Natural resources in the theory of production: the Georgescu-Roegen/Daly versus Solow/Stiglitz controversy

Abstract

This paper provides a theoretical and methodological account of an important controversy between neoclassical resource economics and ecological economics from the early 1970s to the end of the 1990s. It shows that the assumption of unbounded resource productivity in the work of Solow and Stiglitz–and the related concepts of substitution and technical progress–rest on a model-based methodology. On the other hand, Georgescu-Roegen’s assumption of thermodynamic limits to production, later revived by Daly, comes from a methodology of interdisciplinary consistency. I conclude that neither side provided a definitive proof of its own claim because both face important conceptual issues.

Keywords:

• Nicholas Georgescu-Roegen
• Robert Solow
• Joseph Stiglitz
• natural resources
• theory of production

JEL CODES:

• B22
• Q32
• Q57

Acknowledgements

I would like to thank Robert Dimand, Marco Franco, Christophe Goupil, Jérôme Lallement, Antoine Missemer, Antonin Pottier, and Fatma Rostom for their helpful comments and suggestions on earlier versions of this paper. I am also grateful to the participants of the Albert O. Hirschman Seminar, the 2017 Max Weber Seminar, the 2018 Science and Energy Seminar, and the Young Scholars Seminar of the 2018 ESHET Conference. Finally, I want to thank two anonymous reviewers for their valuable remarks. However, all remaining shortcomings are mine.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 The preoccupations regarding the depletion of natural resources had been discussed in economics before this period. See, for instance, Missemer (2017a). Even though they partially relied on these earlier works, the approaches that emerged in the 1970s rested on new concepts and tools that considerably reframed questions.

2 I use this label in order to be more precise than the usual one of “natural resource economics” found in literature. This choice underlines the continuity with the neoclassical theories of production and growth and clearly distinguish it from ecological economics.

3 Kenneth Boulding (1966) is another important early contributor of this new approach and he shares a similar intellectual trajectory.

4 Despite this influence, Daly and Georgescu-Roegen did not always agree with each other. The main point of contention between them was the question of a “steady state” (Daly 1974; Georgescu-Roegen 1977). I will briefly discuss this problem again in Section 4.

5 By “theory” I mean the concepts that constitute the intellectual framework through which economists conceive their objects of study. In particular, I distinguish them from “models” as purely mathematical systems. In this context, “methodology” is primarily understood as the way concepts are built, and how they articulate with models.

6 In a still general perspective, Pottier (2014, chap. 2) provides some insights on the technical issues raised by early works in natural resource economics. A more specific contribution on the influence of John Rawls and Harold Hotelling on Solow is provided by Erreygers (2009). There also exists an important body of literature specifically dedicated to Georgescu-Roegen’s conception of environmental issues (Gowdy and Mesner 1998; Bobulescu 2012, 2013, 2015; Missemer 2017b). While it provides insights on some aspects of the present controversy, no contribution takes it as its central subject.

7 Still in the same issue, Dasgupta and Heal (1974) provided another important contribution, which led some authors to speak of the Dasgupta-Heal-Solow-Stiglitz (DHSS) model (Benchekroun and Withagen 2011). I do not consider the work of Dasgupta and Heal in the present paper for two reasons: first, they did not participate actively in the subsequent controversy with ecological economists; second, their model relies on a utilitarian norm of intergenerational distribution that would require the introduction of additional formal aspects but would not contribute to a better understanding of the controversy.

8 See Erreygers (2009) for a discussion of this aspect.

9 Formally, this can be seen by rewriting the production function as: $\frac{Q}{R}={(\frac{K}{R})}^{\alpha }{(\frac{L}{R})}^{\gamma }.$ If R and L are constants, the productivity of resources on the left may be as large as one wishes, provided K is sufficiently great.

10 Solow’s demonstration relies on the minimisation of ${\int }_0^{\infty }R(t)dt$ under the constraints of capital accumulation. This is summarised by a differential system with two equations: $$\dot{K}=Q-C \text{and} \frac{{\dot{F}}_R}{F_R}=F_K$$ where F_R and F_K are the marginal productivities of resources and capital. Solow shows that there exists a solution of this system that consumes less than the total stock of resources if and only if inequality (3) is satisfied.

11 Stiglitz’s equations of evolution are similar to that obtained by Solow, except that they introduce constant growth rates of technical progress and population. In fact, Stiglitz establishes a more general condition for aggregate consumption to grow at a constant rate g: $$g<\frac{\lambda +\gamma n}{1-\alpha }$$ Setting g=n in this inequality yields condition (5).

