Abstract
The application of the principles of the Sraffian theory to joint production or/and open economies further reveals the inner limits of the traditional value theory: it is found that many statements make no sense or are not verified. If, however, we are willing to consider produced means of production, positive profits, non-“golden rule” steady states, heterogeneous labour (primary inputs), and joint-products as “market failures”, as well as joint production through the lens of single production, then we are not required to move away from the classical–Marxian–neoclassical one-commodity world. In the opposite case, a specific analysis of each particular issue must be made, and the general conclusion is that open, joint-product economies should be treated as the norm, whereas closed, single-product economies and their special properties should be pointed out as limiting paradigms.
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Notes
- 1.
The relaxation of these two assumptions regarding consumption demand is not absolutely necessary for our present purposes (thus, it is left to the reader; also see Chap. 2, footnote 23).
- 2.
As Salvadori and Steedman (1988a) remark, “Sraffa’s phrase “requirements for use” is not a standard term in economic analysis and Sraffa provides no explication of this phrase. Thus one is obliged to be cautious in offering an interpretation. Nevertheless it might seem that Sraffa was seeking to de-emphasize the subjective elements in the determination of the pattern of output, without denying them” (p. 168, footnote 2).
- 3.
It is often overlooked that Sraffa’s (1960) three chapters on “Joint Production” do not provide a general treatment of this issue but “are in the main a preliminary to the discussion of Fixed Capital and Land in Chaps. X and XI” (p. 43, footnote 1). For general treatments, see Bidard (1991, Part 2; 1997), Kurz and Salvadori (1995, Chaps. 7, 8, and 9) and the references (and historical notes) therein. Finally, for critical remarks and broader discussions on the “golden rule hypothesis”, see Latham (1975), Goodwin (1972), Nuti (1970).
- 4.
For an analytical investigation of the 2 × 2 case, see Abraham-Frois and Berrebi (1984).
- 5.
These examples have been built by correcting and modifying, respectively, two numerical examples provided by Bidard (1997, pp. 689–690) and further examined by Mariolis (2004a, 2010, Essay 2; 2019) and Mariolis and Soklis (2018). For other specific features of the joint production economies, see Chaps. 5, 6, 7, 8, and 9 of this book.
- 6.
The non-monotonic w − r curves analysed by, for instance, Filippini and Filippini (1984, pp. 57–62) have no specific economic content and are, therefore, unreal: the authors, on the one hand, do not take into account the requirements for use, and, on the other hand, assume that all the available processes operate. That is to say, those curves are algebraic w − r curves.
- 7.
For r > 0.1, we obtain
$$ {v}_11.05+{v}_20.95=1 $$and, therefore, “labour values” are not uniquely determined.
- 8.
In 2 × 2 economies, \( \ddot{w}\ne 0 \); hence, Eqs. (4.14) and (4.15) imply that a necessary condition for a non-monotonic w − r curve is that the eigenvalues of H are complex. Thus, it is not unexpected that the 2 × 2, no w − r trade-off, numerical example analysed by d’Autume (1988, pp. 343–344) has the same production structure as the present example. According to d’Autume (1986, 1988), when we adopt the viewpoint of the “general equilibrium theory”, the only real paradox, specific to the joint production case, is the possibility that, outside the “golden rule” path, the w − r curve is non-monotonic.
- 9.
- 10.
- 11.
Such a sign change of \( \ddot{w} \) is impossible in the corresponding single production case (i.e. two commodities and one production technique).
- 12.
Compare with Debreu (1984, p. 50). According to Kehoe (1985), the only economically interpretable restrictions that imply uniqueness of equilibrium in models of economic competition are either that the demand side behaves like a single consumer or that the supply side satisfies the “non-substitution theorem”; also see Mas-Colell (1985, Chap. 6).
- 13.
For the bases of the Ricardian, neoclassical, and Sraffian theories of open economies, as well as for their negative and positive relationships, see Baldone (2000), Giammanco (1998), Mainwaring (1974a), Parrinello (1970), Ravix (1979, 1990), Sraffa (1930), Steedman (1979a, Chaps. 1 and 2; 1979b, Essay 1; 1999), Steedman and Metcalfe (1973a, 1973b, 1981). For a comprehensive von Neumann analysis of the “small”, growing open economy case (i.e. a growing economy facing given world prices and a world economy growing at least as fast as the economy under consideration), see Steedman (1979c).
- 14.
- 15.
For a more recent, non-Sraffian exchange on the topic, see Jones (1992) and Samuelson (1992), while Jones (2012) notes: “In early discussions of activity analysis […] activities allowed joint production (i.e., production processes involving not only multiple inputs, but also multiple outputs). […] In trade theory the lack of joint production insures an asymmetry between inputs (many) and outputs (one) that is the basis for the Stolper–Samuelson theorem (1941). As to its effect on the factor-price equalization theorem, opinions differ. For example, see Samuelson (1992) and Jones (1992)” (p. 151, footnote 2).
- 16.
In single production economies also, it is entirely possible for international equilibrium price ratios to exist, which do not lie between the corresponding autarky price ratios (Steedman 1979a, pp. 115–116). However, this presupposes that more than two commodities are produced.
- 17.
