Introduction

The line between exhaustible resources and renewable resources is not always clearly drawn. Exploration and technical change can, for a time at least, “renew” exhaustible resources by making possible production from new deposits and low-grade materials. Models that describe the effects of these activities on resource price and production paths were developed

Just as exhaustible resources can be renewed, renewable resources can be exhausted. In fact, the concern about resource exhaustion appears to involve renewable resources, endangered species ranging from the snail darter to the whale. As one prominent biological scientist discussed it: The worst thing that can happen—will happen [in the 1980s]—is not energy depletion, economic collapse, limited nuclear war, or conquest by a totalitarian government. As terrible as these catastrophes would be for us, they can be repaired within a few generations. The one process ongoing in the 1980s that will take millions of years to correct is the loss of genetic and species diversity by the destruction of natural habitats. This is the folly our descendants are least likely to forgive us. A major purpose of this chapter is to try to shed some light on the reasons that even commercially valuable stocks of plants and animals can be threatened with extinction. It is clear enough how this can happen to a species that is not commercial.

The purpose to describe the ways in which the economy and the natural environment are interlinked. To an extent, these interlinkages are all-embracing; every economic action can have some effect on the environment, and every environmental change can have an impact on the economy. By 'the economy', we refer to the population of economic agents, the institutions they form (which include firms and governments) and the interlinkages between agents and institutions, such as markets. By 'environment', we mean the biosphere, the 'thin skin on the earth's surface on which life exists', the atmosphere, the geosphere (that part of the earth lying below the biosphere) and all flora and fauna. Our definition of the environment thus includes life forms, energy and material resources , the stratosphere (high atmosphere) and troposphere (low atmosphere). These constituent parts of the environment interact with each other: an example is the effect of changes in biosphere composition on the composition of the atmosphere. (The effect of biological entities on their physical surroundings forms the basis of the Gaia hypothesis. Even more important from our perspective are the effects of human activity on the environment, and the consequences of these affects on human well-being. As an example, consider the generation of electricity. In extracting fossil fuels to use as an energy source, we deplete the stock of such fuels in the geosphere. In burning these fuels to release their energy, we also release carbon dioxide (C0₂) and sulphur dioxide (S0₂), both of which may produce undesirable environmental impacts that reduce human (and therefore economic) well-being. These particular effects are considered in detail in Chapter 6. As another example, agricultural support policies may have environmentally damaging effects which in tum rebound on human welfare. Thus, subsidizing cereal production in the European Community (EC) led to higher prices for such cereals, which are important inputs to the livestock sector. Two effects amongst many may be remarked on; higher output prices encouraged farming practices which contributed to soil erosion in both the USA and UK (Heimlich, 1991), while livestock farmers' demand for cheaper substitutes for feed resulted in the loss of rainforest in Thailand, as producers sought to increase cassava production for export to EC livestock farmers. 

The main difference between exhaustible resources and renewable resources, like land or water, is that consuming a unit of such a resource today implies to be unable to consume it later. In other words, the management of an exhaustible resource has an explicit temporal dimension. The introduction of time into economic reasoning is a cause of many difficulties. First, the time horizon must be specified (finite time or infinite time), and it may be the case that the time horizon is a decision variable in the problem (when to start and when to stop). Second, a decision takes now the form of a decision rule for any time period depending upon external variables (prices dynamics, speed of the technical progress, changes in tastes and preferences), that is a vector of actions over time, maybe of infinite size (as for infinite time horizon problems). Such decision rules must satisfy minimal rationality requirements, for example in most cases they should be time consistent. Time consistency implies that if at a given time period t0, the decision maker sets a decision rule to be applied at some future period t₁, when getting to the time period t₁, the decision maker should not decide to change the rule he (she) has previously determined. Such consistency issues play an important role in commitment analysis and in dynamic games theory. Intertemporal decision schemes apply typically in more or less uncertain environments and hence, risky decisions considerations have to be explicitly taken into account. Information about future events may also evolve and makes room for anticipation construction and implementation considerations. Last the decision rule space at any time period may be dependant upon history, that is upon past actions or past outcomes of the decision tree. This historical dependence (or inheritance process) may appear as a constraint upon the decision process itself or as a tool to improve the outcome of the decision process (in learning by doing or information gathering processes for example).

