exhaustible resources a theory of exploration the paper presents a theory of exploration for exhaustible resources exploration serves both to find new reserves and obtain information about potential reserves although any realized time path of the resource price fails to obey the hotelling rule the expected resource price does increase exponentially through time at the rate of discount we obtain sharper results when the resource is assumed to be distributed randomly throughout the exploration region and follows a poisson process with parameter a consumption and exploration decisions are investigated for both the case where a is known and the case where a is unknown

nonrenewable resource scarcity nonrenewable resource theory often is summarized by hotelling s rule this paper reviews theoretical extensions and empirical investigations of resource extraction models observed data are often inconsistent with the hotelling rule suggesting that other characteristics of nonrenewable resource supply including exploration heterogeneous ore quality technological progress and capital investment are important determinants of the dynamic behavior of resource prices given the persistent recurrence of concern about nonrenewable resource scarcity measures of nonrenewable resource scarcity and the empirical evidence for the time trends of those measures are reviewed finally the implications of nonrenewable resource scarcity for economic growth are examined

natural resource prices will they ever turn up abstract natural resource theory predicts that natural resource rents should increase over time however technical progress in resource extraction environmental constraints or great natural abundance could result in stagnant or declining product prices thus there is no theoretical reason to believe that product prices will rise in the near future the prediction of product prices by time series methods is shown to depend critically upon whether the series are modeled as difference or trend stationary dickey fuller and lagrange multiplier tests are used to show that the series are difference stationary long and short sample series are tested trend stationary modeling strongly predicts rising resource prices the result from difference stationary modeling is that there is only a weak supposition that natural resource prices will rise

energy and physical capital a case of non classical dynamics we study the importance of considering different energy requirements for physical capital and final good production in an overlapping generations olg resource economy in contrast to the standard olg framework but consistently with the empirical evidence we assume that the accumulation of physical capital requires more energy than the production of consumption goods focusing on exhaustible energy resources we find that olg equilibria can exhibit non classical dynamics the economy generates complex dynamics where differing from the response predicted by the standard approach resource prices may not increase monotonically this result illustrates that the technological assumptions behind the energy inputs should be taken with caution in particular on dynamic analyses involving exhaustible energy resources

a model of exhaustible resource exploitation with ricardian rent abstract the question of the optimal rate of development of an exhaustible resource such as a mine has long been a concern of resource economists however with few exceptions in the literature it has been implicitly assumed that orebodies are of uniform quality readily distinguished from their surroundings or else that the mining firm is able to choose the order of mining from sections of the mine which may vary in quality e g grade of ore while such simplifying assumptions have led to a rich array of conclusions they stand in contrast to the varying conditions facing the mining engineer in making cut off grade decisions this paper models a situation where because of orebody configurations the firm cannot choose to mine in order of grade an optimal cut off grade is obtained for each point of time of the mine s life in the case of a socially optimizing firm then in a special case the effects of monopoly and various types of mineral taxation are considered for the cut off grade decision and for ultimate recovery

stochastic convenience yield and the pricing of oil contingent claims this paper develops and empirically tests a two factor model for pricing financial and real assets contingent on the price of oil the factors are the spot price of oil and the instantaneous convenience yield the parameters of the model are estimated using weekly oil futures contract prices from january 1984 to november 1988 and the model s performance is assessed out of sample by valuing futures contracts over the period november 1988 to may 1989 finally the model is applied to determine the present values of one barrel of oil deliverable in one to ten years time

evaluating natural resource investments notwithstanding impressive advances in the theory of finance over the past 2 decades practical procedures for capital budgeting have evolved only slowly the standard technique which has remained unchanged in essentials since it was originally proposed see dean 1951 bierman and smidt 1960 derives from a simple adaptation of the fisher 1907 model of valuation under certainty under this technique expected cash flows from an investment project are discounted at a rate deemed appropriate to their risk and the resulting present value is compared with the cost of the project this standard textbook technique reflects modern theoretical developments only insofar as estimates of the discount rate may be obtained from crude application of single period asset pricing theory but see brennan 1973 bogue and roll 1974 turnbull 1977 constantinides 1978 the inadequacy of this approach to capital budgeting is widely acknowledged although not widely discussed its obvious deficiency is its the evaluation of mining and other natural resource projects is made particularly difficult by the high degree of uncertainty attaching to output prices it is shown that the techniques of continuous time arbitrage and stochastic control theory may be used not only to value such projects but also to determine the optimal policies for developing managing and abandoning them the approach may be adapted to a wide variety of contexts outside the natural resource sector where uncertainty about future project revenues is a paramount concern

reserve and land prices with exploration under uncertainty abstract arrow and chang j econom environ manag 9 1 10 1982 analyze an exploration extraction model with uncertainty about the distribution of deposits reserve prices do not exhibit any rising trend when the unexplored land area is big but in order to know what happens when the unexplored area is smaller a probabilistic analysis not yet performed ibid p 10 is required their conjecture of a rising trend at less than the discount rate is confirmed however land prices can be expected to grow faster than reserve prices which helps discriminate between arrow and chang s and other rationalizations of the failure of resource prices to rise at the discount rate

