A qualitative characterization of the competitive nonrenewable resource extracting firm

Using variational differential equations, a systematic qualitative analysis is carried out for the competitive nonrenewable resource extracting firm. The parameters of interest are the output price, variable input price, discount rate, lease length, initial resource stock, and various tax rates. The effects of changes in these parameters on the entire optimal time paths of the current shadow value of the stock, the resource stock, and the extraction rate are characterized in the perturbed phase plane.     

Oil Exploration under Climate Treaties

In this paper we focus on how an international climate treaty will influence the exploration of oil in non-OPEC countries. We present a numerical intertemporal global equilibrium model for the fossil fuel markets. The international oil market is modelled with a cartel (OPEC) and a competitive fringe on the supply side, following a Nash–Cournot approach. An initial resource base for oil is given in the non-OPEC region. However, the resource base changes over time due to depletion, exploration, and discovery. When studying the effects of different climate treaties on oil exploration, two contrasting incentives apply. If an international carbon tax is introduced, the producer price of oil will drop compared to the reference case. This gives an incentive to reduce oil production and exploration. However, the oil price may increase less rapidly over time, which gives an incentive to expedite production and exploration. In fact, in the case of a rising carbon tax we find the last incentive to be the strongest, which means that an international climate treaty may increase oil exploration in non-OPEC countries for the coming decades and reduce OPEC's market share.     

Learning abatement costs: On the dynamics of the optimal regulation of experience goods

We study the introduction of new technologies when their costs are subject to idiosyncratic uncertainty and can only be fully learned through individual experience. We set up a dynamic model of clean experience goods that replace old polluting consumption options and show how optimal regulation evolves over time. In our base setting where social and private learning incentives coincide, the optimal tax on the polluting consumption is increasing over time. We show, however, that if social and private learning incentives diverge because the private discount rate exceeds the social discount rate, it may be optimal to temporarily increase the tax rate beyond net marginal external damages to induce more learning before reducing the tax rate to the steady state level. Alternatively, one could complement the tax with subsidies for first-time users which can be phased out over time. Similar results apply if consumers have biased expectations. We therefore give a rationale for introductory subsidies on new, clean technologies and non-monotonic tax paths from a perspective of consumer learning.     

A model of mining and exploring for exhaustible resources

A model of extractive industries is developed, in which firms select the time-paths of exploration and extraction that maximize their present values. Two externalities unique to the exploration process are found to distort industry behavior. Industry behavior is simulated under conditions of competition, monopoly, and central management, and the effects of percentage depletion allowances and changes in the discount rate are observed. Monopolists overconserve the resource and hold excess reserves; competitors who enter mineral lands freely tend to overexplore and overextract; percentage depletion allowances decrease reserves; and higher discount rates reduce extraction in the long run.     

The taxation of nonreplenishable natural resources revisited

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.     

Valuation of natural capital under uncertain substitutability

Natural capital is complex to value notably because of the high uncertainties surrounding the substitutability of its future ecosystem services. We examine a Lucas economy in which a consumption good is produced by combining different inputs, one of them being an ecosystem service that is partially substitutable with other inputs. The growth rate of these inputs and the elasticity of substitution evolve in a stochastic way. We characterize the socially efficient ecological discount rates that should be used to value future ecosystem services at different time horizons. We show that the inverse of the elasticity of substitution can be interpreted as the CCAPM beta of natural capital. We also show that any increase in risk of this beta reduces the ecological discount rate. If our collective beliefs about the elasticity of substitution of ecosystem services are Gaussian, the ecological discount rates go to minus infinity for finite maturities. In that case, a marginal increase in natural capital has an infinite value. We provide a realistic calibration of the model that is coherent with observed asset prices by using the model of extreme events of Barro (2006). The bliss maturity for infinite discount factors is less than 100 years in this calibration.     

Attitudes towards risk and the optimal exploitation of an exhaustible resource

The exploitation of a nonrenewable natural resource, such as petroleum or mineral ores, is analyzed in a stochastic framework with price uncertainty. The market setting may be either monopolistic or competitive. We demonstrate that the rate of extraction varies directly with the resource owner's willingness to accept risk. Rish-preferring owners use the resource more rapidly than risk-neutral owners, who in turn deplete the resource more rapidly than risk-averse owners. It is also seen that the usual practice of increasing the discount rate to account for risk induces a more rapid rate of resource use, when in fact a slower rate of depletion is desired.     