There is lot of theoretical ideas on exhaustible natural resources. But empirical studies on stone quarrying are limited in number. Geologists agree on all heads that Stone (granite) being an exhaustible resource, the theories of exhaustible resources are applicable to it also. There are several studies have been made, by Dasgupta, Malneg, Solow, Pindyck, Levhari, Davison, Fisher, Devarajan, Ilanson, Farrow Scott, Fazzin, fitzgibbons, Fracer, Gampania, Goldsmith, Harris, Hoel, Hotelling, Mcrae, Sweenly, Livernois, Russell, Stiglilz, Karp, Vcvhari, Lewis, Mukesh Eswaran, Philippe, Gilbert, Halvorsen, Blame, Robinson, and Tracy R. Lewis, on scarcity of exhaustible resources, optimal allocation of a given exhaustible resources, intergenerational equity of resources and environmental problems.

"The economics of natural resource availability" draws a distinction between Malthusian view and Ricardian view on resource Scarcity. MaIthus emphasized an absolute scarcity of natural resource availability while Ricardo spoke of relative scarcity. Scarcity of non-renewable resources would be a constraint on economic growth irrespective of population problem. The time factor involved in exhausting non-renewable resources Lewis C. Gray while dealing with the mode of utilizing exhaustible resources lays emphasis on the need for taking into consideration the level of present consumption to estimate how the rate of consumption of such exhaustible resources will be in future. He argues that as the stock of certain mineral resources remains constant, their current production will certainly preclude future production. Maximum output limits cannot be set by conditions of equality between marginal revenue and marginal cost as it is for agricultural output. Thus in the case of specific mineral deposits, additional unit of output can only be produced in the future if they are not produced today and the postponement of production may mean as the excess of marginal revenue over marginal cost. Hence, according to Gray a discount rate could be introduced for the exploitation of exhaustible mineral resources. With the introduction of a discount rate, present production of an additional unit of output will be postponed to a future period if the present value of the difference between revenue and costs for an additional unit of future production exceeds that for a unit of present.

Extension margin of production

A new Concept of' extensive margin of production has been introduced by Gray. According to him this concept of rent earned by a mine consists ol two elements namely, the return for the mineral used up (royalty) and return for the site value of the land. The mine on the extensive margin can earn no royalty. Grey holds that mines which do not earn royalty cannot fetch rent. So they cannot have a capitalized value and therefore they cannot yield a royalty.

If the Current prices go up, can a period of scarcity be far off?

This is an interesting question which is well answered by Cassel in his theory of social economy. According to him an increase in the price of the output of the mines, would, ceterisbaribus bring about a substantial hike in the production. This phenomenon will certainly enhance the present rate of exploitation of the mines. This will be seriously told upon what is left for the progeny . Thus present prices reflect future scarcity 

Royalty and Rate of interest:

l'hc net price of any ore is usually called the royalty. According to Holelling any rise in the royally fi)r an ore will always be equivalent to the existing rate of interest5. Solow in his lecture on the economics of Resources or the resource economics depicted this as the fundamental principle of the economics of exhaustible resources . But, Levhari and Liviatan show that this principle is valid only under very special conditions. They modified the rule for more general cases by taking into account the effect of cumulative output on costs and of the possibility of incomplete exhaustion. The concept of royalty and its impact on the existing rate of interest has been an excellent avenue for research. Solow who has delved deep into it saying that net price will always rise over time at a rate equal to the rate of interest.