optimal growth resource amenities and the preservation of natural environments this paper examines the conditions for which it is optimal to permanently preserve natural environments in which a productive natural resource is found the conditions are more restrictive than those previously indicated in the literature on the economics of natural environments increasing consumption and declining commodity prices are not sufficient to warrant permanent preservation the initial capital stock can be an important determinant of the optimal level of preservation in addition resource amenity values will increase the initial resource price and decrease the rate of growth of the resource price the natural world provides a variety of services to the human community natural resources are essential inputs in the production of goods and services in addition the natural world generates a variety of amenity services including the scientific recreational and aesthetic value of preserved natural environments krutilla 1967 krutilla and fisher 1975a this paper examines the impact of resource amenity values on the optimal growth of an economy which depends upon natural resource inputs for the production of goods and services in particular the paper examines the conditions under which it is optimal to permanently preserve some natural environments in which the productive resource is found the conditions which warrant permanent preservation are more restrictive than previously indicated by the literature on the economics of natural environments increasing consumption and declining commodity prices are not sufficient to warrant permanent preservation in addition the initial capital endowment can be an important determinant of the optimal level of preservation

statistical measures of unsustainability abstract statistical measures are needed to reveal at a glance how far or near various countries are to meeting the conditions of long run sustainability and how conditions are changing on a year to year basis i e whether sustainability is being approached or not the scheme proposed in this paper presents numerical comparisons of energy and materials use in the real world vis a vis an ideal case where all of the identifiable criteria for sustainability are satisfied apart from population stabilization five general but quantifiable criteria for sustainability are suggested including 1 stabilization of greenhouse gas concentrations in the atmosphere 2 stabilization of acidity ph in rainfall 3 reduction of dissipative uses and wastes of heavy metals to natural mobilization rates or lower 4 elimination of agriculture based on pumping fossil water from non renewable aquifers and 5 elimination of loss of arable land because of salination or erosion other criteria such as preservation of biodiversity and socio economic equity between countries and generations might be added to the list they introduce more difficult measurement problems however which are not considered further in the paper having fixed the list of criteria the next step is to identify measures that either go to zero or unity as the system approaches more and more closely to sustainability at least in the limited sense defined above various types of measures of sustainability unsustainability can be developed viz i measures of relative dependence of the economy on non renewable sources of energy and materials ii measures of the productivity of energy and materials consumed by the economic system and iii measures of dissipative loss especially of toxic and hazardous substances specific examples of each type are discussed

cycles in natural resource commodity prices an analysis of the frequency domain abstract a model is derived that relates price cycles to investment behavior in the mineral industries and predicts that these cycles will be roughly twice as long as the investment period the period between the investment decision and the project completion spectral techniques are used to estimate the principal cycles in metal and fuel prices for the metals the estimated cycle lengths reinforce the model predictions however no significant cycles are found in the prices of the fuels the lead lag relationships between prices of different commodities are also investigated and are found to be significant for those that are jointly produced

interest rates and metal price movements further evidence abstract we offer a theory about the relationship between interest rates and metal price movements the theory is a version of the hotelling rule eq 8 the results obtained from prices of four different metals based on seasonally and unadjusted quarterly data over the period 1968 2 1982 2 suggest that a reformulated hotelling rule which has a dynamic structure can explain the relationship between metal prices and interest rates in view of this result it appears that the return on exhaustible resources is related to changes in rather than the levels of interest rates this result also confirms the results of g m heal and m m barrow rev econom stud 48 161 181 1979 econom lett 7 95 103 1981

a note on mining with investment in capital one of the principal predictions of the theory of the extractive firm is that its rate of output will decline steadily throughout time recently in this journal campbell 1980 presented an interesting analysis suggesting that this behaviour may be altered if one accounts for the fact that firms must invest in some level of fixed capital which is needed in combination with variable inputs to extract the resource in the campbell analysis the fixed capital places a constraint on the maximum rate of extraction it is shown that this constraint is binding and that extraction is therefore constant over some initial period of the mine when the firm behaves optimally this note demonstrates that the campbell result is due to a fixed proportions technology assumption in particular when a neoclassical technology is assumed one finds that the constraint imposed by the level of fixed capital is never binding and that the optimal extraction rate is strictly monotonically declining as a function of time i to demonstrate this an informal argument will suffice let k be the level of fixed capital chosen by the firm let lt be the amount of the variable factor employed in period t assume that the rate of extraction et is given by the production function2

long term swings and seasonality in energy markets abstract this paper introduces a two factor continuous time model for commodity pricing under the assumption that prices revert to a stochastic mean level which shows smooth periodic fluctuations over long periods of time we represent the mean reversion price by a fourier series with a stochastic component we also consider a seasonal component in the price level an essential characteristic of many commodity prices which we represent again by a fourier series we obtain analytical pricing expressions for futures contracts using futures price data on natural gas we provide evidence on the presence of long term fluctuations and show how to estimate the long term component simultaneously with a seasonal component using the kalman filter we analyse the in sample and out of sample empirical performance of our pricing model with and without a seasonal component and compare it with schwartz and smith 2000 model our findings show the in sample and out of sample superiority of our model with seasonal fluctuations thereby providing a simple and powerful tool for portfolio management risk management and derivative pricing

on the portents of peak oil and other indicators of resource scarcity economists have studied various indicators of resource scarcity but largely ignored the phenomenon of peaking due to its connection to non economic physical theories of resource exhaustion i consider peaking from the economic point of view where economic forces determine the shape of the equilibrium extraction path within that framework i ask whether the timing of peak production reveals anything useful about scarcity i find peaking to be an ambiguous indicator if someone announced the peak would arrive earlier than expected and you believed them you would not know whether the news was good or bad however i also show that the traditional economic indicators of resource scarcity price cost and rent fare no better and argue that previous studies have misconstrued the connection between changes in underlying scarcity and movements in these traditional indicators

