Growth Theory

The ‘principle of population’ of the first Essay entailing ‘arithmetical’ and ‘geometrical ratios’ attributed respectively to food and population increase, and necessitating ‘checks’ to the latter, derived—as, Malthus himself later informs us—from Hume, Wallace, Smith, and Price (Malthus 1803: iii). In the light of our concern with possible Cambridge connections, it is significant that Malthus referred critically in 1803 to Paley’s chapter on population in Moral and Political Philosophy (1788), and found the matter of ‘checks’ treated (albeit inconsistently) only in the later Natural Theology (1802). These facts should be borne in mind when evaluating Keynes’s contention that Paley’s Principles ‘must be placed high...amongst the intellectual influences on the author of the Essay on Population (Keynes 1933 [1972]: 79).

The ratios themselves in Malthus’s exposition lack an analytical foundation, entailing the superposition of purported data derived from completely different environments. Nonetheless, the principle of diminishing returns does make an appearance even in the first edition, providing the foundation of a growth model involving a declining path of real average wages in consequence of a decelerating rate of growth of labour demand—what has come to be labelled the ‘canonical’ classical growth model. According to the argument, as population density rises, per capita output and the real wage fall, ultimately leading to a stationary population (Malthus 1798: Chapters IV, VI, VII, XVII). This analysis neglects the profit rate, particularly its downward path along with the real wage, a prime feature of the full model. The fifth (1817) edition of the Essay repairs this deficiency by an impressive formulation of the process of expansion towards the ‘practical limit’ (the theoretical stationary state) entailing deceleration of both capital and population growth rates, in consequence of the increasing paucity of ‘cultivatable land’, and declining returns to labour and capital until their respective minima (ibid.: volume II: 433-435). Malthus also elaborated the conditions, in addition to unchanged technology, that must be satisfied for a ‘regular’ deceleration of population growth and of the wage and profit rates, for a steady pattern was not to be expected in practice.

Malthus’s Principles of Political Economy provides an especially elegant account of the fully fledged canonical growth model, which I believe is the best by far in the entire classical literature. Here, Malthus demonstrates that to assume a constant real wage in the course of growth not only is ‘contrary to the actual state of things’ (Malthus 1820: 297, 1836: 272) but also entails a logical ‘contradiction’:

[I]f from the first [the labourer] had no more than sufficient to keep up the actual population, the labouring classes could not increase; nor would there be any occasion for the progressive cultivation of poorer land. On the other hand, if the real [1836: corn] wages of labour were such as to admit of and encourage an [1836: a considerable] increase of population, and yet were always to remain the same, it would involve the contradiction of a continued increase of population [1836: at the same rate] after the accumulation of capital, and the means of supporting such an increase had entirely ceased (ibid.).

A further passage explains in crystal-clear terms that the incidence of diminishing returns cannot fall solely on labour since the decline in the real (corn) wage, because of its effect on the population growth rate, is constrained relative to the fall in the marginal product. The outcome of increasing land scarcity is accordingly to raise the share in the produce paid to labour at both the extensive and intensive (zero-rent) margins, thereby depressing the profit rate. Thus, the returns to labour and to capital decline simultaneously to their respective minima at which stage further expansion of population and capital ceases (ibid.: 298-299, 273-274). Every feature of the classical growth model is substantiated, including the most basic of all—the functional relation between the profit rate and the proportionate wage such that a fall in the profit rate is consistent with a fall in the real wage during the course of growth, subject to declining agricultural productivity.

I note here that Malthus responds in the typical terms of a theorist to Richard Jones’s so-called inductivist objections to the land-based growth model. ‘I am not sure’, he wrote to Whewell in his letter of 28 February 1831 cited above,

whether [Jones] has not gone beyond the truth in his unwillingness to admit the tendency of continued accumulation, and of the progress of population and cultivation to lower the rates of profits and corn wages on the land ... If the progress of cultivation and population has no tendency to diminish corn wages, I do not see what cause should ever retard the rate at which population is known to increase in the new colonies (italics in original).