Price uncertainty and the exhaustive firm

In the presence of a resource constraint the risk-averse exhaustive firm reacts to price uncertainty in a manner different than its competitive counterpart. In particular: (i) some results are independent of attitudes toward risk; (ii) comparative statics results differ from the no resource constraint case; and (iii) results depend upon the relative magnitudes of the discount rate and quasi-fixed costs. An assumption crucial to the relevance of risk-aversion in an intertemporal setting is the presence of imperfections in capital markets (i.e., the absence of complete contingent commodity markets).     

Discounting and relative consumption

We analyze optimal social discount rates when people derive utility from relative consumption, i.e. their own consumption level relative to the consumption level of others. We compare the social, private, and conventional Ramsey rates. Assuming a positive growth rate, we find that (1) the social discount rate exceeds the private discount rate if the importance of relative consumption increases with consumption, and that (2) the social discount rate is lower than the Ramsey rate given quasi-concavity in own and others’ consumption and risk aversion with respect to others’ consumption. Numerical calculations demonstrate that the latter difference may be substantial and have important implications for long run environmental issues such as global warming.     

Giving green to get green? Incentives and consumer adoption of hybrid vehicle technology

Federal, state, and local governments use a variety of incentives to induce consumer adoption of hybrid-electric vehicles. We study the relative efficacy of state sales tax waivers, income tax credits, and non-tax incentives and find that the type of tax incentive offered is as important as the generosity of the incentive. Conditional on value, sales tax waivers are associated with more than a ten-fold increase in hybrid sales relative to income tax credits. In addition, we examine how adoption varies with fuel prices. Rising gasoline prices are associated with greater hybrid vehicle sales, but this effect operates almost entirely through high fuel-economy vehicles. By comparing consumer response to sales tax waivers and estimated future fuel savings, we estimate an implicit discount rate of 14.6% on future fuel savings.     

Complementarity,impatience, and the resilience of natural-resource-dependent economies

We study how society's preferences affect the resilience of economies that depend on more than one type of natural resource. In particular, we analyze whether the degree of complementarity of natural resources in consumer preferences may give rise to multiple steady states and path dependence even when resources are managed optimally. We find that, for a given social discount rate, society tends to be less willing to buffer exogenous shocks if resource good are complements in consumption than if they are substitutes. The stronger the complementarity between the various types of natural resources, the less resilient the economy is, and even more so the higher is the social discount rate.     

Discounting for personal and social payments: Patience for others,impatience for ourselves

The market rate of return on private investment is often used as the discount rate when conducting cost-benefit analysis (CBA) of public projects. I argue that the decision to invest pits current consumption against future consumption, both of which accumulate to the private decision maker. Public projects, on the other hand, provide benefits that accrue to society in general. To examine the appropriateness of discount rates based on returns to private investment, this paper considers lab experiments designed to test whether individuals discount personal and social benefits at different rates. Personal benefits are captured through personal monetary payments, while social benefits are captured through anonymous donations to charitable organizations. I jointly elicit time and risk preferences and find that subjects discount charitable contributions at significantly lower rates than personal payments.     

Discounting for personal and social payments: Patience for others,impatience for ourselves

The market rate of return on private investment is often used as the discount rate when conducting cost-benefit analysis (CBA) of public projects. I argue that the decision to invest pits current consumption against future consumption, both of which accumulate to the private decision maker. Public projects, on the other hand, provide benefits that accrue to society in general. To examine the appropriateness of discount rates based on returns to private investment, this paper considers lab experiments designed to test whether individuals discount personal and social benefits at different rates. Personal benefits are captured through personal monetary payments, while social benefits are captured through anonymous donations to charitable organizations. I jointly elicit time and risk preferences and find that subjects discount charitable contributions at significantly lower rates than personal payments.     