12 Rewriting the production function as $Q=K^{\alpha }{\left(R{e}^{\frac{\lambda }{\beta }t}\right)}^{\beta }{L}^{\gamma }$ we see that $\frac{\lambda }{\beta }$ can be considered as the rate at which technical progress improves the level of resources, which justifies the label “resource augmenting technical progress”.

13 In the second part of the same paper, Stiglitz studies another model based on a similar production function. Instead of constant growth, he uses a utilitarian norm of intergenerational distribution, which consists of maximising the sum of discounted utilities across generations. Once again, technical progress plays a central role in escaping the scarcity of resources in this model: the asymptotic growth rate of consumption per head is positive if and only if resource augmenting technical progress is greater than the discount rate..

14 Stiglitz (1976) concentrated on the implications of competitive markets and alternative institutional structures on the allocation of resources. Solow and Wan (1976) explored an elaborated version of the growth model with extraction costs of the resource, and Solow (1978) analysed data on the price and the availability of resources.

15 This characterisation of the methodology of Solow and Stiglitz is only intended to capture their approach to the issue of natural resources and not their general methodological outlook. In the case of Solow, a more detailed account of his modelling practice has been given by Halsmayer (2014), which I discuss at various points below. To my knowledge, no such synthetic account exists for Stiglitz. However, he himself provided important methodological insights in the case of neoclassical resource economics (1979), to be discussed later on.

16 This interest for the issue of representation is the main difference with the account of Solow’s modelling practice provided by Halsmayer (2014). Indeed, she insists mainly on the new theoretical and empirical functions that the neoclassical growth model enabled economists to perform. While I also acknowledge similar functions in the case of natural resources, I put more emphasis on the conceptual issues raised by the formalism of production functions.

17 RFF is an independent research organisation, established in 1952 that played a central role in promoting the economic analysis of environmental issues. See, for instance, Spash (1999) or Pearce (2002).

18 CES production functions are of the form: $$Q=F(K,R,L)={[\alpha K^{\frac{\sigma -1}{\sigma }}+\beta R^{\frac{\sigma -1}{\sigma }}+\gamma L^{\frac{\sigma -1}{\sigma }}]}^{\frac{\sigma }{\sigma -1}}$$ The Cobb-Douglas is a special case of this family of functions, where the elasticity of substitution is unitary: σ = 1. When $\sigma \hspace{0.17em}>\hspace{0.17em}1,$ R = 0 does not imply Q = 0–that is to say that resources are not essential to production. In these conditions, it is possible to maintain a constant level of consumption across generations. Conversely, if $0<\sigma <1,$ then resources are essential, but the productivity of resources is bounded and no constant level of consumption can be maintained indefinitely.

19 Halsmayer (2014) shows that the simplicity of Solow’s growth model was acknowledged by himself and conceived as an alternative to complex models, such as Leontief’s input-output tables or Keynesian macro-econometric models. In this context, it was justified, on the one hand, as a “prototype” on which more refined models should be built and on the other hand, as a pedagogical tool in which elementary economic mechanisms could be explained transparently.

20 The transition is well illustrated by his book “Analytical Economics” (1966), which contains his most important contributions to neoclassical theory and an introduction to his new research programme. However, historical accounts of the evolution of Georgescu-Roegen’s thought underline that he has had a critical look on the foundations of neoclassical theory since the beginning of his career (Gowdy and Mesner 1998).

21 This idea had had precursors before Georgescu-Roegen, such as Sergeï Podolinsky and Frederick Soddy. But they are less well known and he was not aware of them when he first suggested it. See Martinez-Alier (1987) for an account of these antecedents.

22 Thermodynamics has two other principles which are not of interest for us here. See, for instance, Callen (1985) for an introduction to thermodynamics.

23 More precisely, if the source of the heat flow Q₁ is at temperature T₁, if it is in an environment at temperature T₀ < T₁, and if W is the amount of work produced, then the efficiency of the engine $\eta =\frac{W}{Q_1}$ is bounded by Carnot’s coefficient: $${\eta }_m=\frac{T_1-T_0}{T_1}<1$$

24 See Callen (1985) for a more complete introduction to this concept.

25 Georgescu-Roegen ended up thinking that the dissipation of matter had been ignored by thermodynamics and that it deserved the status of a fourth law. This has become one of his most controversial claims and it has raised many comments in ecological economics. See, for instance, Cleveland and Ruth (1997), and Ayres (1999).

26 In particular, it does not appear in The Entropy Law and the Economic Process.

27 Georgescu-Roegen’s criticism concerns other aspects of neoclassical resource economics as well. For instance, he denies that the appropriate intergenerational distribution may be achieved by market processes alone and questions the relevance of empirical estimates of production functions. However, these topics were not tackled in the 1997 debate. Therefore, they are less useful to understand the opposition between ecological economists and neoclassical resource economists.

