Introduction

Resource-based industries are typically subject to substantial taxation. In addition to conventional profits or corporation taxes, they are typically required to pay royalties, revenue taxes, excess profits taxes, and are subject as well to a variety of other forms of taxation. It is not coincidental that they are so burdened. As we have seen in earlier chapters, a large part of their profit may be pure rent, and this is obviously a tempting target for taxation. Indeed, it is well known that under certain circumstances one can tax away pure rents with no loss of allocative efficiency and, as we shall see, there are certain forms of tax which can be levied on an extractive industry without distortion. However, it is certainly not the case that all conceivable taxes on extractive industries produce no deadweight loss, and in the ensuing sections we consider the impact of some of the most widely used taxes. We also return once again to the problem of the commons, discussed in Chapter 3 and, making use of techniques and results from the last chapter, analyse the dynamic version of this problem. It is of particular interest in the present context because a resolution of this problem requires the introduction of a fairly complex dynamic tax scheme, and provides an interesting example of taxes as a corrective force, rather than as potentially distortionary revenue raisers.

Population Growth Curves

Some of the most interesting questions that arise in the context of intertemporal resource allocation concern the rate of utilization of those resources that are at the same time self-renewable and in principle exhaustible. Resources such as minerals and fossil fuels, with which we shall be much concerned in the forthcoming chapters, do not fall into this category, for they are not renewable. They are a prime example of exhaustible resources. The act of extracting and utilizing a unit of such a resource reduces the total stock by precisely that amount. There are no means by which the total stock can be increased. Improvement in technology (e.g. enabling one to mine deeper layers) can, of course, increase the quantity that can be extracted. But that is a different matter. Then again, discoveries of new deposits will increase the known available stock. But this too is a different matter.

Durable commodities like buildings and automobiles are also not in this category. Even if the entire stock of such a commodity were to be destroyed at a stroke, at least a part of the original stock could presumably be replaced in time. To the extent that such durables require exhaustible resources in their production, the possibilities of replenishing them will presumably be circumscribed by the availability of these exhaustible resources. But this again is a different matter.

Introduction

In the previous chapter we discussed several notions that could, under different circumstances, be regarded as equilibria of a social system. Such notions are designed to represent viable outcomes. One that came up for particular scrutiny was the notion of a competitive equilibrium of a private ownership economy. A central feature underlying this concept is the existence of a competitive market for each and every commodity in the economy. Interest in such an equilibrium stems largely from the fact that under certain circumstances it sustains an efficient allocation of resources, in a sense that was made precise in the previous chapter. This provides one with a reason for regarding such an equilibrium as a benchmark with which to compare viable outcomes in other circumstances. The precise sense in which this can be done will occupy a great deal of this book. Now, there are many circumstances in which market solutions do not sustain an efficient allocation of resources. Many such situations can be described by saying that certain essential markets do not exist. Sometimes they just happen not to exist for accidental or historical reasons; sometimes there are logical reasons why they cannot exist; sometimes the nature of the physical situation keeps them from existing, or makes them function wrongly if they do exist. It happens that industries producing (or using) renewable and non-renewable resources are especially vulnerable to these difficulties.

1. The role of natural resources in the functioning of an economic system has received intermittent attention from economists. The classical economists of the nineteenth century were very much concerned with this issue: both Malthus and Ricardo saw in a country's land the key to many characteristics of its economy. However, in the considerable developments of economic theory that have occurred in the twentieth century, there has been little explicit mention of natural resources. These differences are perhaps not surprising. In the eighteenth and nineteenth centuries, the ownership and productivity of land were evidently of great importance in determining the distribution of income, and the timing and location of the industrial revolution in the United Kingdom were clearly influenced by the exhaustion of certain traditional resource supplies and the availability of alternatives. To nineteenth-century man, it would therefore have seemed unthinkable that one could explain the dynamics of an economy, or analyse the processes of production and exchange, without giving special attention to the role of natural resources.