price scarcity rent and a modified r per cent rule for non renewable resources since hotelling s seminal paper on the optimal depletion of exhaustible resources much has been published yet confusion remains about whether scarcity rent and price increase or decrease as a resource is depleted when costs tend to rise with depletion we show that hotelling s fundamental results of rising scarcity rent and price paths are sustained and that the path of scarcity rent converges on the r per cent rule provided the objective function is concave predictions of non monotonic or declining scarcity rent paths are due to implicit assumptions that lead to a non concave objective function we identify the sources of these non concavities jel classification q30 d90 c60 prix rente de rarete et une regle modifiee du r pourcent pour les ressources non renouvelables malgre la volumineuse litterature specialisee qui a fleuri depuis qu hotelling a ecrit son memoire fondateur sur l epuisement optimal des ressources renouvelables une grande confusion regne toujours quand il faut etablir si la rente de rarete et le prix augmentent ou chutent a proportion que la ressource s epuise quand les couts tendent a croitre avec l epuisement ce memoire montre que les resultats fondamentaux obtenus par hotelling quant aux sentiers de croissance de la rente de rarete et du prix tiennent toujours et que le sentier de croissance de la rente de rarete converge vers la regle du r pourcent pourvu que la fonction objective soit concave les predictions de sentiers de croissance non monotone ou de declin de la rente de rarete presentees dans la litterature specialisee sont attribuables a des postulats implicites qui engendrent une fonction objective non concave les auteurs identifient les sources de ces non concavites

speculative bubbles in recent oil price dynamics evidence from a bayesian markov switching state space approach abstract motivated by repeated spikes and crashes during previous decades we investigate whether the heavily financialized market for crude oil has been driven by speculative bubbles in our theoretical modeling we draw on the convenience yield approach in order to approximate the fundamental value of the oil price we separate the oil price fundamental from the bubble component by expressing a standard present value oil price model in state space form we then introduce two markov regimes into the state space representation in order to distinguish between two distinct phases in the bubble process namely one in which the oil price bubble is a stable process and one in which the bubble explodes we estimate the entire markov switching state space specification using an econometrically robust bayesian markov chain monte carlo mcmc methodology based on inferential techniques designed for statistically separating both markov regimes in the bubble process from each other we find robust evidence for the existence of speculative bubbles in recent oil price dynamics

on the intergenerational allocation of natural resources it is known hartwick and others that under standard assumptions a society that invests in reproducible capital the competitive rents on its current extraction of exhaustible resources will enjoy a consumption stream constant in time it is shown here that this result can be interpreted as saying that an appropriately defined stock of capital including the initial endowment of resources is being maintained intact and that consumption can be interpreted as the interest on that patrimony this seems like a useful rule of thumb for policy

economic indicators of resource scarcity a critical essay abstract the theoretical arguments of the conceptual and empirical literature on economic indicators of long run resource scarcity are logically flawed if resource allocators were informed of the nature of resource scarcity their behavior and the economic indicators it generates would reflect the scarcity but if they were so informed we could simply ask them if resources were scarce if they are not informed their behavior and economic indicators are as likely to indicate their ignorance as the reality unfortunately there is no way of knowing whether they are informed or not unless we already know whether resources are scarce

price expectations ore quality selection and the supply of a nonrenewable resource abstract economic models of depletion imply that the present value price of a resource and the quality of extracted ore should be directly related the empirical evidence is that in the short run the average quality of extracted ore and in some cases metal output decline in response to a price increase this paper examines a model of extraction with heterogeneous ore quality within a deposit and revised price expectations in which this seemingly paradoxical supply response is rationalized as the outcome of ore quality selection which maximizes the present value of the mine

a test of the theory of exhaustible resources an empirical test of the theory of exhaustible resources requires an estimate of the time path of the shadow price of the unextracted resource that generally is not observable because of the prevalence of vertical integration in natural resource industries in this paper we use duality theory to derive an econometric model that provides a statistical test of the theory of exhaustible resources a restricted cost function is used to obtain estimates of the shadow prices of unextracted resources the procedure is illustrated with data for the canadian metal mining industry for this industry the empirical implications of the theory of exhaustible resources are strongly rejected

short term variations and long term dynamics in commodity prices in this article we develop a two factor model of commodity prices that allows meanreversion in short term prices and uncertainty in the equilibrium level to which prices revert although these two factors are not directly observable they may be estimated from spot and futures prices intuitively movements in prices for long maturity futures contracts provide information about the equilibrium price level and differences between the prices for the short and long term contracts provide information about short term variations in prices we show that although this model does not explicitly consider changes in convenience yields over time this short term long term model is equivalent to the stochastic convenience yield model developed in gibson and schwartz 1990 we estimate the parameters of the model using prices for oil futures contracts and apply the model to some hypothetical oil linked assets to demonstrate its use and some of its advantages over the gibson schwartz model

modelling natural resource scarcity using the error correction approach an error correction framework is used to test the long run hypothesis that prices of natural resources commodities in the united states exhibit scarcity properties from the late nineteenth century to 1988 in the sense that real resource commodity prices have been increasing or following a u shaped pattern introduced by m e slade 1982 the model is formulated to test the validity of the deflation procedure itself along with the scarcity properties results indicate that the model works well as a description of the long term behavior of resources prices and supports the u shaped version of the scarcity hypothesis in a majority of cases an error correction framework is used to test the long run hypothesis that prices of natural resources commodities in the u s exhibit scarcity properties from the late nineteenth century to 1988 in the sense that real resource commodity prices have been increasing or following a u shaped pattern slade 1982 the model is formulated to test the validity of the deflation procedure itself along with the scarcity properties results indicate that the model works well as a description of the long term behaviour of resources prices and supports the u shaped version of the scarcity hypothesis in a majority of cases