28 This distinction is the cornerstone of Georgescu-Roegen’s theory of production, known as the flow-fund model (1971, chap. IX). This approach has been further developed along two distinct lines of research: the organisation of a single production process–see Vittucci Marzetti (2013) for a survey–and the interaction between multiple production processes–see Kurz and Salvadori (2003) for a comparison with Sraffa’s model. However, these developments are not concerned with the role of natural resources.

Other contributions employed the distinction between flows and funds to discuss the notion of substitution (Anderson 1987; Mayumi, Giampietro, and Gowdy 1998; van den Bergh 1999). Yet, the analytical framework of the flow-fund model is not mobilised more extensively, either by Georgescu-Roegen or other ecological economists, to formulate their criticism of neoclassical resource economics. This is the reason why the flow-fund model deserves to be treated separately.

29 Georgescu-Roegen’s later contributions do not give much more details on these arguments. Here and there, some allusions to the work of Solow and Stiglitz can be found (Georgescu-Roegen 1981, 1986, 1988), but the assumption of thermodynamic limits is not mentioned any more. Moreover, I could not find any interesting insights on these issues in the archives of Georgescu-Roegen and Solow, available at the Rubenstein Library of Duke University. No direct correspondence between them is available and no other material brings new and important elements to light, as far as the present paper is concerned.

30 This taxonomy distinguishes “theoretical interdisciplinarity” as above from “methodological interdisciplinarity”, involving only the transfer of methods or tools from one discipline to another. Moreover, theoretical interdisciplinarity is explicitly endorsed by recent contributions to the philosophy of ecological economics (Baumgärtner et al. 2008; Spash 2012), where it appears tightly linked with the influence of Georgescu-Roegen.

31 Georgescu-Roegen illustrated his point of view with, “the case of poisonous mushrooms which, although they contain low entropy, have no economic value” (1971, 282). This led him to criticise earlier attempts to reduce economic value to low entropy, such as those of the German physicist Georg Helm or the Polish sociologist, Leon Winiarski.

32 On another occasion, Georgescu-Roegen put it even more clearly: “The point is that it was the economic distinction between things having an economic value and waste which prompted the thermodynamic distinction, not conversely.” (Georgescu-Roegen 1976, 54).

33 The notion is used here in a slightly different way than before. Indeed, what is at stake is rather a theoretical reductionism, related to which questions are considered relevant and not an ontological reductionism.

34 Georgescu-Roegen’s approach emerged in a rather favourable context, marked by the rise of environmental preoccupations, oil shocks, and the debate on limits to growth. But as it appears from Solow’s work, for instance, this was not interpreted as the necessity for economists to revise the conceptual foundations of their theories, but rather to consider these issues from the point of view of their pre-established theories.

35 For instance, he stated that the economic process, “begins with the extraction (depletion) of low entropy resources at the input end and terminates with an equal quantity of high entropy waste (pollution) at the output end” (Daly 1974, 15).

36 Georgescu-Roegen’s (1966) contribution remains the most detailed criticism, as he was specifically asked to comment on the paper of Stiglitz. Daly instead mostly presented his own vision.

37 This definition has been the most influential, but it was not the first one. For instance, the International Union for Conservation of Nature had already given one of its report on World Conservation Strategy (International Union for Conservation of Nature 1980).

38 This use of the concept of substitution is an extension because it concerns natural capital as a whole, which also includes climate stability and ecosystems, for instance.

39 In this context, Victor (1991) had already highlighted the crucial role played by the different approaches to substitution and technical progress in production. However, he did not identify the idea of thermodynamic limits as a central argument.

40 The debate between weak and strong sustainability had been particularly intense during the 1990s and 2000s (Pezzey and Toman 2005; Neumayer 2013), but it has become less central in recent years.

41 More generally, the implications of physical laws both at the practical and at the cosmological levels are common in physics. The laws of mechanics, for instance, apply to the movement of planets as well as playing basketball.

42 It is useful to make clear that this claim is restricted to the introduction of the laws of thermodynamics in formal models. At the conceptual level instead, the entropy law remains an important reference in ecological economics.

43 This question is not mentioned in the early works of Solow and Stiglitz on natural resources. I could only find an allusion in one of Solow’s original paper on growth theory, where he states that, “Q represents output and K and L represent capital and labor inputs in ‘physical’ units” (Solow 1957, 312). This shows at least that the appropriate units for production are uncertain.

44 Following the same line, van den Bergh asserts that, “both the service output of materials processing and the value of this service output do not seem to be bounded by an identifiable absolute limit” van den Bergh (1999, 554).