However, if the price continued to rise there will come a time when people will have no option other than going in for substitutes to meet their growing demand. This will usher in a new era when such a mineral resource will not be produced any more. Thus according to Solow unbrid led price hikes constitute a harbinger for the advent of a new epoch, when the production of the mineral under consideration would have hit the rock bottom. According to Solow, if the interest rate used by the owners of depletable resource is higher than the social discount rate, resource owners will extract more rapidly than socially optimal and will therefore leave smaller stocks of depletable resources for the future8. This theory thus suggests an orderly progression of exploitation starting with the highest quality resource. As exhaustion proceeds prices are hiked and resources of poor quality are brought into production. He argued that, although lower quality resources are brought into production, market price may fall if the effect of technology more than counters the effect of the declining fertility of mines. In this case market price falls while net price continues to rise.

Classical views on the exploitation of exhaustible mineral resources:

Adam smith offers a comprehensive description of the mineral industries. He states that under static conditions expensive mines will earn normal profits, and under dynamic conditions, the discovery of low cost mines will lead to the abandoning of the expensive mines. The new low cost mines have a prime role in the determination of price.

 David Ricardo confines himself to an analytical treatment of the determination of rent of mines. According to him the basis for rent in the mineral industries is the 'in situ' mineral itself. In a static analysis he emphasized the role of marginal mine as a regulator of price. In a dynamic setup he considered low cost and high cost mines. He lays emphasis on the role of progression from low cost to high cost mines'.

J.S. Mill while discussing the rent of mines deals with the role of differences in fertility of mines in determining the rent they yield. He also explains how the discovery of more fertile mines result in a fall in the value of output. He emphasized that, in the mine, present and future productions are antagonistic and therefore, optimization may involve adjustment of the profile of exploitation, and he asserts that the marginal mine may earn a scarcity rent. Mill also recognizes that the historical development of mines may not always involve a progression from low cost to high cost mines'.

Hotelling in his seminal work pointed out that, on an optimal path, price minus marginal extraction cost (scarcity rent) should steadily grow over time at the social rate of discount. However, there arc certain contrasting views about it in the contemporary literature. According to Kay and Mirrlees the scarcity rent grows exponentially as the finite stock of a resource nears exhaustion. Under conditions where the resource stock is still very rare the price greatly exceeds the marginal extraction cost. This shows that the resource will be over conserved if the actual price is above the optimal level'.

However Heal, in his article analyses the relationship between price and extraction cost for a resource with backstop technology. He maintains quite contrasting view. According to him as the resource stock nears exhaustion, the difference between price and marginal cost falls'. By using the same model, Hanson concludes that the scarcity rent will be monotonically declining over time'.

Solow and Wan have studied still a different situation where resource deposits differ in quality and the unit extraction cost increases as higher grade deposits are exhausted and extraction proceeds to lower grades. They show that along an optimal path the shadow price of a resource mustrise at the real rate of interest despite differential extraction costs, but the difference between price and marginal extraction cost (degradation charge) declines monotonically over time to zero.

As a synthesis of these controversies Farzin, in his work scrutinizes the scarcity rent within a model of exhaustible resource extraction, derives general conditions characterizing the time path of scarcity rent under competitive conditions. He postulates a general extraction cost function that allows for the effects of resource depletion and technological change as well as that of extraction rate. He shows that the time path of scarcity rent, in general non-monotonic. He also contented that the theoretical literature show that the scarcity rent for an exhaustible resource should always increase over time. He further shows that when the discount rate is zero, the scarcity rent always declines over time monotonically to zero, irrespective of the form of extraction costs function. He argued that the hypothesis on non monotonic scarcity rent advanced by him is general enough to reconcile the empirical findings that otherwise appear to have been in defiance of the conventional theory or in conflict with each other. Finally he shows that except for extremely special situation, technological change generally reinforces the non-monotonic behavior of' the scarcity rent path.

