Chinese Studies on the Transformation Problem: A Selective Review

Abstract

Marxian economists in China have put forward several interpretations of the transformation problem that differ from interpretations available in the English Marxian literature. These contributions remain unfamiliar to the English world due to language barriers. Thus, this paper provides a review of four representative Chinese contributions.

JEL Classification: B51, C67, D46

Keywords

labor theory of value transformation problem input-output model

1. Introduction

China might employ the most Marxian economists due to the centrality of Marxism in its official ideology. However, the inability of Westerners to decipher the almost impenetrable Chinese language and the lack of motivation for Chinese Marxian economists to publish in English render their works little known internationally. Among these works are Chinese interpretations on the century-old transformation problem that has not been settled within Marxian economics. This review introduces English readers to four representative Chinese contributions to the transformation problem.¹

The transformation problem was systematically introduced in China in the early 1980s (see Zhu 1981, 1983; Hu 1983). However, it did not capture widespread attention until the 2000s. Beginning then, Zhang (2004), Ding (2005), and Bai (2006) stand out as the three most influential researchers: Zhang claims to have mathematically proved that both of Marx’s aggregate equalities hold simultaneously in a dualist framework; Ding distinguishes the role of variable capital from that of constant capital in the value formation process and argues that both of Marx’s aggregate equalities hold in a dynamic sense; and Bai claims that Marx’s two aggregate equalities approximately hold. More recently, Yan and Ma (2011) present an intertemporal model that attempts to lay bare the dynamic process of the transformation problem by explicitly considering capital movement across sectors; Rong, Li, and Chen (2016) propose the invariant rate of exploitation as an alternative to total surplus value equals total profit. This paper’s in-depth review covers Zhang (2004), Ding (2005), Yan and Ma (2011), and Rong, Li, and Chen (2016).²

All four selected researchers’ works are motivated by the conclusion of the standard interpretation (SI) (see Bortkiewicz 1949; Seton 1957; Morishima 1973) that Marx’s two aggregate equalities cannot hold at the same time in a dualist input-output model.³ They all appear to adopt a dualist interpretation, agreeing on the coexistence of the value system and the price system as two interrelated but separate systems. It turns out that Yan and Ma (2011) are the closest to the SI because their intertemporal model is simply a dynamic version of the SI. However, in an attempt to prove the coexistence of two aggregate equalities (of their own choice), the other three perspectives essentially must reinterpret the value of labor power in a way similar to the new interpretation (NI) (see Duménil 1983; Foley 1982; Lipietz 1982) to achieve consistency in their interpretations.⁴

In the next section, we unify the notations and lay out the common setting used within these four works. We then introduce Zhang (2004), Ding (2005), Yan and Ma (2011), and Rong, Li, and Chen (2016) in chronological order in the subsequent sections. The last section summarizes the conclusions.

2. Setup

Consider a closed economy in which there are n different sectors, each producing a distinct commodity using only circulating capital. The length of the production period in all sectors is assumed to be unified. Since the different authors base their analyses on an input-output model either in physical or value terms, we present both conceptually overlapped notation systems to avoid the trouble of translating one into the other.

A = (a_ij) is the n × n constant capital input coefficient matrix whose generic element a_ij denotes the physical amount of commodity i that is required to produce 1 unit of commodity j (unless indicated otherwise, the generic indexes i and j always run from 1 through n). l = (l₁,l₂,…,l_n) is the productive labor power input vector whose generic element l_i denotes the amount of productive labor power required to produce 1 unit of commodity i. The following vectors are defined similarly: b, x, and y are respectively the n × 1 vectors of the real wage bundle, gross output, and net output, all in physical terms; p, λ, and ρ are respectively the 1 × n vectors of price (of production), value, and the price/value ratio; and c, v, s, and m are respectively the 1 × n vectors of sectoral sums of constant capital, variable capital, surplus value, and profit. Scalars r and π are respectively the (equilibrium) price and (average) value rates of profit; w and ω are the uniform price and value of labor power; and e and ∈ are the profit/wage ratio and the rate of surplus value.

