Robert Torrens and the Ricardian model of dynamic equilibrium growth

ABSTRACT

This paper reconstructs Torrens's dynamic theory of distribution which is based on three notions of wages. In the early stages of growth, capital increases faster than population, so the actual wage rises above the minimum. Thereafter, the economy grows with a tendency for the population to increase faster than the capital while limiting the actual wage below the decreasing maximum until it enters a stationary state and the actual wage and profit rates are reduced to their minimum. Such a theory has been attributed to Ricardo by some scholars, but Torrens proposed a more fully developed account than Ricardo's.

KEYWORDS:

• Robert Torrens
• David Ricardo
• wages
• distribution
• dynamic equilibrium growth

JEL CODES:

• B12
• B31
• O41

Acknowledgments

This work was supported by Japan Society for the Promotion of Science under Grant (B): 25780144; and Grant (B): 16K17095. I am also grateful to Kazuki Kumashiro, Matthew Smith and Takuro Tanaka, as well as two anonymous referees for the very helpful comments and suggestions. Responsibility for this paper's contents, however, must remain with me.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ O'Brien (1966) points out that Torrens's letter to Wilmot-Horton dated 23 March 1826 was in fact the draft of the 1829 Appendix. The Appendix, according to Robbins (1958, 273), was reprinted with minor alterations in four publications: a tract entitled Colonel Torrens on the Wages of Labour, and on the Means of Improving the Condition of the Working Classes. A New Edition, Corrected (1832), which is, according to De Vivo (2000, xxiii), “a reprint (with minor alterations) of the Appendix to the 1829 edition of External Corn Trade,” On Wages and Combination (Torrens 1834), A Letter to Russell (Torrens 1837) and A Letter to Ashley (Torrens 1844a).

² Morishima (1989, 104, 124), who reconstructs Ricardo's economic system as a general equilibrium model, says that “Casarosa's one-sector interpretation of Ricardo's growth theory is the most remote from Ricardo … although it is simple, looks neat and seems appealing” and that “Casarosa's dynamic path too is un-Ricardian.” Hicks and Hollander (1977) also acknowledge that the model rationally reconstructed by them is far from Ricardo's own discourse on economic growth, stating: “We shall allow ourselves… to describe the model in terms that, admittedly, are not Ricardo's, but that we think will quickly make it more intelligible to the modern economist” (353).

³ The actual wage is equal to what Torrens had called “the market price of labour” in the first edition of External Corn Trade (Torrens 1815).

⁴ Considering that capital is composed not only of wages fund but also of non-wages fund, Torrens later changed the phrase “the amount of capital” into “the quantity of the ingredients of capital destined for its maintenance” (1834, 22).

⁵ According to O'Brien (1966, 338), in Torrens's 1826 letter to Wilmot-Horton which is considered to be the draft of the 1829 Appendix, emigration, instead of free trade, had been proposed as one of the means of raising the maximum wage.

⁶ The minimum wage is the same as what Torrens called “the natural price of labour” in the first edition of External Corn Trade (Torrens 1815, 62–63). In the Appendix, Torrens reuses some passages of the first edition with slight alternation and the phrase “the natural price of labour” is replaced with “the minimum of wages.”

⁷ The similar sentence appeared in the first edition of External Corn Trade (Torrens 1815, 63), which Ricardo cited in the Principles of Political Economy and Taxation (Ricardo 1819 [1951], 97).

⁸ There was originally the phrase “the prudential check which may exist with respect to marriage.” However, the prudential check should mean limiting the birth rate under a fixed minimum wage. Therefore, Torrens (1834, 12–13) later corrected the text as shown with the square bracket. In a similar way, the phrase “a prudential check to marriage” (1829, 460) elsewhere in the book was later replaced with “a taste for the comforts of life” (1834, 12). Torrens's notion of “scale of comfort” is considered to stem from the Malthusian idea of habit formation.

⁹ This differs from Rosell's assumption of the inputs of corn and seed to production. He, however, removes the uses of material and machinery in the production from his suppositions (see Torrens 1829, 464). Our simplification as well as Rosell's should be allowed in a single homogeneous corn growth model.