Tonu Puu, in his study shows that models of extraction process of renewable and non-renewable resource stocks, in which the rate of extraction is constrained by the size of the physical capital is undertaken in the initial time period and is terminated before the end of mines life. The resource never exhausts completely. 

The Economics of exhaustible Resources:

A number of studies have been made on the optimal use of exhaustible resources as a response to the problems facing many of the industrial countries. Among them Hotelling's study deserves a special mention. His paper is written in completely modern terms and remains a major contribution to the literature on the optimal use of depletable resource. Levhari and Liviatan discuss some of these special assumptions and try to establish results for more general cases. Hotelling through out his analysis assume that the out put of the mine is reduced to zero at the terminal point. Another more important restrictive assumption is that the firm always continues to produce up to the point where the resource is completely exhausted.

In their notes Levhari and Liviatan point out that, in the case where the demand for the resource is stationary, but costs are an increasing function of the amount already extracted, it is quite possible for the firm to stop producing before physical exhaustion occurs.

They pointed out that in the real world, the firm will stop producing at a stage where "reserves" still exist, but under conditions which make further extraction too costly,. Under complete exhaustion the concept of full marginal cost must include a term which reflects the alternative cost of producing an extra unit rather than selling it at the terminal time. As is well known this element contributes to the exponential growth of marginal profit in the theory of exhaustible resources. However, under incomplete exhaustion the foregoing term vanishes completely from the marginal cost expression. To derive these results they present a novel formula for 'full marginal cost' of extracting exhaustible resources. The principle that the marginal profit has to increase over time exponentially at a rate, equal to the rate of interest, has played a prominent role in the theory under coiisidcral ion. Solow considers it to be the fundamental principle of the economics of exhaustible resources Levhaari and Liviathan show that this principle is valid only under very special conditions. They establish the modification of this rule for more general cases taking account of the effect of cumulative output on costs and of the possibility of incomplete exhaustion.

Hotelling pointed out that, contemplation of the worlds disappearing supply of minerals, forests, and other exhaustible assets has led to demands for regulation of their exploitation. These products are being selfishly exploited at too rapid rate, at cheaper cost leading wasteful consumption. Therefore, for the benefit of future generations, suitable measure to conserve these natural resources must necessarily be adopted. 

The free enterprise views of resource exploitation:

Athol and Stuart have dwelt at length on the free enterprise views on resource exploitation. The doctrine of free enterprise exploitation of resource states that the ultimate constraints as resources are so distant they can be disregarded, and the rate of resource depletion is best determined by the free market system. At the same time it believes in an indefinite exponential growth in the demand for minerals. It also believes that changes in the demand function cannot simultaneously increase the supply of minerals. According to Athol and Stuart the soldiers of free enterprise school of thought on resource exploitation take any resource in the ground as an investment, in that it involves a current sacrifice of consumption with a view to bring about greater consumption in future. They pointed out that the rate of return on all forms of investment natural and man made should be the same. In the sense of economic efficiency, depletion is not a loss of wealth, if the value of the resource is replaced, although the value need not be replaced in kind. They concluded that rather than wait, it is more efficient to extract any resource today, provided the extraction is profitable. Naturally the more high grade the resource, the more likely it is that extraction is profitable, but profits could be reinvested at interest, and in this way the original resource could be transformed into machines or into other capital for the future. Rather than leave posterity a mountain of high grade ore, the advocates of market determined growth would leave behind a benefication plant which could process low grade ore-that is, if the market so decreed. The extraction of the more profitable ores today would make the present more happy and the future more wealthy.

On Tenure system, no free enterprise writer has analysed the system of mineral tenure, or how it might affect resource depletion. Having come to a bridge between economic and political analysis, they resolutely turn their heads and refuse to cross. Yet the form of tenure system which they assume unawares is at least as critical as their assumption of perfect competition. The free enterprise economists have assumed that there prevails a closed tenure system and so the ownership of the minerals are vested with private parties. So the explorer must buy his lease on an active lease market.