Further assume A ≥ 0 and is productive (i.e., there exists x ≥ 0 satisfying y = x – Ax ≥ 0 for any y ≥ 0), l > 0, and b ≥ 0. Limit all analyses to the case r > 0. Relevant to the interpretations presented in this paper are these aggregate equalities: total value equals total price of production (TVTP), or λx = px; total surplus value equals total profit (TSTM), or $\sum_{i = 1}^{n} s_{i} = \sum_{i = 1}^{n} m_{i}$ ; total value of net output equals total price (sales) of net output (NVNP), or λy = py; and the rate of surplus value equals the profit-wage ratio (VEPE), or ∈ = e.

Based on the above definitions, Marx’s original transformation system can be written as follows:

{\begin{cases} ρ_{1} (c_{1} + v_{1} + s_{1}) = (1 + r) (c_{1} + v_{1}) \\ ρ_{2} (c_{2} + v_{2} + s_{2}) = (1 + r) (c_{2} + v_{2}) \\ ⋮ \\ ρ_{n} (c_{n} + v_{n} + s_{n}) = (1 + r) (c_{n} + v_{n}) \\ π = \sum_{i = 1}^{n} s_{i} / \sum_{i = 1}^{n} (c_{i} + v_{i}) \\ r = π \end{cases} .

In this model, the c_i s, the v_i s, and the s_i s are all given, while the ρ_i s, r, and π are unknown. It is easy to first solve for π with the givens, and then for r and the ρ_i s. Once those solutions are determined, value is transformed into price of production, and Marx’s two aggregate equalities TSTM and TVTP hold simultaneously because total profit:

$\sum_{i = 1}^{n} m_{i} = r \sum_{i = 1}^{n} (c_{i} + v_{i}) = π \sum_{i = 1}^{n} (c_{i} + v_{i}) = \sum_{i = 1}^{n} s_{i}$

in which the last term is total surplus value; then, total value:

$\sum_{i = 1}^{n} (c_{i} + v_{i} + s_{i}) = \sum_{i = 1}^{n} (c_{i} + v_{i}) + \sum_{i = 1}^{n} s_{i} = (1 + r) \sum_{i = 1}^{n} (c_{i} + v_{i}) = \sum_{i = 1}^{n} ρ_{i} (c_{i} + v_{i} + s_{i})$

in which the last term is total price of production.

The so-called transformation problem is then as follows: Marx does not transform the constant and variable capital inputs in the sense that the cost of an input can be different from its price as an output. This anomaly renders Marx’s transformation inconsistent, or at least not an equilibrium outcome.

3. Zhang (2004)

Zhang, when rectifying Marx’s transformation process, argues that the two aggregate equalities TVTP and TSTM should be used as presumptions rather than propositions that need to be proved. This treatment, though controversial, seems justified if a solution to a model as such exists. He claims that it does.

Formally, let ρ₀ be the price/value ratio of variable capital, which is assumed to be uniform across sectors. Let d_ij be the value of constant capital that is purchased by sector j from sector i. Then, Zhang’s model becomes as follows:

{\begin{cases} ρ_{1} (c_{1} + v_{1} + s_{1}) = (1 + r) (\sum_{j = 1}^{n} ρ_{j} d_{j 1} + ρ_{0} v_{1}) \\ ρ_{2} (c_{2} + v_{2} + s_{2}) = (1 + r) (\sum_{j = 1}^{n} ρ_{j} d_{j 2} + ρ_{0} v_{2}) \\ ⋮ \\ ρ_{n} (c_{n} + v_{n} + s_{n}) = (1 + r) (\sum_{j = 1}^{n} ρ_{j} d_{j n} + ρ_{0} v_{n}) \\ \sum_{i = 1}^{n} ρ_{i} (c_{i} + v_{i} + s_{i}) = \sum_{i = 1}^{n} (c_{i} + v_{i} + s_{i}) \\ π = \sum_{i = 1}^{n} s_{i} / \sum_{i = 1}^{n} (c_{i} + v_{i}) \\ r = π \end{cases} .