For further on the “gains from free trade”, i.e. “specialization gain” and “transition (from autarky to free trade) gain”, the possibility of negative “overall gain from free trade” and the consequent implications for the theories of “economic integration” and economic policy, see Mainwaring (1976a, 1979, 1991, Chap. 2), Mariolis (2000, 2005a, 2005b), Montani (2010, 2012), Steedman (1979a, 1979b, 2018).
- 18.
Compare with Fig. 2 in Mainwaring (1974b, p. 541).
- 19.
See point Δ in Fig. 4.7. At point Γ it holds that D = 0.
- 20.
We recall, therefore, Ricardo’s (1817) view, “[T]he rate of profits can never be increased but by a fall in wages, and that there can be no permanent fall of wages but in consequence of a fall of the necessaries on which wages are expended. If, therefore, by the extension of foreign trade, or by improvements in machinery, the food and necessaries of the labourer can be brought to market at a reduced price, profits will rise.” (p. 132).
- 21.
Such a sign change of {C, D} is impossible in the corresponding single production case.
- 22.
There are also cases of non-validity of this law, which are attributed to features of consumption demand only (see, e.g. Chacholiades 1978, pp. 149–151).
- 23.
- 24.
Or, according to Samuelson (1994), “Ricardo–Viner–Harrod–Balassa–Samuelson–Penn–Bhagwati effect”.
- 25.
- 26.
Z = 1 iff A is strictly triangular and, therefore, nilpotent (as in the Austrian-type models).
- 27.
For simplicity, the reader may consider the fixed input coefficients case.
- 28.
The two-sector case is often used for the analysis of real phenomena (such as inflation differentials across Eurozone economies).
- 29.
On the invalidity of these two theorems, also see Mainwaring (1976b, 1978), Steedman (1979b, Essays 5), Steedman and Metcalfe (1973b). Nevertheless, the prices of the non-Sraffian Standard commodities (see Sects. 3.2.1 and 10.4 of the present book), in terms of the Sraffian Standard commodity, are strictly decreasing functions of the profit rate and, therefore, in accordance with these two theorems (Mariolis 2004b; Mariolis and Tsoulfidis 2011, pp. 93–96).
- 30.
The relaxation of the assumption regarding “small” economies complicates the analysis (without substantially changing its basic conclusion), because it implies that π3/π2 is determined in terms of international relative supply and demand.
- 31.
Their model is a two-sector model. The existence of a second tradable commodity necessitates the introduction of additional assumptions.
- 32.
Traditionally, it is argued that, “Empirically, nontraded goods tend to be at least as labour-intensive as traded goods, so the condition θL1 ≥ (θL2, θL3) [using our symbols] holds in practice. Furthermore, productivity growth in nontradables historically has been lower than in tradables. One reason for relatively low productivity growth in the nontradables sector is its substantial overlap with services, which are inherently less susceptible to standardization and mechanization than are manufactures or agriculture” (Obstfeld and Rogoff 1998, p. 209; emphasis added. Also see the relevant Special Issue of the Review of International Economics 1994). However, these observations are highly disputable: consider what was said on the basis of Eq. (4.34), as well as the fact that the empirically relevant case of joint production creates a new kind of insurmountable problems for the traditional approaches. For instance, in that case, (i) the definition of a commodity as “relatively labour-intensive” makes no sense; (ii) relative prices depend on the demand conditions; and (iii) productivity growth does not necessarily lead to an increase in the real wage rate.
- 33.
It should be noted that θL2 = θL3 implies that
$$ \overset{\frown }{w}={\overset{\frown }{\tau}}_1{\theta}_{L1}^{-1}={\overset{\frown }{\tau}}_2{\theta}_{L2}^{-1}={\overset{\frown }{w}}^{\ast },\kern0.5 em \overset{\frown }{\mathrm{I}}={\overset{\frown }{\mathrm{I}}}^{\ast }=0 $$while θ12 = θ13 implies that θL2 = θL3.
- 34.
Both Balassa (1964, pp. 585–586) and Samuelson (1964, pp. 147–148) refer to the non-tradable commodities as services. Thus, in the relevant literature it is considered that Eq. (4.42) are in accordance with this reference. Of course, all these are simplifications (also see Steedman 1979a, pp. 99–105).
- 35.
The hitherto available empirical evidence on the relative price effects of total productivity shift (see Eq. (4.34)), with \( {\overset{\frown }{\boldsymbol{\uptau}}}^{\mathrm{T}}=\overset{\frown }{\tau }{\mathbf{e}}^{\mathrm{T}} \)) suggests that the direction of the price movements is, more often than not, governed by the labour cost condition, while this is reduced to the “skew distribution” (see Chap. 3 of this book) of the eigenvalues of the matrices, ΘK, of the relative shares of the capital commodities (Mariolis et al. 2015). The empirical evidence on the H–B–S effect provides rather mixed findings, while, for instance, according to Tica and Družić (2006), “[t]he growing body of evidence makes it difficult to ignore the HBS theory and definitely points towards professional rethinking about the contemporary significance of the Harrod–Balassa–Samuelson theory.” (p. 15).
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Mariolis, T., Rodousakis, N., Soklis, G. (2021). Value Theory, Joint Production, and International Trade Issues. In: Spectral Theory of Value and Actual Economies. Evolutionary Economics and Social Complexity Science, vol 24. Springer, Singapore. https://doi.org/10.1007/978-981-33-6260-4_4
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