But in practice the dominant tenure system in the non-socialist countries is the open tenure system, under which the formal ownership of minerals is vested in the state. In practice the state transfers the beneficial ownership to the discoverers of the resources. Production is usually one of the conditions of lease tenure. Market behaviour depends upon the lease tenure system to such an extent that a competitive exploration industry under one tenure system is identical in behaviour to a monopoly industry under a different tenure system. Under closed tenure system, the owner of a lease would act to maximise its value. Production would begin around the point of time when the value of the minerals left in the ground was not rising more rapidly than the interest rate. But under open tenure system, minerals would be explored for, and the lease developed, at an earlier date when the expected value of the lease was equal to the cost of exploration. Any firm which delayed exploration would find itself pre-empted by another firm operating under the hypothetical competitive stimulus. Under the closed system production begins at a time that maximizes the value of the lease, whereas under the open system, production begins at an earlier time when the lease value is merely positive. Only a regional monopoly industry under an open style tenure system would cause exploration to begin at the same time as a competitive industry under a closed tenure system.

Athol and Stuart have argued that resources development is related to expenditure on resources exploration which in turn has been stimulated by new technology, which has been associated with military strength and the force of cultural transmission. However, to the extent that changes in economic, military and cultural scale reflect changes in population and economic growth there is a supply relationship between resources development and growth.

The rate of resource depletion is influenced by strategic national position and strategic incident, technological drive and technological incident, cultural vigor and the factors which underline mighty economic scale such as the inequality of incomes and the force of social hierarchy in the central nations. They point out two sequential factors of possible economic efficiency theory of resource depletion. Initially the rate of exploration is too slow for economic efficiency, because of exploration externalities caused by each firm waiting for others. Later the rate of exploration is too fast for efficiency, because firms compete to gain the limited, free lease tenure. In their concluding comments they mention that the economist's optimal rate of depletion can only be a limited short-run concept, in which the important underlying determinants of depletions are implicitly assumed to be unchanging and except in the limited economic sense, the rate of resource depletion is an intermediate concept and not a fundamental goal.

Falling trend in scarcity rent:

According to Donald A. Hanson the extraction cost of non renewable resources as the depletion process assumes a rising trend. As the exhaustion of the resource under consideration nears. the maximum point, the scarcity rent registers a gradual decline in view of the tremendous increase on the extraction cost. Hanson is very emphatic when he argues that scarcity rent decrease as extraction cost rise. This contention is in sharp contrast with the well known case with the concept of constant extraction cost put forward by Herfindhal. Thus the extraction cost assumes a concave shape indicating thereby rising trend as extraction proceeds. Hanson shows that if the extraction cost path is concave as a function of' time, then the scarcity rent path is decreasing and the resource price path is concave. Hence, resource prices rise relatively rapid initially and then level off as the resource approached depletion. In general, whenever the scarcity rent path is increasing (decreasing) the resource price path is convex (concave).

On pricing of durable exhaustible resources Levhari, David and Pindyck, Robert.S, show that with rising marginal and average extraction cost, the Hotelling rule (price minus marginal cost rising at the rate or interest) still holds if the resource is produced in a competitive market, but does not hold for a monopolistic market. However, even in a competitive market the behaviour of price depends critically on the extent of durability and the characteristics of demand. In particular, price is always falling for a perfectly durable resource and constant demand, and the price profile is U-shaped for a partially durable resource or growing demand or both. They conclude that the price profile for most resources have shown long secular declines during at lease part of their history, and in many cases have indeed been U-shaped over the long term. The other factors which help in the pattern of price behaviour include the process of reserve discovery and accumulation during the early periods of resource use, technology linked reductions in extraction and processing costs, or declines in the prices of resource substitutes and an increased ability of firms to use substitutes as a result of technological change. 