It is readily seen that TVTP is assumed by the third-to-last equation. TSTM holds because total profit:

$\sum_{i = 1}^{n} m_{i} = r \sum_{i = 1}^{n} (\sum_{j = 1}^{n} ρ_{j} d_{j i} + ρ_{0} v_{i}) = r \sum_{i = 1}^{n} ρ_{i} (c_{i} + v_{i} + s_{i}) / (1 + r)$

by the first n equations, and total surplus value:

$\sum_{i = 1}^{n} s_{i} = π \sum_{i = 1}^{n} (c_{i} + v_{i} + s_{i}) / (1 + π)$

by the second-to-last equation; further, because r = π and TVTP, it renders $\sum_{i = 1}^{n} m_{i} = \sum_{i = 1}^{n} s_{i}$ . Zhang’s system has n + 3 unknowns (the ρ_i s, ρ₀, π, and r) and n + 3 equations, which proves to yield a unique and economically meaningful solution under some extra (and loose) conditions (Huan and Zhang 2005).⁵

Zhang’s treatment of the price/value deviation ratio of variable capital (ρ₀) is controversial. Within the SI where a physical wage bundle is given, ρ₀ is itself endogenous to the ρ_i s. However, in Zhang’s model, ρ₀ is a variable independent from the ρ_i s, which leads one to question what the price of production of labor power means since labor power is not (re)produced for profit (e.g., see Ding and Li 2005; Yue and Kou 2005). Were ρ₀ to be based on a physical wage bundle, another restriction linking ρ₀ and the ρ_i s would exist through this bundle. Consequently, Zhang’s system would be overdetermined and insolvable. One hopeful way out seems to be using an NI line of treatment by breaking the linkage between the physical wage bundle and the value of labor power.⁶ In this case, ρ₀ can be reinterpreted as the price of labor power (still an unknown) and v_i reinterpreted as the exogenously given amount of labor power hired in sector i so that the alleged extra restriction will not emerge.⁷

If the above rectification were made, Zhang’s interpretation would be consistent and provide a unique and positive solution under his assumptions. How, then, does this compare to the NI (especially Lipietz 1982) in addition to their similar treatment of the variable capital? Though they share a common invariance postulate TSTM, the NI adopts NVNP, while Zhang retains TVTP. Zhang’s model becomes an alternative to the NI and represents a complete conservation of value, whereas the NI only conserves the value of net output.

4. Ding (2005)

Ding is mainly concerned with the interpretation of Marx’s famous phrase “modified significance of the cost price” in the transformation problem (Marx 1981: 265). Ding argues that workers must reproduce the amount of variable capital in price terms during the value formation process, which then becomes the base of surplus value extraction. His main substantiation of this argument is this quote from Theories of Surplus Value: “Variable capital, whatever difference between value and cost price it may contain, is replaced by a certain quantity of labour which forms a constituent part of the value of the new commodity, irrespective of whether its price expresses its value correctly or stands above or below the value” (Marx 1975: 352).

This quote, however, does not seem strong enough to buttress Ding’s peculiar way of visualizing variable capital because it is unclear what Marx means exactly by that “certain quantity of labour.” Moreover, in the same paragraph, Marx goes on to say, “On the other hand, the difference between cost price and value, insofar as it enters into the price of the new commodity independently of its own production process, is incorporated into the value of the new commodity as an antecedent element” (352). This famous paragraph supports a single-system interpretation.⁸ Ding seems to have only traveled halfway in the single-system direction without giving constant capital the same treatment. His quotation of Marx is therefore out of context.

Despite its weak support, Ding’s reinterpretation of the role of variable capital in the value formation process necessitates a different definition of surplus value, given that he still wants to differentiate between the price and value of labor power because, according to his interpretation, surplus value is no longer seen as a surplus over the value of labor power but instead seen as a surplus over the price of labor power. Nonetheless, he does not provide a justification for the implied reinterpretation of surplus value.