The economic theorists of the twentieth century have, however, proceeded on the basis of just such an omission, at least until recently: in the works that have exercised a dominant influence on the evolution of economic theory in the last half century—Hicks's Value and Capital, Samuelson's Foundations of Economic Analysis and the developments of the Arrow—Debreu model—there are few explicit references to natural resources.

The Arrow—Debreu Theory of Contingent Markets

In the previous chapter (see section 1) we noted how one may include the state of nature in the characteristics of a commodity. In this approach a commodity is characterized not merely by its physical attributes, but also the date and state of nature in which it is made available. Using this device we developed some aspects of consumer-choice under uncertainty. We now extend the notion of an intertemporal competitive equilibrium to incorporate such environmental uncertainty.

For ease of exposition suppose time is discrete, and that there are precisely (T+1) periods; t = 0, 1, …, T. Define a state of nature as, ‘…a description of the world…’, from t = 0 to t = T, ‘… so complete that, if true and known, the consequences of every action would be known’. As earlier, let S be the number of states of nature (s = 1, …, S). At the initial date (t = 0), no one knows what the true state of nature is. By hypothesis all uncertainty is resolved for everyone at t = T. Therefore, at T everyone will know precisely what the state of nature is.

It is assumed that with the passage of time all individuals continually receive information about the true state of nature. However, the point to emphasize is that this flow of information is costlessly obtained by all, and is not influenced by policy.

Introduction

Our earlier discussion has on several occasions alluded to the impact of uncertainty on allocations involving exhaustible resources. But we have not gone into such issues in any detail. Instead, we have supposed an absence of uncertainty, or at the very least, that one would not go far wrong if all random variables were replaced by sure values (e.g. their expected values). It is time to remedy this. The need for such an exploration is plain. Uncertainty about future possibilities looms rather large, and this may have a telling impact on the rates at which we ought today to deplete our stocks of exhaustible resources. Thus, for example, any appraisal of the rates at which fossil fuels are depleted today must surely be based on an assessment of the likelihood of major technological discoveries in energy generation in the future—such as ‘clean’ breeder reactors or controlled nuclear fusion. Likewise, an appraisal of the depletion rate for iron ore reserves must depend inter alia on a view of the likelihood of alternatives to steel being found in many uses. Then again, new reserves of extractive resources are continually being discovered. But such discoveries cannot be predicted with certainty.

A discussion of uncertainty and its effects on natural resource allocation readily invites one to consider the production and transmission of information. Seismic surveys and laboratory experiments designed to help control nuclear fusion are both aimed at producing information.

The Perfect Myopic Foresight Case

(i) Formulation of the problem: The discussion in the previous chapter was designed to explore the consumption possibilities open to a closed economy making use of exhaustible natural resources as inputs in production. It is time that we imposed a specific institutional structure on the economy and analysed its implications. The environment most thoroughly explored is undoubtedly the competitive case. We shall analyse such an economy here.

A difficulty that arises in tracking down the implications of a competitive private ownership economy is the ambiguity in its definition when time is introduced explicitly into the construct and the horizon is assumed to be infinite. We noted an important feature of this in Chapter 6 section 3. There we found that it was possible to have a sequence (in our continuous time example, a continuum) of momentary equilibria along which price expectations are fulfilled at each instant despite an absence of a complete set of forward markets. Further modifications suggest themselves. For example, an absence of forward markets may result in price expectations not being realized. The story is difficult to unravel even when it is assumed that all individuals at a given date are identical and have the same ‘point expectations’—viz. that expectations about future prices are held with certainty. This is so since there are various accounts that one can offer about how expectations are formed.

Introduction

This chapter is by way of being introductory. It is also the most formal of the chapters in the book. We shall introduce several concepts that will prove essential in discussing the economics of exhaustible natural resources. Since these notions form the basis of resource allocation theory it will prove useful to avoid mentioning exhaustible resources at this stage. This is so for two reasons. One of our aims in this book is to explore the extent to which economics can usefully be applied to analyse the allocation of exhaustible natural resources under various circumstances. As a minimum we must then sketch the theory to which we shall be appealing. This forms our first reason. Our second reason is that while exhaustible resources are much like any other resource, they possess some strong special features. The remainder of this book will analyse these special features. This being so, it is important to make precise what they are special features of.