 Taxation on exhaustible resources:

Gamponia and Mendelsohn made an extensive study on the impact of taxation on exhaustible resources. In their opinion in contrast with the taxation of most of the economic goods, taxation on non renewable resources tends to induce "complex intertemporal avoidance behaviour". According to them the complex intertemporal equation which generate the market response to each tax cannot be solved analytically, consequently there is no possibility of whatsoever to make any useful comparison among the various types of taxes on exhaustible resources with respect to their relative efficiency. According to them when the yield from taxes on exhaustible resources is generally the most efficient, the least efficient will be the basis of taxation of movable and non-movable properties, further it is a considered opinion that, its base price are equal to extraction cost the windfall profit creates no welfare loss. They further affirm that on the price rise alone the extraction cost, welfare losses will certainly come down. 

Radford Schantz Jr. in his analysis treats the payment for the mineral ores extracted and sold as a royalty earned by the government for the uncharted exhaustible and inexhaustible natural resources. In other words, it is a price paid for the precious metallic ores in the bonds of earth. This according to Radford could be viewed on a mineral rent paid to the custodian of the rights of mineral wealth ownership. With regards to the effect of royalty, Radford holds that it will reduce the expected return on exploration. Consequently, all kinds of exploration and discoveries will receive a major set back. Radford concludes his analysis that a ascertain hike in Royalties will have an adverse and crippling effects on the exploration and exploitation of mineral ores.

Risk factor in depletion of exhaustible resource:

Tracy R. Lewis, in his theoretical analysis, comparing extraction rates of an exhaustible resource for owners who are risk preferring, risk neutral or risk averse regarding variations in the returns from extraction. He found that the rate of pumping or extraction varies directly with owner's willingness to accept risk. According to him, risk preferring owners use the resource more rapidly than risk neutral owners, who in turn deplete the resource more rapidly than risk averse owners. Exhaustible Resource Price Movements: Richard V. Howarth has made an epoch making study on intergenerational allocation of exhaustible resources. One of his basic precepts is that under certain conditions, exhaustible resources have nothing but a zero cost. In point of fact they are nothing but a free good. But, when the demand for them goes up they appreciate in value and the rate of growth of their prices is perfectly equal to the rate of interest prevailing in a competitive economy. But under conditions of uncertainty, the movement of prices would be erratic like the expected rate of interest. Richard Howarth has analysed the problem of intergenerational distribution of exhaustible resources on the basis of the assumption that exhaustible resources are owned and managed by households and not by firms.

Strategically Interdependence between Exporting and importing nations as Exhaustible resources

The concept of strategic interdependence between exporting and importing nations of exhaustible resources has been dealt with at length by Dasgupta et. al. According to them, the nations which export certain exhaustible vital resources do always have a monopolistic attitude towards their importing counterparts. As the stock of such resources at their command, they tempt to quote higher prices with every fall in the size of their stock. Hence, with paradoxical enough, the marginal returns keep increasing until finally. The last unit is sold at the maximum price, which the consumers are willing to pay. The importing countries in their turn try to make use of their ingenuity in rendering the exploitative tactics of exporting nations exercise infertility. The handiest method available to them is to invest a back stock technology for destroying the monopoly enjoyed by the exporting nations. They can either advance the time of introducing the back stock technology or delay the time involved in destroying the same. If they delay the time, they can avoid a mamoth export on the back stock technology and at the same time get the exporting nations deplete their entire stock of the exhaustible resources on which they have monopoly control at relatively lower prices for the fear of the introduction of back stock technology which is in the offing. Thus, by manipulating the time factor involving in the invention of back stock technology, the importing nations can thwart the monopolistic controls and pressures exercised by their exporting counterparts2 . This idea has been upheld by Lewis et. at 29 . While dealing with the same problem Hotelling puts forward his thoughts about innovation of substitutes based mostly on the uncertainty about the monopolist's time horizon. In his opinion, it is the monopolist who motivates the dependent nations to embark on programmes of substitute innovation. He concludes his analysis with a critical remark that the intertemporal price discrimination unleashed by the economists, has a monopolist hold over exhaustible resources, which irks the dependent nations and goads them on to innovate substitute for such exhaustible resources.

