Introduction
Economists assume that the fundamental principle underlying the process of all economic decision-making is that of scarcity: scarcity in means and in time. Homo Economicus is characterised as having unlimited desires, which, given the linear nature of time, Earth's finite resources cannot satisfy. Not only are all resources finite, many resources are also exhaustible. This implies that their existence is limited. Even though Solow demonstrated that an economy can be sustained indefinitely in a world of exhaustible resources, a major concern is if economic progress can still be made in such a world. Especially as a greater population growth rate than the economic growth rate leads to diminishing wealth per capita.
The theories dealing with economic growth, finite and exhaustible resources, and population growth date back to the eighteenth century, when Malthus, Ricardo and Mill developed their theories on these matters. Since then these theories have been elaborated, formalised, adapted and newer theories have been developed. Two main schools of thought can be identified: the conservationists and the optimists. It is not attempted to discuss both doctrines in great detail, rather to portray the fundamental lines of reasoning of two seemingly opposite theories.
Economic Growth
If one assumes well-behaved indifference curves, a Pareto-optimal income distribution, and no externalities, a higher level of real output per capita will be preferred to a lower level of real output per capita. As economic growth implies an increase in output, economic growth is of paramount importance in the attempt to meet Homo Economicus's unlimited desires.
Economic growth can be defined as the change in the national/domestic product of an economy over a certain period. In order to distinguish between nominal and real economic growth, the price level at the beginning and end of a period is to be taken into account. Furthermore, in order to distinguish between economic growth brought forth by higher productivity, and hence an increase in wealth per capita, and economic growth brought forth by an increase in population, economic growth per capita is to be measured.
Mathematically:
(1.1)
where stands for the real change in the national product per capita over period t-1 to t, ,, and stand for the national product, the price level, and the population size at time t respectively.
Hence the real economic growth per capita rate over period t is
(1.2)
Even though equation (1.2) is used to measure economic growth, mathematical economists prefer to define economic growth differently. By taking the limit to zero of the difference in time between the beginning and end of each period, they obtain the first derivative of the real production function per capita. This is a result of them preferring to treat time not as a discrete but rather as a continuous phenomenon.
Mathematically, the real output per capita can be expressed as definition (1.3).
(1.3)
where , and stand for the amount of capital, labour and natural resources 'employed' at time t, respectively. All variables are a function of time. Nota Bene: the production function is also a function of time, changing as the level of technology changes. Furthermore, human capital, or human resources, are defined to be included in the level of technology, and hence in the production function, and are not part of capital, labour or natural resources.
As the first differential expresses the rate of change, expression (1.4) equates the real growth rate per capita,
(1.4)
and real economic growth per capita occurs if expression (1.4) is greater than zero.
The Production Process, Demand, and Supply
Cost minimisation occurs if the marginal return relative to the marginal cost of the factors of production are equal, i.e. the ratio of marginal return to price for each factor is to be identical.
For cost minimisation:
(2.1)
Furthermore, it is assumed that the marginal return of each factor of production is positive but diminishing, and that partial, but not total, factor substitution is possible.
So,
(2.2)
If the factors of production are assumed to be heterogeneous, the following postulate is necessary: a unit of a factor demanded is weakly preferred to its succeeding units demanded, i.e. the units of better quality will be used in the production process before units of lesser quality.
Mathematically,
(2.3)
where i denotes the factor, and j the unit in the sequence of usage.
The demand for a factor of production is therefore determined by the marginal product of the factor and by the price of the factor. As the price is the outcome of the interaction of demand and supply, the supply of a factor of production influences the utilisation of a factor in the production process. The quantity supplied is a function of the total stock of the factor and the cost of extraction from this stock. It is assumed that the supply curve (see Graph 1) is upward sloping, reflecting the higher cost needed to supply an additional product, up to the point that the total stock has been supplied (point S), after which the supply curve will be vertical.
Graph 1: The Supply Curve
Reaching the Limit: Finite Resources
In most cases the finiteness of resources is of no concern, as the quantity demanded is considerably less then the maximum quantity that can be supplied. In other cases demand is ever increasing only to be curtailed by an ever increasing price as supply is constant. For example the amount of inner-city 'land' is fixed, whilst demand for inner-city 'land' is increasing. As dictated by the market, the equilibrating price of inner-city 'land' increases.