Formally, based on Marx’s system shown in section 2, Ding further defines the α_i s and β_i s as the price/value deviation ratios of constant capital and variable capital, respectively. He treats these ratios as pregiven from the previous round of transformation, which he considers an intertemporal process. However, he only presents one period of that dynamic process, which is as follows:

{\begin{cases} ρ_{1} (c_{1} + β_{1} v_{1} + s_{1}) = (1 + r) (α_{1} c_{1} + β_{1} v_{1}) \\ ρ_{2} (c_{2} + β_{2} v_{2} + s_{2}) = (1 + r) (α_{2} c_{2} + β_{2} v_{2}) \\ ⋮ \\ ρ_{n} (c_{n} + β_{n} v_{n} + s_{n}) = (1 + r) (α_{n} c_{n} + β_{n} v_{n}) \\ π = \sum_{i = 1}^{n} s_{i} / \sum_{i = 1}^{n} (α_{i} c_{i} + β_{i} v_{i}) \\ r = π \end{cases} .

One can solve this system by first determining π with the givens, and then determining r and the ρ_i s. Notice that no spelled-out relationship exists between the ρ_i s, α_i s, and β_i s in Ding’s formulation. Put differently, Ding allows the price of production of a commodity as an input to be different from that of the same commodity as an output that is produced after a new round of production. However, he does not specify how the α_i s and β_i s in the current period can becalculated based on the ρ_i s from the last period. In addition, note that the value of output is defined as c_i + β_iv_i + s_i, that is, the sum of value transferred from constant capital, the part of living labor that is equal to the variable capital in price terms, and a surplus value, respectively.

In regard to what aggregate equalities hold in Ding’s system, one can easily see that TSTM holds by assumption: Total profit $\sum_{i = 1}^{n} m_{i} = r \sum_{i = 1}^{n} (α_{i} c_{i} + β_{i} v_{i})$ is equal to total surplus value $\sum_{i = 1}^{n} s_{i}$ according to the last two equations of the system. However, total price is different from total value in general. The difference can be expressed as:

$(1 + r) \sum_{i = 1}^{n} (α_{i} c_{i} + β_{i} v_{i}) - \sum_{i = 1}^{n} (c_{i} + β_{i} v_{i} + s_{i}) =$

$\begin{array}{l} \sum_{i = 1}^{n} (α_{i} c_{i} + β_{i} v_{i}) + r \sum_{i = 1}^{n} (α_{i} c_{i} + β_{i} v_{i}) - \sum_{i = 1}^{n} (c_{i} + β_{i} v_{i} + s_{i}) = \sum_{i = 1}^{n} (α_{i} c_{i} + β_{i} v_{i}) + \\ \sum_{i = 1}^{n} s_{i} - \sum_{i = 1}^{n} (c_{i} + β_{i} v_{i} + s_{i}) = \sum_{i = 1}^{n} (α_{i} c_{i} - c_{i}) . \end{array}$

It is obvious from the last step that the difference is not necessarily equal to zero and it carries over solely from the price/value deviation in constant capital. Because of this element, even though TVTP does not hold in general at any iteration, Ding argues that it still holds in a dynamic sense so that the current period is innocent of the deviation. This argument sounds like sophistry since a never-converging iterative process must be assumed, and no discussion of the initial conditions is provided. Instead, one can easily see that the NVNP holds because the above gap implies:

$[(1 + r) \sum_{i = 1}^{n} (α_{i} c_{i} + β_{i} v_{i}) - \sum_{i = 1}^{n} α_{i} c_{i}] - [\sum_{i = 1}^{n} (c_{i} + β_{i} v_{i} + s_{i}) - \sum_{i = 1}^{n} c_{i}] = 0$

in which the first bracketed term is net output in price terms and the second bracketed term is living labor—thus, they are equal.

Therefore, Ding’s transformation system arrives at the same aggregate equalities as does the NI. To have them hold simultaneously, both interpretations must give special treatment to the variable capital, but their specific treatments are different: Ding reinterprets the role of variable capital in the value formation process, while the NI (especially Lipietz 1982) explicitly severs the link of variable capital to the physical wage bundle.