Harris and Vickers analyse strategic interaction between the resource monopolist and the importing country in terms of a differential game in which the strategies of exporting country and importing country specify their behaviour as a function of the remaining resource stock. They content that the countries cannot commit their extraction or R&D plans in advance. Their decisions depend on the circumstances as they evolve. Since the stock at any time depends entirely upon the behaviour of the exporting country, it becomes imperative that the exporter acts 'strategically' with a view to influence the behaviour of' the importers. The main finding of Harris and Vickers is that, equilibrium in the dilierential game with Markov strategies exists and is unique. The expecled future pay oil ol both communities is increasing in the amount ot remaining stock and so decrease with time. Country B's R&D efforts are decreasing in the stock and so increase over time. This is because the urgency to innovate grows as the stock dwindles. It is often the case that country A's output decrease over time, but strategic considerations imply that this need not always happen. The importers R&D efforts are decreasing in the stock of the resource will lead to further innovation. The growth rate of marginal revenue over time is equal to the sum of three terms, the rate of interest, the hazard rate implied by the importers innovative efforts and strategic term that reflect the growth in importers efforts as the resource stock falls. if the importers R&D effort rises sharply when the remaining stock reaches a certain level, thus the exporter will slow down depletion as that level approaches, so as to delay in jump in the hardened rate. Thus strategic considerations can have quite significant efforts. 

Criticising the Standard aggregate exploration extraction model of non-renewable resources, John R. Livernois and Russel S. Uhier content that there is positive relation between extraction cost and the size of the resource. The reasons they cite are the other characteristics of deposits besides the state oldepiction affect the level of extraction cost and deposits with characteristics producing lower extraction costs tend to be found first. If the best deposits tend to be found first, then even if new discoveries are enough to make the resource base rise, the extraction cost may not fall. In the alternative dis-aggregate model presented by the authors, they point out that the extraction cost of individual deposits rise as they are depleted, at the same time it incorporates the belief that best deposits tend to be found first, and it accounts for cost effects at both intensive and extensive margins. The model leads to a new interpretation for the purpose of exploration. It helps to predict the shape of the price path. The model provides now insight into understanding exploration as a process of balancing marginal extraction costs and user costs between the intensive and extensive margins. Exploration is the scarce of increased production, which is an alternative to increased exploitation of existing deposits. In the absence of stock effects the model suggests that exploration is carried out until the cost of discovering the marginal deposits equals to present asset value.

Robert S. Pindyck, in his study on Uncertainty and exhaustible resource markets shows two kinds of uncertainties with regard to the behaviors of the exhaustible resource markets. They are, uncertainty over the future demand for the resource and uncertainty over the reserve base that will be ultimately available for exploitation. Demand uncertainty is modelled by assuming that the market demand function shifts randomly but continuously through time according to a stochastic process. Thus, although today's demand is known exactly, the future demand may be larger or smaller and has a variance that incases with time horizon. Similarly, reserves shift upward downward, again according to a stochastic process. Thus, he holds that as exploitation proceeds over time, resource procedures may find that more or less resources are available for production than originally expected.