environmental and land use regulation in nonrenewable resource industries implications from the wyoming checkerboard this paper examines how the oil and soning that these effects should be similar gas industry responds to changes in environmental to those of production and property taxes and land use regulations pertaining to drilling by like stollery however they do not conexamining differences in regulatory practices on sider the situation where environmental federal and private land a simulation model for regulations directly affect explo ration and wyoming is used to estimate losses of oil and gas development output over the next 60 years because of higher activities in any case the drilling costs found on federal property the pres limited number of studies in this area and ent value of these losses comes to about 800 mil their narrow scope is surprising in light of lion a lso this case study is of interest because it the importance of environmental complishows that future production is more sensitive to ance costs to firms that produce from nonchanges in environmental regulations that apply to renewable resources and because of the drilling than to changes in severance taxes levied observation by jaffe et al 1995 that a on production

testing the efficiency of extraction from a stock resource the theoretical conditions for efficient extraction from a known stock resource by a competitive mining firm are reviewed these conditions are tested using proprietary data from a mining firm output price data and coefficient estimates from a translog cost system are used to compute the in situ value of the resource and the stock effect changes in the in situ value over time are then statistically compared with the expected price path the results reject the hypothesis that the data are consistent with the theoretical model and the maintained hypotheses variations of the basic model that incorporate a time varying discount rate an alternative expected price series and a constraint on the rate of output are also tested and rejected 46 references 10 tables

the pricing of oil and gas some further results the hotelling valuation principle hvp implies that the unit value of an exhaustible natural resource can be written as a function of its current price net of extraction costs other variables such as interest rates have no additional explanatory power the results of earlier tests using data from 1979 1981 strongly support the hvp this paper presents a series of follow up tests using time series cross section data covering the period august 1981 to december 1983 because the variance of petroleum prices in this period was substantially less than in the earlier period the follow up sample proved generally noninformative the sample also contains some observations on oil and gas royalty trusts tests of the hvp using these trust data yielded generally satisfactory results although given the limited sample size the results must be viewed with caution the purpose of this paper is to present follow up tests of the hotelling valuation principle hvp for exhaustible resources the hvp and the earlier tests are described in detail in an earlier paper miller and upton 5 and we will limit ourselves here to a brief summary the principle that the unit price of an exhaustible natural resource less the marginal cost of extraction will tend to rise at the rate of interest was first stated by harold hotelling 2 it follows from intertemporal profit maximization on the part of a price taking owner of an exhaustible natural resource if the unit price of resources net of extraction costs is expected to rise by less than the rate of interest why not extract it now and if it will rise by more why extract any today the hotelling principle has become the standard paradigm for natural resource economics although perhaps more from the absence of any viable alternative than from strong empirical validation earlier tests of the hotelling principle generally based on time series of resource prices have yet to provide convincing support

learning and stock effects in environmental regulation the case of greenhouse gas emissions abstract this paper concerns the optimal regulation of greenhouse gases that lead to global climate change in particular we focus on uncertainty and learning which over time resolves uncertainty we present an empirical stochastic model of climate economy interactions and present results on the tension between postponing control until more is known vs acting now before irreversible climate change takes place uncertainty in our model is in the damage caused by global warming the results suggest that a temporary carbon tax may dominate a permanent one because a temporary tax may induce increased flexibility

scarcity growth and r d abstract the limits to economic growth due to resource scarcity can be alleviated only by the development of backstop substitutes this paper combines resource based economic growth with r d to reduce the cost of backstop technologies characterizing the entire dynamics of optimal growth and r d processes we find that an economy s growth prospects depend on its type as determined by its production technology and learning ability and by its knowledge capital endowment a wide variety of growth patterns emerges ranging from cases in which an economy that without r d eventually stagnates converges to a steady state is diverted by r d onto a path of sustained growth to cases in which r d is not warranted resource scarcity is shown to encourage r d due to the increased reliance on the backstop technology

concepts and measures of natural resource scarcity with a summary of recent trends a general model of resource scarcity is presented from which previous models can be derived as special cases previous models of scarcity are compared and contrasted refining the concept of scarcity and leading to a resolution of current disputes over the appropriate measure of scarcity an update of the original work done by barnett and morse is summarized leading to reconsideration of their original conclusions it is found that energy and forest products experienced increasing scarcity during the 1970s

net national product as an indicator of sustainability net national product nnp can potentially serve several objectives among others to measure value added and to be an indicator of welfare in the aftermath of the world commission on environment and development however it also seems important to investigate whether the concept of nnp can serve as an indicator of sustainability my point of departure following hicks 1946 ch 14 is therefore to require that nnp should measure what can be consumed in the present period without reducing future consumption possibilities and in line with this to argue that the nnp should equal the maximum per capita consumption level that can be sustained if sufficiently many facilitating assumptions are made then a concept of nnp that serves as an exact indicator of sustainability can easily be constructed for instance for a closed economy with a constant population a stationary technology and with only one capital good it follows that the present does not reduce future consumption possibilities if and only if it does not decrease the stock of the single capital good hence under the assumption that the one capital good k is identical to the one consumption good x nnp defined as y x k measures the maximal sustainable consumption at time t because then x y is equivalent to k the purpose of this note is to establish that with multiple capital goods it is not in general possible to construct an exact indicator of sustainability on the

