The Marginal Productivity Theory of Distribution

A Critical History

John Pullen

• Publisher: Taylor & Francis
• Year: 2009
• Print ISBN: 9781138804968
• eBook ISBN: 9781134010882
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

The Marginal Productivity Theory of Distribution (MPTD) claims that in a free-market economy the demand for a factor of production will depend upon its marginal product – where "marginal product" is defined as the change in total product that is caused by, or that follows, the addition or subtraction of the marginal unit of the factor used in the production process, with all other inputs held constant. From its inception in the early nineteenth century the MPTD has been claimed by some economists to be a solution to the ethical problem of distributive justice, i.e. to be a means of determining fairness in wages, profits, interest and rent. Other economists have rejected this ethical claim, but have seen the MPTD as a valid demand-side criterion in the determination of equilibrium and efficiency.

This book argues that the MPTD is valid, neither as a normative theory of social justice, nor as a positive law of economics. It suggests that economics is yet to develop a satisfactory theory of distribution that is scientific in the quantitative or mathematical sense. Through a survey of the origin and subsequent evolution of the MPTD in the writings of over 50 contributors over 150 years, John Pullen presents a critical history of the concept. The book begins by examining the conceptual tools that have been deployed to facilitate this analysis of past contributions to the MPTD and then looks at various economists and their contribution to the debate including its supporters such as Wicksteed, Marshall, Wicksell and Stigler, and its critics such as Pareto, Hobson, Edgeworth, Adriance and Cassel.

1
Basic concepts

A major theme in this attempt to trace and interpret the volatile history of the MPTD is the distinction between two possible meanings of the expression ‘the marginal product’ of a factor of production. On the one hand, the expression can mean the portion of the product that has been actually produced by the marginal unit of the factor. On the other hand, it can mean the change (in the total output) that occurs after the addition or subtraction of the marginal unit of the factor. Both meanings have been used, and are still being used, in the MPTD literature, often without being clearly distinguished. Given the centrality of the distinction in the following study of the history of the MPTD, it is essential that it be explained and justified in some detail. To simplify the explanation the following definitions and acronyms are deployed:

• SMPL, or the specific marginal product of labour. When labour (the variable factor) is combined with other (fixed) factors in a productive process, the SMPL is the portion of the product that has been physically produced or caused by the marginal unit of labour, as distinct from the portions causally attributable either to the fixed factors or to previous, intra-marginal units of labour. Similarly, SMPK and SMPN are the specific marginal products of capital and of land (or natural resources).

• MPAL, or the marginal product after labour, is the increase in the total product that occurs after the employment of the marginal unit of labour. Similarly, MPAK and MPAN.

• MPL is the marginal product of labour, without specifying whether it be SMPL or MPAL.

The distinction between the SMPL and the MPAL appears to be fundamental to any attempt to understand and evaluate the arguments and counter-arguments surrounding the MPTD. It derives from the obvious fact that the MPAL is a multicausal phenomenon. Every production process obviously requires more than one factor. Capital produces nothing without labour. Even the simplest form of labour produces nothing without material resources. Every unit of output, even a marginal unit, is therefore a multicausal or joint product, composed of the specific products causally contributed by the different factors.

The MPTD proceeds on the assumption that while one factor varies, the other factors are held constant. From this it might appear that the change in total product is caused by the marginal unit of the variable factor alone. But this appearance of monocausality would be deceptive, since the marginal unit of the variable factor does not act alone. It acts in combination with the factors that are held constant or assumed to be constant. These constant factors contribute causally to the change in the total product, even when they are being held constant. Holding them constant does not eliminate their effectuality. It would be an illusion to conceive of an unchanged factor as being incapable of producing changes; or to claim that, when labour is the only thing that changes, labour is the only cause and the only cost. Ceteris paribus is not the same as ceteris inefficacibus. An active, causal factor is not magically transformed into a passive, non-causal factor simply by intoning ceteris paribus. The factories and machines that perform causative and productive functions in cooperation with labour are not suddenly rendered impotent by the incantation of the ceteris paribus clause. In calculating the marginal product of labour, ceteris paribus eliminates the effect of any changes to capital, but does not eliminate the ongoing causal influence of existing capital.¹

To regard the marginal product of labour as being caused by the marginal unit of labour alone is to argue post hoc ergo propter hoc, and to interpret a correlation as a causation. The longevity and popularity of the MPTD may be seen as a tribute to the awesome ubiquity and influence of that fallacy in economics. The change in the total product that occurs after the application of a marginal unit of labour is not caused by that marginal unit of labour alone. The MPAL is produced by the other factors as well as by labour, even if the other factors remain unchanged when an extra unit of labour is employed. The MPAL involves specific contributions caused by capital and land as well as the specific contribution caused by labour.