In this chapter we shall discuss resource allocation in the simplest of environments—one that is timeless and where the agents face no uncertainty. In fact the construction can be reinterpreted to accommodate both time and uncertainty. This will be done in Chapters 4, 8 and 14. It is possible that all readers are familiar with the material of this chapter. If a glance persuades the reader of this he can go directly to Chapter 3.

Market Mechanism and Inter generational Distribution of Welfare

It was noted in Chapter 2 that while a competitive equilibrium of a private ownership economy has several virtues (e.g. that under certain conditions it is Pareto efficient), ensuring a reasonable distribution of welfare among individuals is not one of them. This should hardly be surprising. The equilibrium is contingent on the distribution of initial endowments in the private ownership economy. There is nothing in the construction to rule out a distribution of initial endowments which leads to an undesirable distribution of welfare at an equilibrium. Although a commonplace, this observation immediately invites a few clarificatory remarks. The issue that we are concerned with here is the distribution of welfare. To the extent that the consumption of goods and services affect individual welfare we are, by implication, concerned with the distribution of goods and services. But this raises several points. A diverse pattern of consumption within a population is not an evidence of an undesirable welfare distribution. Man 1 may prefer wine to beer and man 2 may have the opposite preference. If we now observe man 1 consuming wine and man 2 beer, the pattern of consumption is no doubt diverse. But one would be inclined to say that this is a superior state of affairs to one where the two persons share the wine and beer equally. This suggests that diversity of consumption patterns can be justified on the ground that preferences differ among individuals.

Introduction

In earlier chapters we have discussed, among other matters, the behaviour of perfect resource markets. In fact, of course, many of these markets are substantially imperfect. In this chapter, therefore, we shall analyse the consequences of some of these imperfections. But before doing this it will be useful to make precise the sense in which the issues to be dealt with here differ from those in Chapters 3 and 5. There the focus of attention was the implication of the non-existence of certain markets. Here, matters will be different. We shall take it, in what follows, that all relevant markets exist; but that for various reasons they function wrongly. In short, we shall be concerned here with what is traditionally called imperfect competition.

Even in a timeless setting imperfect competition is difficult to model, with no widely accepted framework for the analysis. The difficulties, if anything, are compounded when one moves to an intertemporal setting that is essential for an analysis of resource depletion problems. We shall begin with the case that is the least controversial: the case of a single owner of a resource. This will lead the way for an exploration of the theory of dynamic oligopoly.

Monopoly: The Basic Issues

Consider the case of a monopolist with a stock, S0, of a resource, facing a downward sloping market demand function, p(Rt, t) where p is the price at which the flow Rt, is sold at time t.

A Basic Result

It is clear that in developing the economics of exhaustible resources time must be brought explicitly into the construction. It is equally clear that the problems concern the allocation of a fixed stock of a commodity, perhaps unknown in size, between competing uses at different dates. In developing the theory it is as well to discuss the simplest considerations first. We shall add complications as we go along.

Assume for the moment that time is discrete. In what follows we shall always regard the ‘present’ instant as t = 0. Since the past is past, choice affects the present and future only. Given this, we can without loss of generality consider the case where time assumes the non-negative integer values, t = 0, 1, 2, … Imagine, to begin with, an individual concerned simply with three instants of time, t = 0, 1, 2. Imagine also that there is a single commodity whose stock at t = 0 is known by him to be S0. The commodity does not deteriorate over time (unlike ice-cream on a hot day). Nor does it grow (unlike forest resources). Nor indeed does it provide a constant flow of service over the three dates (unlike land). In fact, assume that there is no production in this world. But assume that storage is possible costlessly. In effect the commodity is much like a non-deteriorating piece of cake, or a quantity of hard-tack.