the contingent valuation debate why economists should care t he contingent valuation method involves the use of sample surveys questionnaires to elicit the willingness of respondents to pay for generally hypothetical projects or programs the name of the method refers to the fact that the values revealed by respondents are contingent upon the constructed or simulated market presented in the survey a spirited and occasionally mean spirited battle over such methods is currently being waged involving competing factions within the federal government economists and lawyers representing business and environmental groups and interested academics as well at issue is a seemingly quite specific question should environmental regulations currently under development at both the department of the interior and the department of commerce sanction the use of the contingent valuation method in estimating the damage done by spills of oil chemicals or other substances covered by federal law more generally the debate raises broad questions about what economists have to say about the values that individuals place on public or private goods the two papers that follow this one make cases for and against the use of the contingent valuation method my aim here is to provide an overview of the technique and the debate surrounding it i also want to suggest why this debate should matter to economists both professionally and in their roles as citizens and consumers

the behavior of foreign exchange rates comment the distributors of foreign exchange rates are important for model building and empirical analysis for example many studies have examined foreign exchange market efficiency and currency portfolio management under the assumption that foreign exchange rates are normally distributed the statistical tests in these studies and thus their conclusions may not be reliable if the foreign exchange rates follow non normal distributions realizing the importance of the distribution of exchange rates professors calderon rossell and ben horim 1982 hereafter c b have conducted a study analyzing these distributions based on the skewness of the distribution c b have classified foreign currencies into three groups in the first group the skewness statistic was not significantly different from zero for all currencies and subperiods in the second group the distribution of changes in the foreign exchange rates was close to symmetric except for at least one subperiod in the third group the skewness statistic suggests strongly that all the distributions were asymmetric their results reveal that

convenience yield in commodity price modeling a regime switching approach this paper attempts to model the futures term structures of crude oil and natural gas using the notion of convenience yield in a regime switching framework unlike the existing studies which assume the convenience yield to have either a constant value or to have a stochastic behavior with mean reversion to one equilibrium level the model of this paper extends the gibson and schwartz 1990 model to allow for regime switching in the convenience yield along with the other parameters a closed form solution for the futures price is derived and the model parameters are estimated using the maximum likelihood method the results show that the estimated regimes are very close to the contango and backwardation regimes commonly seen in futures markets the results also show that the transitional probabilities play an important role in shaping the futures term structure implied by the model

commodity convenience yield and risk premium determination the case of the u s natural gas market this paper contributes to the understanding of commodity pricing issues by measuring and modeling two of the most important concepts in the storable commodity markets the convenience yield and risk premium an emphasis is placed on the empirical determination of these factors in the u s natural gas market we find that the convenience yield and risk premium are measurable and economically significant while we find that the determination of the convenience yield is largely consistent with economic theories the evidence regarding the determination of the risk premium is mixed

cost specification and firm behaviour in a hotelling model of resource extraction in applied resource economics much attention has been focused on the ability of the hotelling model to explain observed firm behavior in this paper a preliminary specification search is performed to determine the appropriate cost function parameterization for the firms in the sample before proceeding to the estimation of the euler equation once a cost function specification is chosen the corresponding euler equation is estimated via the generalization method of moments gmm which allows for better estimates of the euler equations than in previous studies even with the preliminary specification search and the use of gmm estimation the behavior of the panel of fourteen canadian copper mining firms in the data set examined does not seem to be consistent with the basic hotelling model used

grade selection under uncertainty least cost last and other anomalies abstract grade selection rules for heterogeneous resource deposits with increasing marginal extraction costs are derived it is shown that contrary to the conventional wisdom it can be optimal to extract the least cost deposits last there are a number of rules that are compatible with dynamic profit maximization under certainty nevertheless none explains empirical regularities in actual extraction patterns when uncertainty about future price is introduced however the theoretical model conforms closely not only to observed grade selection patterns but also to observed mineral industry price paths

exploration and exhaustible resources the microfoundations of aggregate models the appropriate specifications for aggregate extraction and exploration cost functions are derived from a disaggregate model of the search for low cost deposits of an exhaustible resource the common practice of combining the no discovery extraction cost function with exploration is shown to result in a misspecified model for which the total cost of extracting the resource is not well defined the widely accepted prediction that the anticipated discovery of low cost deposits results in a u shaped price path appears to be an artifact of this misspecification for the authors properly specified cost functions the predicted resource price always rises copyright 1989 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

the conservationist s dilemma it is typically thought that conservation of natural resources is encouraged by low interest rates however when capital goods are used to extract the resource low interest rates may discourage rather than encourage conservation using a model of a capacity constrained extractive industry in competitive equilibrium i find the relationship between the initial rate of exploitation and the interest rate if capital is so important that for sufficiently high interest rates the industry is nonviable the graph of initial quantity versus the interest rate is u shaped the traditional result holds at small interest rates but not at large ones copyright 1993 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

a markov regime switching approach for hedging energy commodities abstract this paper estimates constant and dynamic hedge ratios in the new york mercantile exchange oil futures markets and examines their hedging performance we also introduce a markov regime switching vector error correction model with garch error structure this specification links the concept of disequilibrium with that of uncertainty as measured by the conditional second moments across high and low volatility regimes overall in and out of sample tests indicate that state dependent hedge ratios are able to provide significant reduction in portfolio risk

sectoral supply of minerals of varying quality in this sectoral model of mineral production investment in capacity and variation in orebody grade and volume help explain some stylized facts more than one grade of ore may be exploited simultaneously mine exhaustion but not necessarily entry occurs in declining order of grade the price may rise or fall but is likely to fall initially young industry and must eventually rise at less than the interest rate unless demand expands rapidly these trends exhibit fluctuations due to entry and exhaustion of deposits resource price cyclicality is reinforced because mines keep producing at capacity when the price is falling