The causative role of the fixed factors, as well as that of the variable factor, may be illustrated by applying Alfred Marshall’s famous metaphor of the two blades of a pair of scissors to explain the dual roles of demand and supply in the determination of value. One blade acting alone will not be sufficient; a pair of scissors requires a second blade, even if it is held in a fixed position. Applying this metaphor to the MPTD, the marginal unit of the variable factor, acting alone, will not produce any change in the product. To be productive, it requires also a causative input exercised by the fixed factors, even though they are held fixed.

This distinction between the MPAL and the SMPL may also be described as a distinction between the proprietorial and non-proprietorial uses of the preposition ‘of’. Previous studies of the MPTD (e.g. Machlup ([1936] 1950) have discussed some of its main concepts such as marginal product, marginal physical product, marginal value product, and so on. This study extends the linguistic analysis to the meaning of ‘of’, and highlights the ambiguities that occur in the use of ‘of’ in the concept ‘marginal product of a factor’.

The word ‘of’ is one of the shortest and most frequently used in the English language, but one of the most difficult to define. The Oxford English Dictionary gives no fewer than 63 senses in 16 categories. This paper will be concerned with the fourteenth category: ‘In the sense of belonging or pertaining to; expressing possession and its converse: ‘the owner of the house’, ‘the house of the owner’’, and in particular with sense no. 49a conveying the notion of proprietorship: ‘Belonging to a person (etc.) as something that he (etc.) has or possesses.’

Discussion of the proprietorial ‘of’ is also extended to other words connoting a proprietorial relationship, such as pronouns in the possessive case (his, hers, its, their); nouns in the genitive case (labour’s, capital’s); and words such as ‘from’, ‘by’ and ‘to’ (as used in the phrases ‘arising from’, ‘created by’, ‘due to’) that suggest a causative and hence a proprietorial connection.

The language of the pioneers of the MPTD – their frequent use of the proprietorial ‘of’; the possessive adjectives ‘his’, ‘its’, ‘their’; and verbs such as ‘results from’ and ‘occasions’ – provides undeniable textual evidence of a concern with causal connections. The view that the MPTD is concerned only with costs and not with causes is a later development in the history of the MPTD.

The use of the proprietorial sense of ‘of’ in the expression ‘marginal product of labour’ might conceivably be justified by arguing that, in saying the marginal product is the product ‘of’ labour, we are not saying it is the marginal product of labour alone in an exclusionary sense. But that qualification is rarely mentioned in the literature. Readers are rarely warned against interpreting the use of ‘of’ in a sole proprietor sense. In the absence of such warning, the implication is that those who use ‘of’ in the expression ‘marginal product of labour’ intend to use it, and intend it to be interpreted, in an exclusive, monocausal, sole-proprietor sense. An appropriate subtitle for this study would be ‘The use and abuse of the proprietorial ‘of’’.

Another important element of the conceptual apparatus deployed in the following critique of the MPTD is the distinction between gross marginal product and net marginal product – or ‘marginal net product’, to use Alfred Marshall’s term. Marshall emphasised this distinction in recognition of the fact that when a marginal unit of labour is employed, it is often necessary, for technical reasons, to employ extra units of non-labour factors to assist the marginal unit of labour. In Marshall’s example, the extra shepherd requires an extra crook. The cost of the extra non-labour factors is deducted from the gross MPAL to arrive at the net MPAL.