5. Yan and Ma (2011)

Yan and Ma approach the transformation problem within a dynamic framework wherein capital movement driven by differential sectoral rates of profit is explicitly considered together with supply and demand functions. Their goal, as they put it, is to lay bare the dynamic transformation process by specifying the behavioral functions for variables, such as price, output, and capital flows.

Yan and Ma consider the transformation problem as an actual economic process. They argue that capital movement that equalizes the rate of profit might alter the output proportions and consequently the average organic composition of social capital, rendering the end point production system different from what it is at the beginning of the transformation process. Their concern coincides with Lipietz’s (1982) critique of the SI—that output plays no role in the transformation problem.

Formally, let superscript t denotes time period, k^t the 1 × n vector of sectoral capital outlays in price terms, and r–^t (scalar) the economy-wide average rate of profit. Further, assume the economy is in simple reproduction wherein the different types of constant capital inputs in physical terms remain constant at the aggregate level, denoted as a 1 × n vector a–. Given the production technique {A,l}, the unit labor value is calculated as λ = l (I – A)–1 according to λ = λA+l. Using λ as the initial value for price, that is, p–1 = λ, and given x0, a–, and a physical wage bundle b, Yan and Ma’s dynamic transformation system is the following:

{\begin{cases} k^{t} = p^{t - 1} (A + b l) d i a g (x_{1}^{t}, x_{2}^{t}, \dots, x_{n}^{t}) \\ p^{t} = p (x^{t}), p^{'} (\cdot) < 0 \\ r_{i}^{t} = (p_{i}^{t} x_{i}^{t} - k_{i}^{t}) / k_{i}^{t} \\ {\bar{r}}^{t} = \sum_{i} (p_{i}^{t} x_{i}^{t} - k_{i}^{t}) / \sum_{i} k_{i}^{t} \\ x_{i}^{t} = f (r_{i}^{t} - {\bar{r}}^{t}), f^{'} (\cdot) > 0 \end{cases} s . t . {\begin{cases} A x^{t} = \bar{a} \\ x^{t} = p^{t} x^{t} - p^{t - 1} A x^{t} \end{cases} .

Note that the movement of capital across sectors is reflected in the change of gross output. This reflection occurs because constant returns to scale are assumed and capital advanced is evaluated at a predetermined price according to the first equation in Yan and Ma’s system. Based on this principle, function f(.) implies that capital moves in or out of a sector depending on whether the sectoral rate of profit is higher or lower than the average rate of profit. Function p(.) reflects the negative effect of capital movement (supply) on output price. In addition, Yan and Ma assume NVNP, or, in other words, $l x^{t} = p^{t} x^{t} - p^{t - 1} A x^{t}$ . Yan and Ma’s system contains 4 × n endogenous variables ${k^{t}, x^{t}, p^{t}, r^{t}} .$ Instead of investigating the existence, uniqueness, and stability of the solution to the system, they simply provide a numerical example to demonstrate its convergence, only to find neither TSTM nor TVTP holds in the limit.

One might immediately question if such a system admits a convergent solution in general. Nikaido (1977), using a two-sector input-output model, demonstrates that a dynamic system as such might not converge simply due to free capital mobility. It is possible that more restrictions are needed for their model to converge to a steady state. In the case where a steady state exists, their model simply reduces to the SI model. This feature can be seen as follows by dropping the superscript t. In the steady state, $k = p (A + b l) d i a g (x_{1}, x_{2}, \dots, x_{n})$ and $r_{i} = (p_{i} x_{i} - k_{i}) / k_{i},$ which implies $p = (1 + r) p (A + b l) .$ This resulting price system is the same as in the SI. The reduction of a dynamic model into a static one in this manner renders Yan and Ma’s exercise an unnecessary detour in regard to the purpose of the transformation problem. However, their formulations turn out to be an intuitive and effective response to the kind of critique made by Lipietz (1982). Capital movement and output do play an important role in the process of profit rate equalization and thus in the transformation problem. This role is not absent, though implicit, in the SI, which only focuses on the steady state of the underlying dynamic process.⁹