the stochastic seasonal behavior of energy commodity convenience yields abstract this paper contributes to the commodity pricing literature by consistently modeling the convenience yield with its empirically observed properties specifically in this paper we show how a four factor model for the stochastic behavior of commodity prices with two long and short term factors and two additional seasonal factors may accommodate some of the most important empirically observed characteristics of commodity convenience yields such as the mean reversion and stochastic seasonality based on this evidence a theoretical model is presented and estimated to characterize the commodity convenience yield dynamics that are consistent with previous findings we also show that commodity price seasonality is better estimated through convenience yields than through futures prices

regime shifts in a dynamic term structure model of u s treasury bond yields this article develops and empirically implements an arbitrage free dynamic term structure model with priced factor and regime shift risks the risk factors are assumed to follow a discrete time gaussian process and regime shifts are governed by a discrete time markov process with state dependent transition probabilities this model gives closed form solutions for zero coupon bond prices an analytic representation of the likelihood function for bond yields and a natural decomposition of expected excess returns to components corresponding to regime shift and factor risks using monthly data on u s treasury zero coupon bond yields we show a critical role of priced state dependent regime shift risks in capturing the time variations in expected excess returns and document notable differences in the behaviors of the factor risk component of the expected returns across high and low volatility regimes additionally the state dependence of the regime switching probabilities is shown to capture an interesting asymmetry in the cyclical behavior of interest rates the shapes of the term structure of volatility of bond yield changes are also very different across regimes with the well known hump being largely a low volatility regime phenomenon jel g12 this article develops and empirically implements an arbitrage free dynamic term structure model dtsm with priced factor and regimeshift risks the risk factors are assumed to follow a discrete time gaussian process and regime shifts are governed by a discrete time markov process with state dependent transition probabilities agents are assumed to know both the current state of the economy and the regime they are currently in this leads to regime dependent risk neutral pricing and an equilibrium term structure that reflects the risks of both changes in the state and shifts in regimes

extraction costs and the economics of nonrenewable resources the study questions the fundamental assumption of the standard aggregate exploration extraction model of nonrenewable resources that extraction costs and the level of reserves are inversely related it also raises questions about the model s conclusions regarding exploration incentives and the valuation of reserves an empirically tested disaggregate model is presented that suggests that exploration activity occurs from firms attempting to balance marginal extraction plus user costs at the intensive and extensive margins exploration is carried out until the marginal discovery cost of a deposit equals its present asset value and a u shaped price path is indicated

mineral depletion with cost as the extraction limit a model applied to the behavior of prices in the nickel industry abstract this article follows papers by pindyck and heal and barrow in applying a hotelling type depletion model to a particular resource industry in this case that of nickel by means of the model the resource rent per ton of nickel is calculated as the proper index of extractive resource scarcity the time path of this resource rent indicates that the model explains industry behavior well and that as in the two previous studies depletion has been an important determinant of prices and rents in this industry

the effect of the discount rate on depletion of exhaustible resources this paper argues that despite its widespread acceptance in the literature the basic proposition that a reduction an increase in the discount rate leads to greater conservation faster depletion of an exhaustible resource is not generally valid it shows that the effect of the discount rate on the rate of resource depletion depends on capital requirements for production of the substitute and extraction of the resource and on the size of the resource stock in fact it shows that there always exist at least two ranges of the resource stock size for which the effect is opposite to that conventionally believed

the time path of scarcity rent in the theory of exhaustible resources there is now a consensus in the literature on resource economics that a depletable resource should command a price in excess of its marginal extraction cost simply to reflect the opportunity cost of using a unit of it today rather that conserving it for the future but how this excess is to change along an optimal or competitive equilibrium path of resource use is still an unresolved question this might at first seem puzzling since according to the fundamental theorem of economics of exhaustible resources or hotelling i 93 i rule on an optimal path price minus marginal extraction cost also termed interchangeably as scarcity rent user cost or royalty should steadily grow over time at the social rate of discount however the literature contains sharply contrasting views on the subject for example kay and mirrlees 1975 have argued that since along an optimal path the scarcity rent grows exponentially as a finite stock of a resourcexnears exhaustion then situations in which the resource stock is still very large and yet the price greatly exceeds the marginal extraction cost should indicate that the price is significantly above its optimal level and that the resource is overconserved in stark contrast to this view heal i976 has argued that as the resource stock nears exhaustion the difference between price and marginal cost or what he termed social cost of extraction falls monotonically to zero hanson i980 analyses the same model as heal s but unlike heal who assumes the unit extraction cost to be convex he postulates it to be concave and yet like heal concludes that the scarcity rent will be monotonically declining over time solow and wan i976 analyse a still 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 must rise at the real rate of interest despite differential extraction costs but that the difference between price and the marginal extraction cost or what they call degradation charge declines monotonically over time to zero these sharply differing conclusions suggest that far from being resolved the question of how scarcity rent changes over time is much in want of a close scrutiny the need for such a scrutiny becomes even stronger once it is noted

capital gains and net national product in open economies it is shown within a given framework that with the world economy following an egalitarian path the aggregate capital gains being positive is equivalent to the interest rate tending to decrease this result is of importance for the concept of net national product in open economies in particular with positive aggregate capital gains an open economy cannot sustain consuming the return on its capital stocks since some part of the return must be used to augment the country s national wealth it is established that a country s share of world wide sustainable consumption equals its share of worldwide wealth

stochastic trends and structural breaks in the intensity of metals use abstract this research examines whether innovations in the relationship between metals demand and economic activity are of a deep nature such that they have persistence or whether such innovations are transitory conditional on a break point resulting from the 1973 oil price shock evidence was found to suggest that at least for some of the metals studied in this research intensity of use is well represented as a stationary process after accounting for a break point at 1973 one interpretation of this result is that technological shocks are not as pervasive as one might have thought and that only extraordinary events have a measurably long lasting influence on metals demand