The explanation for the falling profit rate outlined above runs in aggregative terms. Malthus should also be recognized as probably the first serious proponent of a dual-sector model wherein the profit rate is determined within agriculture and then applied to industry by way of variation in the terms of trade between food and manufactures (Malthus 1820: 300). Values in the sense of exchange rates only enter the picture in transferring from the agricultural rate to the general rate, and not in the determination of the agricultural rate itself. The 1836 version of the Principles confirms that there are two forces at play in profit-rate determination: ‘In the cultivation of land, the cause of the necessary diminution of profits is the diminution in the quantity of produce obtained by the same quantity of labour’—a physical quantum; in ‘manufactures and commerce it is the fall in the exchangeable value of the same amount of [manufactured] produce’ (Malthus 1836: 275; italics in original). For,

corn, on account of its being the main support of the labourer, is the only object in the production of which a comparison may be instituted between the quantity advanced and the quantity produced ... In manufacturing and mercantile employments, there is no approach towards a possibility of comparing the advances with the products in regard to quantity (ibid.: 265—266).

It is the homogeneity of input and output in agriculture that holds the key. To justify the expression of the agricultural profit rate in physical terms, a particular assumption is made to preclude short-term or seasonal price fluctuations or the exceptional closing of markets that create situations where ‘a part of the crop might be of no value [at all]’ (Malthus 1820: 296, fn., 1836: 272, fn.). The disturbance to a physical or corn-profit calculation by sudden corn-price movements is however irrelevant in the growth context. Also in that context, Malthus, in the Inquiry into the Nature and Progress of Rent (Malthus 1815a), applied a sort of Law of Markets to corn whereby the physical surplus—‘the excess of their quantity above the quantity necessary to maintain the labour required to produce them’—guarantees a value surplus by generating, via population growth, the requisite demand for food; in other cases, value reflects scarcity or ‘the smallness of the supply compared with the demand’ (ibid.: 12). The Principles too reiterates that only specialty products—where demand is ‘exterior to, and independent of, the production itself’—are treatable in scarcity rather than surplus terms (Malthus 1820: 146-147, 1836: 145-146).

Malthus laboured under the misconception that Ricardo failed to apply demand-supply analysis to long-run cost pricing, allowing solely for supply conditions. Certainly, Malthus insisted that ‘cost of production itself only influences the prices of commodities as the payment of this cost is the necessary condition of their continued supply [1836: in proportion to the extent of the effectual demand for them]’ (ibid.: 1820: 74-75, 1836: 71), a much admired formulation often said to presage Jevonian doctrine. I perceive here more of a Marshallian flavour, but in either event there is no justification for regarding Malthus as a ‘subjective value’ theorist in any sense that would not apply to Ricardo, who argued only for the primacy of supply and protested against Malthus’s refusal to treat the long-run pricing of corn in demand-supply terms (Ricardo 1951, volume I: 405-406).

In so far as science is a social enterprise, it is sometimes said that should contemporaries be unfamiliar with a contribution it is as if that contribution had never been made as far as concerns the scientific endeavour. To take this line, I suggest, would be to ignore information pertinent to the origins of scientific ideas and for the progress of science. For even when a contribution goes unnoticed, we learn from it—when it finally sees the light of day—what technically could be achieved within the early intellectual and empirical environment, and also which causal conditions may be excluded as required for similar notions emerging independently at a later stage. Much the same may be said of misinterpretation by contemporaries.

The Malthus case illustrates these propositions. Most contemporaries— Ricardo is an exception—seem to have been unaware of Malthus’s outstanding contribution to growth theory. Judging from the textbooks the neglect continues to this day. Had Malthus’s account been properly addressed, we might have been spared decades of fixed-wage theorising taught to thousands as a logical structure.

Taking proper account of Malthus’s contribution also undermines much of the Sraffian version of the historiography of economics. In his early Cambridge lectures on advanced value theory (1928-1931), Sraffa attributes embryonic features of a corn model entailing calculation of surplus in physical terms to William Petty and Francois Quesnay. Subsequently, he famously attributed the construct—though as a ‘rational reconstruction’—to a brief statement in 1814 by Ricardo that ‘it is the profits of the farmer that regulate the profits of all other trades’ (Sraffa 1951, volume I: xxxi). Malthus is mentioned but only to emphasize his opposition to the formulation of 1814. His elaboration of just such a model in his later texts goes wholly unnoticed.