6. Rong, Li, and Chen (2016)

Rong, Li, and Chen propose an interpretation that uses an innovative invariant postulate—the invariant rate of exploitation (VEPE)—with TVTP. Though Laibman (1973) precedes them in using the VEPE postulate in a heuristic two-sector geometric model, Rong, Li, and Chen’s multisector model is, among other differences, considerably more general than Laibman’s treatment.¹⁰

Rong, Li, and Chen object to presupposing a unified physical wage bundle. They argue that the reproduction of labor power takes place outside the sphere of production and cannot be reduced to the consumption of a physical wage bundle. They also criticize the NI for failing to maintain TVTP, which they consider a fundamental axiom—the complete conservation of labor value. Though aware that Fujimori’s (1985) and Zhang’s (2004, in a modified sense) interpretations do not suffer from these two drawbacks (in their opinion), they prefer VEPE over TSTM and argue that Marx himself does not stubbornly adhere to the latter—it is the regulating role of the value system that is important to Marx. They quote: “Since the total value of the commodities regulates the total surplus-value, and this in turn regulates the level of average profit and thereby the general rate of profit—as a general law or a law governing fluctuations—it follows the law of value regulates the prices of production” (Marx 1981: 134). Thus, Marx’s focus within the transformation problem, to them, concerns not the aggregate equalities but the “way an equal average rate of profit can and must come about, not only without a violation of the law of value, but on the very basis of it” (Engels, 1981); it is about the redistribution of surplus value among capitalists in different sectors rather than the readjustment of the rate of exploitation between the two classes. Therefore, Rong, Li, and Chen suggest that TSTM should be relaxed and replaced by VEPE, which preserves the distributive relationship between the two fundamental classes—a precondition for the equalization of the rate of profit.

Formally, given the production technique {A,l} and the gross output vector x, the net output y is determined by y = x – Ax. The value vector λ is determined by λ = λA + l. Then, Rong, Li, and Chen’s transformation system is as follows:

{\begin{cases} p = (1 + r) (p A + w l) \\ p y / (λ y) = w / ω \\ p x = λ x \end{cases} .

The last equation stands for TVTP. The second equation implies VEPE: Multiply through by lx on the right-hand side, rearrange, and then it follows that $e = \frac{p y}{w l x} - 1 = \frac{λ y}{ω lx} - 1 = \in .$

Note especially that ω, the value of labor power, is given exogenously, and only p, r, and w are unknowns in their system. Substituting the middle equation into the price system for w, then:

$p = (1 + r) (p A + ω \frac{p y}{λ y} l) = (1 + r) p H$

where $H \equiv A + \frac{ω}{λ y} y l$ is assumed to be non-negative and indecomposable. By the Perron-Frobenius theorem, a unique r and a unique positive relative price vector can be solved for. The last equation serves to normalize price.

An inconsistency seems to exist in Rong, Li, and Chen’s treatment of the relationship between the physical wage bundle, the value of labor power, and the price of labor power. On the one hand, they reject considering the physical wage bundle in the transformation problem; on the other hand, they want to maintain the concept value of labor power alongside the price of labor power and allow them to differ. This dichotomy of the value and price of labor power is essential in their interpretation since they define the rate of exploitation in both the value and price terms. The inconsistency can be delineated by this observation: Without the physical wage bundle, it is unclear how the value of labor power can be defined and assumed to be pregiven. If it is determined outside the sphere of production (as they argue), it is also ambiguous as to how it is related to the value system and serves as the basis of the value rate of exploitation.

However, Rong, Li, and Chen’s work does represent a new perspective by identifying (indeed, rediscovering, if we consider Laibman’s contribution) an innovative postulate. The idea of assuming a constant worker-capitalist class relationship across the value and price system seems legitimate if one considers that the theoretical purpose of the transformation problem is to demonstrate how an equalized rate of profit can emerge from a given rate of exploitation (see, e.g., Roemer 1981, ch. 7).

7. Concluding Remarks

As we have shown, the four Chinese contributions findings introduced in this paper are either incomplete or potentially inconsistent without further substantiation. Thus, they are more heuristic in nature rather than being conclusive.