trends in natural resource commodity prices an analysis of the time domain abstract this paper attempts to reconcile the theoretical predictions of increasing real prices for nonrenewable natural resource commodities obtained from hotelling style models with the empirical findings of falling prices for these commodities a theoretical model for relative price movements is derived for the case of exogenous technical change and endogenous change in the grade of ores mined the model suggests a u shaped time path for relative prices the implied price movements are tested for all the major metals and fuels and the model parameters are found to be statistically significant for 11 out of the 12 commodities tested

option value under income and price uncertainty abstract we present a rigorous examination of the sign of option value under income and price uncertainty we state and prove three theorems on the sign of option value when preferences are state independent if income is uncertain the sign of option value is opposite the sign of the income elasticity of the good in question the analysis of price uncertainty is in two parts one covers the case of own price uncertainty and the other the case where the price of some other good is uncertain in both cases the sign of option value is generally ambiguous

optimal exploration for and exploitation of heterogeneous mineral deposits abstract we model exploration for and production from a multiple deposit nonrenewable resource exploration is viewed as a bayesian process involving learning about undiscovered reserves and is undertaken both to improve the quality of and to replenish known reserves known reserves are not physically defined but depend on the realizations of discrete episodes of exploration elsewhere and on decisions at each instant about the margin between ore to be mined and low grade material to be rejected the appropriate measure of resource scarcity the sustainable level of the contribution of the resource and the treatment of depletion in the national accounts are considered

optimal pricing use and exploration of uncertain natural resource stocks abstract units of natural resources to be called mines are assumed distributed over an unexplored territory according to a poisson process in space at any moment total reserves and unexplored land are given society can determine the rate of consumption and the rate of exploration reserves are drawn down by consumption and increased by discoveries made during exploration the amount of unexplored land is decreased by exploration at any moment the payoff of society is a concave function of consumption less a linear function of exploration with future payoffs discounted optimal policies are considered and in particular it is shown for a large amount of unexplored land the shadow prices of reserves and of unexplored land move in random cycles but show only a slight upward tread thereby casting some light on the failure of mineral prices to rise at the market rate of interest

on the welfare significance of green accounting as taught by parable abstract green nnp is a national accounting concept that subtracts off from gnp not just depreciation of capital but also depletion of environmental assets for a time autonomous technology green nnp has a rigorous welfare interpretation as an exact measure of the economy s future power to consume the present paper extends the standard framework to cover the case of labor augmenting technological progress for this special case of time dependence a powerful conceptual parable applies it is as if the conclusion from a simple minded welfare story told by the standard neoclassical one sector growth model covers a far more general situation involving any number of different types of capital any convex production possibilities set and fully optimizing behavior implications and applications are discussed

local labor markets job matching and urban location we present a new way of modeling local labor markets by linking the space of workers skills and the physical space of cities the key lesson of our analysis is that firms exploit workers in these two spaces by setting wages that are below the competitive level the degree of monopsony power depends on the elasticity of the firm s labor pool which is inversely related to the costs workers incur in commuting and acquiring skills our analysis thus shows how socioeconomic ghettos emerge as workers with poor skill matches are also those who incur the highest commuting costs

the taxation of nonreplenishable natural resources revisited abstract the theory of nonreplenishable resource extraction has been extended to allow for extraction costs which increase as deposits are increasingly depleted in these cases profit maximization may result in the cessation of extraction before reserves are totally exhausted the effect of various taxation policies on optimal extraction patterns in these models are derived with a few exceptions the results are that the imposition of a tax will cause operators to extract at faster rates over shorter periods of time and to reduce the total amount of ore extracted the analysis allows for an output price which increases over time

on comparing monopoly and competition in exhaustible resource exploitation abstract it is widely believed that exhaustible resource monopolies do not enjoy as much market power as standard non resource monopolies and may even produce in a socially optimal way we argue that this paradoxical result arises from an inappropriate comparison methodology when similar assumptions are applied to the resource and the conventional cases we show that the resource monopoly behaves as expected i e restricts supply

a test of the hotelling valuation principle time series tests of the hotelling r percent rule for natural resource prices have not been strongly supportive but the tests and the data are subject to serious difficulties we propose here an alternative testing strategy based on another but less widely known implication of the hotelling model we test this implication which we call the hotelling valuation principle by regressing the market values of the reserves of a sample of u s domestic oiland gas producing companies on their estimated hotelling values we find that the estimated hotelling values account for a significant portion of the observed variations in market values and that the hotelling measures are better indicators of the market values of petroleum properties than two widely cited publicly available alternative appraisals

information and exhaustible resources a bayesian analysis abstract we develop a continuous time bayesian model of investment in information about an exhaustible resource because of the way that information affects expectations the deterministic hotelling rule turns out to be more appropriate as a description of how resource owners forecast the value of their stocks than as a predictor of observed changes in the resource price a flow of information generates both unanticipated changes in expectations which cause the mean rate of change in the resource price to deviate systematically from the deterministic hotelling rule and reductions in uncertainty which do not affect the hotelling prediction

