پویایی های اقتصادی در یک مدل ساده با منابع تمام شدنی و نرخ دستمزد واقعی

The paper elaborates a dynamic input–output model with exhaustible resources. Discoveries of new deposits and technical progress are set aside. It is assumed that there is a ‘backstop technology’ (based on solar energy), which implies that exhaustible resources are not indispensable in production. Given the real wage rate and the consumption pattern of profit and royalty recipients, it is then shown that the paths followed by the royalties paid to the owners of resources, the quantities produced of the different commodities, and their prices are determined once a sequence of nominal profit rates is given.

For well-known reasons, an economic system using exhaustible resources, such as ores of coal, oil or metal, constitutes one of the most difficult objects of investigation in the theory of production (see, for example, Kurz and Salvadori, 1995, ch. 12; Kurz and Salvadori, 1997). In order to render the problem manageable, theorists frequently have recourse to strong simplifying assumptions. In much of the literature the problem is studied in a partial framework with a single kind of exhaustible resource: the prices of all commodities except the price of the resource are assumed to be given and constant over time. With natural resources that are used to produce energy, for example, this is clearly unsatisfactory, because it can safely be assumed that energy enters as an input in the production of most, if not all, commodities, which implies that a change in the price of energy has an impact on the prices of many, if not all, commodities. Hence, a general framework of the analysis is needed. Moreover, since with exhaustible resources both relative prices, income distribution and the quantities produced will generally change over time, in principle a dynamic analysis is required tracing the time paths of prices, quantities and the distributive variables. Piero Sraffa, a pioneer of the modern ‘classical’ theory of production, distribution and value (see Sraffa, 1960; and Unpublished Papers and Correspondence, Trinity College Library, Cambridge, UK, as catalogued by Jonathan Smith), was perfectly aware of these difficulties already at an early stage of his work. As is well known, he adopted the concept of production as a circular flow, which he had encountered in the writings of the physiocrats and the classical economists, and also in Marx. However, he was clear that the assumption of self-replacement of an economic system, which is to be found in these authors and on which he based some of his analysis, was a bold one. In the following note dated 25 March 1946 from his hitherto unpublished papers1 he first points out a difference between a physical real cost approach to the problem of value and distribution, which he endorsed, and the labour theory of value: The difference between the ‘Physical real costs’ and the Ricardo–Marxian theory of ‘labour costs’ is that the first does, and the latter does not, include in them the natural resources that are used up in the course of production (such as coal, iron, exhaustion of land) [Air, water, etc. are not used up: as there is an unlimited supply, no subtraction can be made from ∞]. This is fundamental because it does away with ‘human energy’ and such metaphysical things. He added: But how are we going to replace these natural things? There are three cases: a) they can be reproduced by labour (land properties, with manures etc.); b) they can be substituted by labour (coal by hydroelectric plant: or by spending in research and discovery of new sources and new methods of economising); c) they cannot be either reproduced nor substituted2 - and in this case they cannot find a place in a theory of continuous production and consumption: they are dynamical facts, i.e. a stock that is being gradually exhausted and cannot be renewed, and must ultimately lead to destruction of the society. But this case does not satisfy our conditions of a society that just manages to keep continuously alive. (Sraffa’s papers, D3/12/42: 33; Sraffa’s emphasis). Obviously, any economic model is bound to distort reality in some way. Otherwise it would be identical with the ‘seamless whole’ and thus useless in interpreting aspects of the latter. In no way do we want to dispute the usefulness of Sraffa’s approach in his 1960 book, which hardly needs to be justified, given the rich harvest of important findings it yielded. At the same time the ‘dynamical facts’ Sraffa speaks of cannot be ignored and ought to be studied. In this paper we shall make a further probing step in this direction. Our aim is very modest, though. In two previous contributions we studied the problem of exhaustible resources in a multisectoral framework, using a dynamic input–output model. In this paper we shall propose a significant modification of our previous formalizations, which, it is to be hoped, sheds some of their weaknesses. Compared with the earlier conceptualization, the new one exhibits the following features. While previously we started from a given nominal wage rate and a constant nominal rate of interest, we shall now assume a given and constant real wage rate, specified in terms of some given bundle of wage goods. Treating one of the distributive variables as given from outside the system of production (or treating it as independently variable) and taking the other variables (rate of profits and royalties) as endogenously determined is much more ‘classical’ in spirit than the previous premises. In particular, the classical concept of the ‘surplus’ product, and its sharing out between capitalists and resource owners as profits and royalties, is given a clear physical meaning. Further, we shall assume that all realised nonwage incomes, profits and royalties, will be spent on consumption; for simplicity it is assumed that this part of consumption will be proportional to a given vector of consumption goods, which does not change over time. We shall set aside technical progress both in the methods of production extracting and in those using resources. Discoveries of new deposits (or resources) are excluded; existing stocks of resources are taken to be known with certainty at any given moment of time. To avoid the implication mentioned by Sraffa — the ‘destruction of society’ — we shall assume that there is a ‘backstop technology’, which allows one to produce the given vector of consumption goods without using any of the exhaustible resources. The example given in our previous contributions was solar or geothermal energy which could replace other forms of energy. The composition of the paper is as follows. Section 2 states the main assumptions that underlie the argument and presents the dynamic input–output model. Section 3 contains some preliminary result. Section 4 presents the complete analysis and the main results. Section 5 contains some concluding remarks.

In this paper a dynamic input–output model has been developed which is able to deal with exhaustible resources based on a number of simplifying assumptions. In particular, each resource is taken to be available in a quantity which, at time 0, is known with certainty. Discoveries of new resources (or deposits of known resources) are excluded. Technical progress in the industries extracting or utilizing the resources is set aside. It is assumed that there is a ‘backstop technology’, which implies that exhaustible resources are useful but not indispensable in the production and reproduction of commodities. The real wage rate is given and constant. The annual consumption of commodities by profit and royalty recipients is assumed to be proportional to a given vector of commodities which is constant over time. On the basis of these assumptions the paths followed by the endogenous variables — especially the royalties paid to the owners of the exhaustible resources, the quantities produced of the different commodities and their prices — are determined once a sequence of nominal profit rates is given. A change in such a sequence does not affect the quantities produced or the relative royalties and prices actualized at any time. One aspect of the solution of the model is the structural change of the economy over time, that is, the change in the methods of production adopted to satisfy effectual demand and the intensities with which the processes are operated, the overall level and composition of employment, etc.