In regard to the purpose of proving that any two aggregate equalities can hold simultaneously, the four theories implicitly or explicitly point to a fundamental trade-off regarding the treatment of the value of labor power: It is impossible in general to have two invariance postulates hold at the same time within the SI framework, and the reinterpretation of the value of labor power is vital in having any two invariance postulates hold at the same time. It is by this reinterpretation that, within the input-output framework, an extra degree of freedom is created to allow for one more invariance postulate than found in the SI (Fujimori 1985)—be that TSTM and NVNP in the NI, TSTM and TVTP in Zhang’s model, or TVTP and VEPE in Rong, Li, and Chen’s interpretation. However, it comes at a cost. For example, to sever the linkage between the physical wage bundle and the value (or price) of labor power, one has to sacrifice the analytical usefulness of the concept value of labor power as an amount of socially necessary labor time in analyzing the reproduction of labor power. This drawback is especially evident in the NI since the redefined value of labor power does not even have a unit; it simply reduces a wage share in the net product under any price system (Mohun and Veneziani 2017). To the best of our knowledge, no satisfactory clarification exists on how the value of labor power can be economically determined without reference to the consumption of physical goods. Any explanation without this reference simply deprives the value of labor power of its material foundation and serves to mystify the reproduction of labor power.

Given the preoccupation of the literature with whether two invariance postulates can hold simultaneously, in concluding this review, we want to take a step back and ask the following questions: Why is it necessary to have two aggregate equalities hold for the Marxian labor theory of value? Why is one aggregate equality such as TVTP not enough for value conservation if that is the theoretical concern? Why must a certain amount of surplus value be exactly transformed into profit (TSTM) and not creep into the price/value deviation of the entire capital outlays? These questions are worth exploring before one attempts to prove the compatibility of any two aggregate equalities.

Footnotes

Acknowledgements

We would like to thank Deepankar Basu, Bruce Roberts, Fusheng Xie, and the three reviewers for their helpful comments. We would also like to thank Jingjing Wu and Yan Ma for their generous help with access to the Chinese literature. All errors are ours.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Kuochih Huang

Junshang Liang

1

The reader may be better served by first having some familiarity with English discourse on the topic; see, e.g., for a review.

2

A detailed review of is omitted according to the reviewers’ suggestion but is available on request.

3

A primary goal in the Chinese literature by and large is to overturn this conclusion within the input-output model or the scheme of reproduction. To the best of our knowledge, no researcher in the Chinese literature explicitly opposes the multisectoral treatment of the transformation problem.

4

Except for the SI and the NI, all other interpretations present in the English literature are noticed but do not catch much attention in the Chinese literature. Though not introduced in detail, the following contributions are worth mentioning: Yue (2002) modifies Ding’s model to make Marx’s two aggregate equalities hold simultaneously; Zhu (2004) presents both a static and a dynamic model based on Ding (2005); Lü (2004), in a framework similar to the temporal-single-system interpretation (TSSI), and Li (2020), in a multiperiod TSSI model, show that Marx’s two aggregate equalities can hold simultaneously; , in a two-department simple-reproduction model, argues that Marx’s two aggregate equalities can hold if the realization of surplus value is taken into account.

5

The proof is not straightforward and thus not reproduced here.

6

Rong, Li, and Chen (2016) interpret Zhang’s model in this way.

7

This modified model then in effect coincides with .

8

We thank Bruce Roberts for pointing this out.

9

responds to Lipietz’s critique in a less straightforward way by pointing out that the price equilibrium is a duality of the quantity equilibrium so that output also plays a role in the background.

10

Thanks to a reviewer who points out this reference, which is not cited by Rong, Li, and Chen.

Author Biographies

Kuochih Huang is a policy research specialist at the University of California, Berkeley Center for Labor Research and Education. His research focuses on the labor movement, corporate governance and control, and social economics.

Junshang Liang Junshang Liang is Assistant Professor in the School of Economics, Nankai University. His research revisits the Marxian falling rate of profit hypothesis mathematically and econometrically.

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