Price Stability:

The economics of exhaustible resource as developed by Hotelling (1931) Scott(1967) Herfindahl(1967) and Gordon (1967) suggest that the flow market condition may be derived by maximizing the firm's discounted sum of profits over the period of operation, subject to the constraint that the total resource harvested cannot exceed its physical availability. James J. Mc Rae on the stability of non-replenishable resource prices show that the industry price along the optimal extracltion path wiII increase over the fixed average cost level because of ever increasing scarcity rent element rising at the exponential rate. As prices keep rising over time, firms in the industry will be indifferent between producing now or leaving the resource in the ground as the basis for future production. The possibility that Ihis price path may be unstable comes from the role of expectations in affecting the scarcity rent element of total costs. If the owners of the resource base expect the final selling price to rise more rapidly then the required weighted interest rate, then the owners will anticipate a capital gain on their unexploited resource stock. In other words, the resource left in the ground is exploited to earn a rate of return above the market rate of return on equivalent risk assets, so that leaving the resource untouched is the best possible way for the firm to hold its wealth. When the final selling price is expected to increase at too slow rate, owners will liquidate their resource stock by producing more current resource products: This excess supply reinforces expectations of capital losses on the resource base and thus causes more current production and more excess supply.

By judging from 53 year sample of monthly ore price for five minerals James J. Mc Rae concludes that the potential resource price instability is over stated. This may be due to the fact that resource markets are characterized by a monopolised industrial structure, real resource price show remarkable stability. When the stabilizing trend element is removed, resource price appear to fluctuate in a fashion corresponding to efficient resource allocation.

Time path of natural resource prices:

A major empirical study of the time paths of natural resource prices was conducted by Barnett and More (1963). The purpose of their study was to examine the hypothesis of increasing economic scarcity of natural resources. (by using natural resource product prices) They used product prices for minerals and total extractive output for a period of 87 years(1870-1957) and concluded that the trend was approximately horizontal . 

Heal and Barrow, made an attempt to test the empirical relevance of the theory of Exhaustible resources. They observed that, the price variable of interest is the price of the resource in situ. Their findings do not provide a strong reflection of the standard theory of exhaustible resources. Smith extended the Heal Burrow analysis to a wider range of natural resource products and examined long term price movements. In his analysis he rejected a Hotelling type mode! in which extraction costs were assumed to be zero.

Stollery in his study tested the theory of exhaustible resources using time series estimates of in situ prices of resources. He used annual data for the International Nickel Company for the years from 1952-1973 to estimate a log-linear demand function and a Cobb-Douglas production function. The estimated results were used to calculate the price of the resource in situ as the difference between marginal revenue and marginal cost. The null hypothesis that the estimated time path of in situ prices was consistent with the theoretical model.

Farrow (1985) in his study estimated a translog cost function for a US metal mining firm using monthly data from 1975-1981. The estimated price of' the resource in situ was calculated as the difference between the product price and the estimated marginal cost of output. His estimation of a number of alternative specification of test equations yielded results inconsistent with the theoretical model.

Miller and Upton (1985) used Cross Section estimate of in situ energy prices to test what they refer to as Holelling valuation Principle. They found that if the time path of the in situ price of a resource is expected by market participants to follow the Hotelling Rule, the asset value of a stock of the resource during any period will depend mainly on the current period product price and extraction cost.

However, Swierzbinski and Mendelsohn show that when the stock of a resource is uncertain, the Hotelling Rule may provide the best available prediction of future resource prices, even though unanticipated changes in expectations, due to the arrival of information cause the actual time paths of resource prices to deviate from the Hotelling predictions.

Robert and Tim (1991), in their study on the test of the Theory of Exhaustible Resources concluded that the empirical validity of the implications of the theory of exhaustible resources for the time paths of resource prices remain an open question. Previous empirical studies have clearly been severely constrained by the availability of time-series data on the prices of resources in situ and the effects of' cumulative extraction on marginal  extract cost.

They, using data for the Canadian Metal mining industry, for the years from 1954 to 1974, found that the empirical implications of' the theory of exhaustible resources are strongly rejected. The model developed by them provides a direct test of' the theory's implicates for the dynamic behaviour of implications for the dynamic behaviour of vertically integrated resource industries. By rejecting the empirical validity of the theory of exhaustible resources, they maintain that, the theoretical mode! does not provide an adequate characterization of privately optimal behaviour or that resource firms do not behave in a privately optimal way