CONCLUSION

It has been the aim of this thesis to develop models which throw light on some of the basic questions associated with the

intertemporal use of exhaustible resources. As foreshadowed in the introduction the main preoccupation has been with problems of

"conservation", the trade-off between the present and the future being central to such problems.

At the most basic level (Chapter 3) it was possible to see how the optimal time profile of exploitation of an exhaustible resource is affected by the form of the utility and production functions, the size of the discount rate and the length of the planning period. It was found that:

(a) For an infinite time horizon a positive discount rate is needed to ration the stock, of the resource between

generations;

(b) If there is a region of increasing returns to the resource input, it will be optimal to operate beyond that region

whenever the resource is being exploited (the case of class II and III u-functions) — consequently exhaustion of the resource in such a case will generally be more rapid than when there are always diminishing returns to the resource (a class I u-function;

(c) The existence of a conservation motive and/or a depletion effect in extraction of the resource opens up the possibility

that it is not optimal to exhaust the resource (conditions under which the resource should be exhausted were derived).

In addition the social analogue of the Hotelling "rule" that net price should rise at the rate of discount was found to hold when conservation motives and depletion effects were ignored. However, once these aspects of the problem were acknowledged the rule collapsed and there were found to be several situations where the social price of the resource should decline in the later stages of the period of

exploitation. This was because the marginal net social value of the resource is eroded as depletion effects (for example) force up the costs of extraction.

Chapter 3 was concerned with the most basic form of scarcity associated with exhaustible resources — that arising from the finite nature of their stock. Chapter 4 went on to incorporate a more

conventional kind of economic scarcity into the problem — the limited supply of the variable factor of production (labour) which was to be used both in conjunction with the resource and in the extraction of the resource. The emphasis in the first part of Chapter 4 was on

determining the best intertemporal way of allocating a given finite labour supply between sectors, given that some of it was to be used to extract the resource, and the rest was to be used to produce one or more consumption goods. It was possible to identify the following forces at work in the determination of a time path for the allocation.

(a) When the only consumption good in the economy uses the

resource as an input, consumption should decline over time and the economy should move towards the labour allocation which maximizes consumption at a point in time.

(b) The labour allocated to resource extraction should ultimately decline over time for very long time horizons, however when the planning period is short the movement of this variable is ambiguous — in order to approach the myopic rule as T is

approached the labour allocated to extraction must rise, however the depletion effect will (because of the falling marginal product of labour in the resources sector) have the

reverse effect; when there is no depletion effect, the labour in the resources sector should fall over time.

(c) If the economy produces a second consumption good without the

resource, then the relative preferences for the two

consumption goods become important; without a depletion effect the labour allocated to resource extraction should still fall over time, however the time paths of labour going towards production of the two consumption goods will be the net outcome of two influences: (i) the innate preference for one consumption good (as embodied in the utility function) will tend to prevent the labour allocated to production of that good from falling, and (ii) the scarcity of the resource will work, to lower the allocation of labour to the resource based consumption good over time.

The second part of Chapter 4 extended the basic Chapter 3 model by considering the "relative scarcity" of two resource deposits. These deposits differed in both size and cost. A generalization of the "Ricardian" rule that resource deposits should be extracted in order of ascending costs was proven and it was noted that the presence of

depletion effects makes it possible to manipulate these costs and (for a while) maintain a situation where the marginal (and average) costs of

extraction are the same for both deposits and both deposits are

exploited simultaneously. The final part of Chapter 4 was devoted to an extension of the conservation motive model of Chapter 3 and a

generalization of the exhaustion/non-exhaustion conditions obtained there. The conditions obtained for the disaggregated model are very similar to those obtained for a single resource.

Having analysed the different types of scarcity which are relevant to the exhaustible resource planning problem the next step was to examine some ways in which the basic scarcity might be mitigated.

Chapter 5 analysed the process whereby an increasingly expensive exhaustible resource is replaced by a substitute which is essentially inexhaustible. A comparative dynamic analysis revealed that the availability of cheaper such substitutes will make it optimal to use less of the exhaustible resource in the earlier stage of a plan, if

depletion effects are present. In the absence of depletion effects, the prevailing intuition that "cheaper substitutes means conserve less now" was supported.

The possibility of lowering the cost of using the backstop technology by investing in capital equipment and/or knowledge was then examined. It was found that:

(a) Unless the planning period is sufficiently long, it would not be worthwhile to initiate such a development project; the economy is better off remaining with the original resource. (b) If it is worthwhile to invest in development of the substitute

(i.e. the time horizon is long enough), such investment should date from the beginning of the plan, regardless of the initial stock of the resource.

If there Is no investment required for development of the substitute, but there is uncertainty concerning the date at which it will become available, it was found that the optimal amount of the exhaustible resource left unexploited should be higher the higher the probability that the substitute will eventually become available.

Another way in which an economy may choose to relieve (or benefit from) resource scarcity is by importing (or exporting) the resource good. Chapter 6 presented a model in which a country facing a fixed terms of trade plans its pattern of trade and specialization over time so as to maximize the present value of its stream of returns. The nature of the optimal path was dependent on the economy's terms of trade and set of preferences. It was shown that for short time-horizons, the economy should operate at the static competitive optimum for a trading country while for longer time horizons the level of extraction should be less than this static optimum and falling. A set of taxes was devised to bring the competitive optimum into line with the social optimum. Wlien allowance was made for foreign borrowing, the introduction of an exhaustible resource into the conventional foreign borrowing model worked to increase any tendency the economy might have to move from

surplus into deficit and offset any opposite tendency.

Beyond the problems outlined above and discussed in the thesis there are a whole range of other interesting questions. Some of them

(recycling, market failure, bias in certainty-equivalent planning,

uncertainty about the size of resource deposits) are already being given close scrutiny by a number of economists. Others (exploration, tax policies, imperfect futures, markets, etc. and intertemporal resource price determination) have been generally neglected. It is to be

expected that the urgency of most of these problems will encourage more research in the future. When that happens, economics might finally be justly called a "science of scarcity".