The first economist to voice his concern with the finiteness of resources was Thomas Malthus who developed his theory on the finiteness of resources, economic growth and population growth. This theory was later elaborated by David Ricardo, and structured by John Stuart Mill.
Malthus assumed that the stock of agricultural land was finite, as it could not exceed the total amount of land within a territory. Given that the population was increasing, more land was to be employed in the agricultural process. However, once the limit of the land available to agriculture had been reached, an increase in output could only be brought forth by an increase in the 'employment' of labour and capital, i.e. an increase in cultivation through more labour and capital. This is similar to the example of inner-city 'land', in which older buildings (capital) are replaced by others that have a greater economical return. As the factors of production have diminishing marginal returns, each additional labourer will yield less return. The relative change in output will hence be smaller than the relative change in population. The result will be diminishing wealth per capita.
The most important postulates for the Malthusian theory to hold are that the technological and social framework was constant, i.e. no technological progress. Apart from the production function being static, Malthus assumed that the amount of 'tools' per worker was also constant, i.e. factor substitution between labour and capital was not possible, as each labourer could for instance only operate one plough at a time. This meant that the ratio of labour and capital was held constant. Diminishing wealth per capita would therefore immediately set in as soon as the limit of land was reached.
So,
Subject to and the production function is static.
and
Unlike Malthus, Ricardo assumed that the agricultural land was heterogeneous, but a condition similar to (2.3) ensured that land of better quality would be used before land of lesser quality. In the case of homogenous quality diminishing marginal returns would only set in once the limit of supply had been reached. For heterogeneous quality diminishing marginal returns would immediately set in.
Malthus and contemporaries therefore argued for the control of population growth, to ensure that the upper limit of supply of land would not be reached.
A Declining Limit: Exhaustible Resources
As where Malthus and Ricardo were concerned with the finiteness of resources, the first theory concerning the exhaustibility of resources was developed by Harold Hotelling in 1931. With the ever increasing reliance on exhaustible natural resources decreasing finiteness rather than static finiteness became an issue of concern.
By defining exhaustible natural resources as the extracts of a structurally declining physical stock which are 'consumed' in the production process, the stock of resources, the extraction and replenishment rate are taken into account. If the extraction rate is structurally greater than the replenishment rate, the stock will decline.
The aggregate of all the future extracts cannot be greater than the total stock of resources and the aggregate of all future replenishments.
(5.1)
where stands for the stock at time 0, and for the replenishment rate at each respective period.
(5.2)
And for an exhaustible resource the extraction rate is greater than the replenishment rate, so
(5.3)
(5.4)
where stands for the excess extraction rate at each respective period
This gives a dynamic element to a stock. Even if Homo Economicus could limit population growth so that the limit of a resource would not be reached, a decreasing stock would eventually lead to 'too high a population level', and hence diminishing wealth per capita. However, where Malthus and his contemporaries did not take the level of technology into account, the theories of the twentieth century do.
Exhaustible Resources: A Problem or No-Problem?
From (1.4) it can be seen that economic growth can also be brought forth by an increase in technology. As long as Homo Economicus can increase the level of technology the marginal return of the factors of production will increase through a shift of the production function, i.e. due to a higher level of technology the return of the factors of production are increased. Nevertheless, this does not solve the problem of exhaustibility; or does it?
In answering the above question, two different schools of thought can be identified: the 'conservationists' and the 'optimists'. The conservationists, echoing Malthus, argue that technology will never be able to totally substitute exhaustible resources. In the apocalyptic case, it is not inconceivable that once the last of a resource has been used, the production process will grind to a halt. Hence, measures should be imposed to preserve exhaustible resources, or to utilise resources according to an optimal depletion plan.
The optimists, on the other hand, voice little concern over the exhaustibility of resources. Some even claim that there are no exhaustible resources. One of the most optimistic 'optimists' is Julian Simons, whose line of reasoning is worth discussion.
The Optimists: No-Problem
Simons argues that exhaustible resources do not exist. They are merely a fiction created by Homo Economicus's pessimistic 'scarcity-driven' mind. Simons argues that scarcity is, among other things, a function of the estimated time remaining before total depletion occurs. Depletion in a hundred years time is less of a concern than depletion next year. A resource that will deplete in a million years time can hardly be called exhaustible, as, to put it in Keynesian terminology, in the long-run we are all dead.