I turn to the common charge against Malthus of trumpeting the inevitability of low living standards. This misreading characterized Marx and all manner of utopian reformers. In fact, Malthus, in common with other classical thinkers including Ricardo, used the growth model not as a predictive device but as an engine of analysis to demonstrate how, by the practice of population control, a low-wage outcome might be avoided. For while increasing land scarcity dictated a deceleration in the rate of population growth, ‘a gradual change in the habits of the labouring classes would...effect the necessary retardation in the rate of increase’, so that ‘in the progress of cultivation and wealth the condition of the lower classes of society would be in a state of constant improvement’ (Malthus 1817, volume III: 420-421).

Prudential population control is treated by Malthus not merely as an exogenous matter, the outcome in particular of appropriate education, but as endogenous to the growth process itself. Already in the 1803 Essay there is mention of the possibility that rising wages further stimulate such control by generating more sophisticated tastes (Malthus 1803: 246). The 1817 version adds the analytical insight that the rising corn-manufactures price ratio during the growth process alters taste patterns in favour of manufactured wage goods, thereby contributing to a deceleration of the population growth rate (Malthus 1817, volume III: 23-24).

Mill therefore rightly posited Malthus as one of the great reformers (Mill 1848 [1965]: 753). Bonar took this same line in his delightful allocution at the Cambridge Commemoration in 1935 (Bonar 1935: 221-225). All the more heroic is Malthus when we recall his status as a Church of England clergyman and the risk to his reputation he was prepared to take by championing ‘prudential’ restraint should ‘moral’ restraint prove too much to ask. Charles Fay in his allocution touches effectively and amusingly on this feature (Fay 1935: 228-229). Malthus’s courage is no less apparent when in 1815 he opted for agricultural protectionism, notwithstanding the damage to his standing with the progressive journals. His abandonment of this position, it must be allowed, was made with little fanfare.

A word more on Malthus as reformer in the light of his harshly expressed objections to in-house poor relief that have stamped him with gross illiberal- ity. His position, I suggest, can be more accurately portrayed by supposing the general practice of prudential restraint, such that ‘low’ family size is the rule. With the removal of population pressure, the practical approach to policy is transformed. A case is even made out as early as the second Essay for family allowances to help those who had more children than they could be expected to foresee (Malthus 1803: 595).

Marx’s strictures apply to Paley rather than to Malthus. In his Moral Philosophy, Paley had argued ‘that the condition most favourable to the population of a country, and, at the same time, to its general happiness, is, “that of a laborious frugal people ministering to the demands of an opulent luxurious nation’” (Paley quoted in ibid.: 592). Moreover, in Natural Theology Paley deduced from the principle of population—citing Malthus on the arithmetic and geometric ratios—the impossibility ‘to people a country with inhabitants who shall all be in easy circumstances’ leading him to justify ‘the distinctions of civil life’ (Paley 1802: 340-341). This sort of deduction Malthus could not fathom, considering Paley’s concession in 1802 that ‘mankind will in every country breed up to a certain point of distress’ (ibid.: 539), for in that case ‘that country will evidently be the happiest, where the degree of distress at this point is the least, and consequently, if the spread of luxury, by producing the check sooner, tend to diminish this degree of distress, it is certainly desirable’ (Paley quoted in Malthus 1803: 592, fn.).

It may be noted that as early as 1796—in a non-extant manuscript (The Crisis)—Malthus had apparently objected on theoretical grounds, with evident Smithian pedigree, to Paley’s proposition whereby ‘the quantity of happiness in any country is best measured by the number of people’; for Malthus, ‘[i]ncreasing population is the most certain possible sign of the happiness and prosperity of a state; but the actual population may be only a sign of the happiness that is past’ (Malthus quoted by Empson 1837: 482). Malthus is also reported as later regarding Paley and Pitt as ‘the two converts of whom he was most proud’ (ibid.: 483).