energy backstop endogeneity and the optimal use of groundwater to meet the growing demand for freshwater many regions have increased groundwater pumping in recent years resulting in declining groundwater levels worldwide a promising development to address these declines is technical change regarding groundwater substitutes such as desalination and wastewater recycling however because these technologies are energy intensive optimal implementation also depends on future energy price trends we provide an operational model for the case of reverse osmosis seawater desalination in an application to the pearl harbor aquifer in hawaii we find that allowing the cost of desalination to increase at an average annual rate of 2 4 over the next century results in a substantially steeper efficiency price path for water the higher prices decrease optimal groundwater extraction and induce a slower head drawdown over a longer period of time thereby delaying the transition to desalination by over 30 years because the rise in energy costs exacerbates efficiency losses from under pricing any delay in implementing efficiency pricing will cause either a greater future increase in prices or the need for rationing reforming prices sooner rather than later may be more politically feasible given that consumers may be more amenable to a gradual rise in prices today than a sudden doubling or tripling of prices ten years from now using this as a foundation we outline a research agenda for extending the framework to other groundwater substitutes and for adapting to climate change

a hotelling faustmann explanation of the structure of christmas tree prices we examine the relationship between a tree price and a tree age height using a hotelling faustmann type model of optimal plantation management which accounts for the possibility of replanting and biological growth the model predictions are tested using the data on christmas tree prices in north carolina collected in december 1997 the estimates show that in general the rates of change in prices between adjacent age cohorts reflect a competitive equilibrium in the capital market thus supporting the hotelling faustmann paradigm rigorous empirical testing of the basic economic models of optimal natural resource pricing has proven to be difficult the source of the difficulty has been the unavailability of micro level data on either prices or extraction harvest rates for in situ resource stocks 1 for nonrenewable resources hotelling s famous pricing rule has rarely been tested with firm level data stollery s study of the international nickel company of canada supported hotelling s rule and miller and upton s study of oil company values supported a corollary called the hotelling valuation principle most other studies such as halvorsen and smith and farrow have refuted this bedrock of natural resource economics in fact two studies of old growth timber essentially a nonrenewable resource provide some of the most compelling support for the hotelling model berck johnson

hotelling confronts capm a test of the theory of exhaustible resources a model of pricing of natural resource commodities that integrates financial and product markets is derived and tested the model unifies two strands of the economic and financial literature one that builds on the hotelling model of pricing of exhaustible resources and the other that extends the capital asset pricing model of pricing risky assets tests of the predictions make use of a cost function that was estimated from a panel of small canadian copper mines young 1992 the authors tests fail to reject the theoretical restrictions that are implied by the hotelling capital asset pricing model

intergenerational resource rights efficiency and social optimality the discipline of economics is generally defined as the science of the allocation of scarce resources between competing social objectives given an initial distribution of resources between economic agents how would they behave so as to improve their welfare according to the pareto criterion the agents would exchange commodities until the opportunities for fruitful exchange were fully exhausted and no agent could be made better off without rendering at least one other agent worse off pareto efficiency is a powerful concept in microeconomic analysis provided that the initial distribution of property rights is equitable allocative efficiency gives rise to the best of all possible worlds acknowledging that the assumptions of perfect competition are often violated firms are monopolistic information is incomplete and externalities exist economists have argued for the modification of institutions so that economic reality will conform more closely to the assumptions of the model that yields such gratifying results but microeconomic theory has always maintained that allocative efficiency is in itself insufficient to maximize social welfare bator 1957 a social welfare function is required to discriminate a social optimum among the array of efficient allocations that correspond to alternative assignments of property rights though economists have posited alternative functional forms for the sake of pursuing conceptual arguments welfare functions have remained elusive constructs for well known theoretical and practical reasons consequently a sharp line of demarcation has been drawn between questions of efficiency the province of economics and equity the principal focus of ethical and political discourse in resource economics however the line demarcating efficiency and equity is often crossed the term optimal depletion appears regularly where only efficient depletion is meant while political debates about resource exploitation over time are laden with questions of the proper distribution of our natural patrimony between generations resource economists have predominantly espoused particular use rules that guarantee efficiency but overlook potential improvements in social welfare achievable through the reassignment of property rights across generations we document the evolution and current status of the misuse of the term optimal depletion in section ii we develop a simple two generation three period general equilibrium model in section iii to illustrate how alternative distributions of resource rights between generations relate to alternative pareto efficient solutions in section iv we demonstrate how different social welfare functions affect the optimal solution and associated assignment of resource rights between generations

what is ecological economics ecological economics addresses the relationships between ecosystems and economic systems in the broadest sense these relationships are the locus of many of our most pressing current problems i e sustainability acid rain global warming species extinction wealth distribution but they are not well covered by any existing discipline environmental and resource economics as it is currently practiced covers only the application of neoclassical economics to environmental and resource problems ecology as it is cur rently practiced sometimes deals with human impacts on ecosystems but the more common tendency is to stick to natural systems ecological economics aims to extend these modest areas of overlap it will include neoclassical environmental economics and ecological impact studies as sub sets but will also encourage new ways of thinking about the linkages between ecological and economic systems we have chosen the name ecological economics for this area of study because it implies a broad ecological interdisciplinary and holistic view of the problem of studying and managing our world the earth from space cover of the journal reflects this global holistic perspective we did not intend to imply with the ordering of the two words in the title that the journal is mainly an economics journal it is intended to be a new approach to both ecology and economics that recognizes the need to make economics more cognizant of ecological impacts and dependencies the need to make ecology more sensitive to economic forces incentives and constraints and the need to treat integrated economic ecologic systems with a common but diverse set of conceptual and analytical tools there was much discussion of other possible names such as economic ecology or ecology and economics or some conjoining of the two words that to me end up being confusing tongue twisters like ecolnomics or econology but ecological economics seemed to get closest to the mean ing we desired while still being evocative to the uninitiated