Mathematically,
(6.1)
(6.2)
where is the point in time when the stock of resources is exhausted.
This point of time can be estimated either through economical or technical forecasting methods. Technical forecasting methods estimate the present total stock and the rate of depletion. Scarcity is then measured by subtracting extrapolated future extraction rates from the 'inventory'. A point in time can then be calculated at which none of the resources are left.
(6.3) where 0 is the point in time at which the estimation is made.
The optimists' critique on this estimation technique is twofold. Firstly, equation (6.3) is irrelevant as the stock of resources has more than one dynamic element, i.e. the stock of resources cannot be described by equation (6.3). The level of technology, economical conditions, and various exogenous factors (such as the element of chance for instance) determine the size of proven reserves over time. As Vincent McKelvey's diagram below shows, 'Proven Reserves, ( in equation (6.3)), is only a small part of the total resources present on Earth, and should hence be replaced by .
Total Resources
Discovere Undiscovered
d
B High
Proven o
Economic Reserves Hypothetical u
n Inconceived
and d Resources
Speculative
Sub-Econo Resources a
mic Resources r
y
Boundary of Potential Economic Threshold
Resources not likely to be economic in
Non- the foreseeable future
Economic Boundary of Mineralogical Threshold
Material
Resources in earth but not obtainable
with present technology
Geologic
Assurance
Vincent McKelvey's Box
Technical forecasts are therefore not a valid estimation technique. Economic forecasts on the other hand extrapolate trends of past costs (prices) and therefore incorporate - to a certain degree - trends of technological progress and economical change. Economical forecasting methods should therefore be preferred to technical forecasting methods in the field of resource economics. For is it not more realistic to estimate the measurement of scarcity than to estimate the factors that cause scarcity?
How, though, should economic scarcity be defined? Scarcity can be defined in terms of prices or costs. The greater the scarcity for a product is, the higher its price will be. For exhaustible resources it is to be expected that their prices will increase at a higher rate than the inflation rate.
(7.1)
where stand for the price of resources at time t and the cost of extraction at time t, respectively.
When function (7.1) is empirically tested it can be shown that scarcity defined in terms of the above economical variables has been declining significantly over time. The prices of resources such as copper, iron ore, oil, coal, aluminium and many more have nominally increased, but in real terms they have declined. This implies that there are no exhaustible resources.
The Answer: Innovation
The paradoxical result of exhaustible resources that are becoming less scarce can be explained in several ways. Firstly, innovation leads to a greater amount of resources being found and becoming suitable for extraction, as explained by the McKelvey Box. Secondly, innovation leads to an increase in the marginal return of resources due to a change in the production function, i.e. the factors of production are used more efficiently. Thirdly, innovation leads to substitutes for 'exhaustible' resources, e.g. with the introduction of fibreglass the demand for copper has been significantly reduced.
Recapitulation
Empiricism have proven the optimists right in claiming that Homo Economicus has been able to outrun exhaustibility through innovation. The conservationists do not disclaim this, but point out that may be one day Homo Economicus will not be able to do so, as running away from a problem does not solve a problem. The crucial issue is therefore if innovation is an indefinite phenomenon.
Furthermore, let it be said that Homo Economicus remarkably resembles Homo Sapiens, but as where Homo Economicus can afford to ignore ecology, Homo Sapiens cannot.
Bibliography
Brobst, D.A., (1979) 'Fundamental Concepts for the Analysis of Resource Availability', in Smith V., 'Scarcity and Growth reconsidered', John Hopkins Press for resources for the future, London.
Heilbronner, R.L., (1969) 'The Worldly Philosophers', Allen Lane, London
Heal, G., (1993) 'The Economics of Exhaustible Resources', E.Elgen, Aldershot
Hotelling, H., 'The Economics of Exhaustible Resources', Journal of Political Economy, April 1931, 137-75
Simons, J.L., (1981) 'The Ultimate Resource', Martin Robertson, Oxford
Solow, R.M., 'Intergenerational Equity and Exhaustible Resource', Review of Economic Studies, 1972