Marshall’s concept of net marginal product is further elaborated in what follows by distinguishing between the ‘partially net marginal product of labour’ and the ‘fully net marginal product of labour’ – with apologies to readers for the unavoidable cumbersomeness of the terms. This distinction occupies a key position in assessing the validity of the MPTD as a principle of positive economics. It is developed in detail below, but in simple introductory terms the concept of the partially net MPAL is arrived at by deducting from the gross MPAL the cost of the extra units of other variable factors that need to be employed along with the marginal unit of labour; whereas the concept of the fully net MPAL requires that a portion of the costs of the fixed factor(s) be also deducted.²

2
Forerunners and founders

This chapter deals with 15 authors who contributed to the early development of the MPTD. Some of the contributions could only be described as vague intimations or approximations that were not recognised by the contributors themselves or by their contemporaries as formal statements of the MPTD. Other contributions in this chapter, however, have come to be regarded as the seminal foundations of the MPTD to which future scholars continually return.

W. Petty (1623–1687), T.R. Malthus (1766–1834), M. Longfield (1802–1884) and I. Butt (1813–1879)

There are a number of possible claimants to the title of founder of the MPTD. According to Routh (1975, 40), one such is William Petty who in his Political Anatomy of Ireland (1672) calculated what each factor could produce in the absence of the others, and so enunciated the essence of the MPTD. Thomas Robert Malthus could also be considered as an early contributor when he said in his Principles of Political Economy (1820): ‘[Profits] are only a fair remuneration for that part of the production contributed by capitalists, estimated exactly in the same way as the contribution of the labour’ (1989, I, 81).

On the basis of this statement, Schumpeter (1954, 114) heralded Malthus as a pioneer of ‘the productivity theory of distribution’. Malthus’ pioneer status could also be seen in his concept of the rent of land as the product of the ‘quality of the earth, by which it can be made to yield a greater portion of the necessaries of life than is required for the maintenance of the persons employed on the land’ and as ‘a boon most important to the happiness of mankind’ (1989, I, 139, 239). His concept of rent in this absolute sense, as distinct from differential rent, could be regarded as a precursor of the notion of the specific product of a factor, as explained above.

The classical theory of differential rent is another possible precursor. As Steedman (1997, 48) notes, ‘it is not difficult to present the logic of the Anderson-Malthus-West-Ricardo theory of (intensive) rent as a marginal productivity theory, applied to at least one input’; and this view appears to be shared by Kurz (1999, 145), who interprets marginalism as ‘an offspring of the theory of differential rent as it had been developed by authors such as Thomas Robert Malthus’, and as a ‘generalisation of the principle of intensive diminishing returns to the treatment of all sorts of economic phenomena’.

Schumpeter claimed that Mountifort Longfield, in lectures delivered at Trinity College, Dublin, in 1833, and published in 1834, presented ‘a reasonably complete and reasonably correct theory of distribution based upon the marginal productivity principle, not only the marginal cost principle’ (Schumpeter 1954, 465). Longfield ‘explained both profits … and wages in terms of the contributions to total product that result from the addition to the productive set-up of the last element of capital (tools) or labor’ (Schumpeter 1954, 465; cited by Black (1971), who notes that Bowley (1937, 185) also attributed a marginal productivity theory of wages to Longfield). The strongest evidence for the claim that Longfield was a pioneer of the MPTD appears to be the following:

If a spade makes a man’s labour twenty times as efficacious as it would be if unassisted by any instrument,

only of his work is performed by himself, and the remaining

must be attributed to the capital. And this is the measure of the intensity of the demand for such an instrument. A labourer working for himself would find it for his interest to give

of the produce of his labour to the person who would lend him one, if the alternative was that he should turn up the earth with his naked hands; or if he worked for another, his employer might pay a similar sum for the purpose of supplying him with an instrument.

(Longfield [1834] 1931, 195; quoted in Moss 1973, 327)

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Table of contents

• Routledge Advances in Heterodox Economics
• Contents
• Acknowledgements
• Introduction
• 1 Basic concepts
• 2 Forerunners and founders
• 3 Followers and critics, 1900–1920
• 4 Followers and critics, 1920 to 1940
• 5 Followers and critics after 1940
• 6 Summary of the main themes
• 7 Miscellaneous considerations
• 8 The normative language of the non-normative MPTD
• 9 General conclusion: neither normative nor positive
• Appendix A W.S. Jevons (1835–1882) and the MPTD
• Appendix B Marshall’s concept of net marginal product: fully net or partially net?
• Appendix C Wicksteed’s recantation
• Notes
• References
• Index