¹⁰ Hollander (1968) and O'Brien (2004, 131–135) reconstruct the wages fund model incorporating non-wages in Torrens's Wages and Combination, in which the 1829 text was reproduced. According to Hollander, Torrens took the theory of (actual) wages, the rate of which is determined by the ratio between the circulating capital stock – or the aggregate wage bill – and the given working population and the technical coefficient of production between labour and fixed capital through the equilibrium of the labour market. This contrasts with the Millian theory where the wage rate is predetermined by the ratio between the circulating capital stock and the given working population before market-clearing. Hollander calls the former “the ex post wages-fund theory,” and the latter “the ex ante wages-fund theory.” In contrast to Hollander's reconstruction, O'Brien reformulates Torrens's theory which involves a labour demand curve of unit elasticity while the (actual) wage rate depends on the circulating-capital/population ratio and the fixed-capital/labour coefficient. In a single corn model in our reconstruction, however, the fixed-capital/labour coefficient cannot be involved in the determination of the actual wage rate. As later clarified by Torrens's through a correction, he states that the actual wage rate is determined by “the ratio between population and capital, or, more correctly, between the quantity of labour and the quantity of the ingredients of capital destined for its maintenance” (1834, 22; also see footnote 4). When he considers the issue of the growth rate between “population” and “capital,” the term “population” stands for “the number of labourers to be maintained” and the term “capital” for “the quantity of those ingredients of capital which are destined for their maintenance” (1834, 21). Thus, we do not need to take the technical coefficient into consideration of Torrens's vision of economic dynamics.

¹¹ This differs from Rosell's constant returns assumption.

¹² In Chapter 2 of Wages and Combination, Torrens, in illustrating the case in which the farmer obtains 24% of profits above the minimum rate, 7%, states, “Increasing profits always occasion a more rapid accumulation of capital” (1834, 33–36).

¹³ A dot over a variable denotes a derivative with respect to time.

¹⁴ In the () plane, the maximum wage is described as the convex curve by satisfying and

¹⁵ As a necessary and sufficient condition for the system not to traverse up through the maximum wage curve, the elasticity of the working population with respect to the maximum wage rate is equal to or strictly more than minus one (see Dome 1992, 32–33): The elasticity of the working population with respect to the maximum wage rate is . From , the condition must be . The diminishing returns assumption, , satisfies this and allows the system, as Torrens describes, to move between the maximum and the minimum wages and to converge on the stationary state point.

¹⁶ Torrens states that “though there will exist no physical, yet there will be a moral impossibility that wages should exceed that which remains after the replacement of the capitalist's other advances with the lowest rate of increase, for the sake of which he will carry on his business. This, then, we may call the moral maximum of wages” (457; Torrens's emphasis).

¹⁷ Torrens mentions the possibility that the surplus capital “will be invested in foreign loans and foreign adventures” (1829, 469). Further research is needed into his analysis of international trade and his theory of systematic colonisation, topics which lie outside the scope of the present work.

¹⁸ Against O'Brien (1966, 337), Vint properly argues “Torrens is here making use of a long run analysis and not the short run wages fund doctrine” (1994, 105).

¹⁹ In the () plane, the dynamic equilibrium wage is described as the convex curve by satisfying and

On the other hand, since the maximum wage curve and the minimum wage curve intersect when it follows that Multiplying both sides of this equation by (), we obtain Adding () to the left side, we obtain the following inequality. Furthermore, adding () to both sides, we obtain the following inequality: Multiplying both sides by (), we obtain (). Therefore, considering that the dynamic equilibrium curve intersects the maximum wage curve at the point and that and , we can find that in the range , the dynamic equilibrium curve exists below the maximum wage curve, while in the range , the former is above the latter.

²⁰ Let us consider the case of the actual wage rate above (below) the dynamic equilibrium wage: . From this, we obtain . That is, if . This means that population (capital) increases faster than capital (population) in the system which exists above (below) the dynamic equilibrium curve. Considering if , we can find that the actual wage rate rises when the system starts from the lower regions, [i], [v] and [vi], compared to the dynamic equilibrium curve. However, this actual wage rate falls when the system initiates from the upper regions, [ii], [iii] and [iv]. It is evident that the actual wage rate remains stationary when the system converges on the dynamic equilibrium curve. On the other hand, it is clear from Equation (6)(6) that population decreases when the system starts from the upper regions, [i], [ii] and [iii], above the minimum wage line – that is, if the actual wage rate is above the minimum – while it decreases when the system is from the lower regions, [iv], [v] and [vi] – that is, if the actual wage rate is below the minimum. Given this, the motion in each region is shown by the arrows in Figure 3.

