (1984b, 1987a) uses a similar analysis to provide a
theory of technological change.
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