²¹ We believe we are justified in setting the starting point of the economy at the same state as “new countries, where … capital continues to bear that proportion to labour which makes actual wages permanently high” (Torrens, 1829, 475). In Region [i], capital increase faster than population so that the wage rate continually rises.

²² Consistent with Malthus (1798 [1986]), Torrens (1817, 523) states that “population… must have a tendency to increase in a geometrical ratio.” However, he also argues, “If we were to extend tillage over inferior tracts, or to heighten the cultivation of our fertile lands, each additional quantity of capital applied to the soil, would yield a less proportional return; and while the generative powers (unless reduced by the deterioration of the human constitution) remained unimpaired, the productive powers which supply subsistence would be perpetually decreasing” (523–524). According to Blaug (1958, 104), “Malthus never emphasized the law of diminishing returns in the Essay on Population,” but the “Ricardian economists… were quick to relate the arithmetic ratio explicitly to the assumption of diminishing returns in agriculture.” In such a sense, Torrens was one of the Ricardian economists.

²³ The other way Torrens (1817, 518) thought of was a self-supporting emigration for “removing” the superfluous numbers who had already come into the world.

²⁴ A long-run tendency in capital stock, constituting labour demand, to increase faster than population, constituting labour supply, could achieve continuous full employment of labour. In Chapter 2 of Wages and Combination, however, Torrens acknowledges the existence of temporal frictional unemployment, stating “that the general good which results from the employment of new and improved machinery is accompanied by partial evil.” Furthermore, he suggests that the government should provide relief for the temporarily unemployed: “Whenever a new application of mechanical power throws a particular class of operatives out of employment, a national fund should be provided, to aid them in betaking themselves to other occupations… A comprehensive plan for their relief should be one of the earliest measures of the reformed Parliament” (1834, 44). It also should be noted that Torrens much later states: “The ultimate effect of every new application of mechanical power, causing the same quantity of work to be executed by fewer hands, is to increase national wealth and to enlarge the field of employment. The immediate effect of every such improvement is to diminish the demand for labour in the particular trade to which it is applied” (1844b, 260; original emphasis). The present subject, however, is destined for the long-run analysis of Torrens on growth, not for the short-term discussion. As for Torrens's other mention of the temporarily negative but permanently positive effects of introducing machinery upon workers, see Torrens (1821, xii). Also, as for Torrens on Machinery, see Karayiannis (2000).

²⁵ Workers’ acquiring superior habit of living indicates the exogenously raised in our reconstruction. In this case, the dynamic equilibrium wage curve shifts upward – from Equation (10)(10) , while the maximum wage curve remains the same – from Equation (8)(8) . Thus, the continuously improved workers’ habit of living might cause the economy to arrive at the stationary state in the earlier stage. This, however, would be never dismal for working classes because they could reap the benefits of superior living rather than enduring the “animal life” that would oblige humankind to stand “on the extreme verge of existence.”

²⁶ We should briefly treat Torrens's late position on the relationship between population and capital. In 1857, he re-published his early pamphlet entitled The Economists Refuted (Torrens 1857). The re-published pamphlet has not only some trivial corrections and the deletion of Chapter 6 on “observations on the expediency of making peace with France” which appeared in the 1808 edition (Torrens [1808] 1993), but also substantive revisions to Chapter 4. In particular, it should be noted that the following sentence was added: “[F]rom the relative proportions according to which population and capital have, in all old countries, been hitherto found to increase, the supply of labour has such a tendency to exceed the demand for it that the labouring classes, even when there is no extraordinary stagnation or revulsion in the channels of industry, are commonly reduced to a degree of distress” (Torrens 1857, 35). Torrens here apparently reverted back to his earliest view that population constituting labour supply tends to increase faster than capital stock constituting labour demand. This reversal should be observed and considered in future research.

Additional information

Funding

Japan Society for the Promotion of Science [grant number (B): 16K17095], [grant number (B): 25780144].