Defining trade-offs among conservation, profitability, and food security in the California current bottom-trawl fishery

Although it is recognized that marine wild-capture fisheries are an important source of food for much of the world, the cost of sustainable capture fisheries to species diversity is uncertain, and it is often questioned whether industrial fisheries can be managed sustainably. We evaluated the trade-off among sustainable food production, profitability, and conservation objectives in the groundfish bottom-trawl fishery off the U.S. West Coast, where depletion (i.e., reduction in abundance) of six rockfish species (Sebastes) is of particular concern. Trade-offs are inherent in this multispecies fishery because there is limited capacity to target species individually. From population models and catch of 34 stocks of bottom fish, we calculated the relation between harvest rate, long-term yield (i.e., total weight of fish caught), profit, and depletion of each species. In our models, annual ecosystem-wide yield from all 34 stocks was maximized with an overall 5.4% harvest rate, but profit was maximized at a 2.8% harvest rate. When we reduced harvest rates to the level (2.2% harvest rate) at which no stocks collapsed (<10% of unfished levels), biomass harvested was 76% of the maximum sustainable yield and profit 89% of maximum. A harvest rate under which no stocks fell below the biomass that produced maximum sustainable yield (1% harvest rate), resulted in 45% of potential yield and 67% of potential profit. Major reductions in catch in the late 1990s led to increase in the biomass of the most depleted stocks, but this rebuilding resulted in the loss of >30% of total sustainable yield, whereas yield lost from stock depletion was 3% of total sustainable yield. There are clear conservation benefits to lower harvest rates, but avoiding overfishing of all stocks in a multispecies fishery carries a substantial cost in terms of lost yield and profit.     

Minimax regret discounting

The paper considers an environmental policy decision in which the appropriate approach for discounting future costs and benefits is unknown. Uncertainty about the discount rate is formulated as a decision under Knightian uncertainty. To solve this, we employ minimax regret, a decision criterion that is much less conservative then the related criterion maximin—in particular, it can be shown to implement a “proportional response” in that it equally balances concern about the mistake of doing too little with that of doing too much. Despite the criterion's balanced nature, the minimax regret solution mimics a policy that maximizes the present discounted value of future net benefits with an effective (certainty-equivalent) discount rate that declines over time to the lowest possible rate. In addition to reinforcing Weitzman's (1998) original limiting result, the approach generates concrete policy advice when decision makers are unable to specify a prior over possible discount rates. We apply it to the Stern–Nordhaus discounting debate and find that the effective discount rate converges to the Stern rate in just under 200 years.     

Minimax regret discounting

The paper considers an environmental policy decision in which the appropriate approach for discounting future costs and benefits is unknown. Uncertainty about the discount rate is formulated as a decision under Knightian uncertainty. To solve this, we employ minimax regret, a decision criterion that is much less conservative then the related criterion maximin—in particular, it can be shown to implement a “proportional response” in that it equally balances concern about the mistake of doing too little with that of doing too much. Despite the criterion's balanced nature, the minimax regret solution mimics a policy that maximizes the present discounted value of future net benefits with an effective (certainty-equivalent) discount rate that declines over time to the lowest possible rate. In addition to reinforcing Weitzman's (1998) original limiting result, the approach generates concrete policy advice when decision makers are unable to specify a prior over possible discount rates. We apply it to the Stern–Nordhaus discounting debate and find that the effective discount rate converges to the Stern rate in just under 200 years.     

A note on environmental risk and the rate of discount

This paper examines the use of risk-adjusted discount rates to evaluate future environmental risks. It is determined that the risk-adjusted discount rate should be lower—not higher—than the risk-free rate if evaluation of future environmental risks is to point toward optimality.     

Discounting under uncertainty: Disentangling the Weitzman and the Gollier effect

The uncertainty of future economic development affects the term structure of discount rates and, thus, the intertemporal weights that are to be used in cost benefit analysis. The U.K. and France have recently adopted a falling term structure to incorporate uncertainty and the U.S. is considering a similar step. A series of publications discusses the following concern: a seemingly analogous argument used to justify falling discount rates can also justify increasing discount rates. We show that increasing and decreasing discount rates mean different things, can coexist, are created by different channels through which risk affects evaluation, and have the same qualitative effect of making long-term payoffs more attractive.     

A note on the effect of tax brackets on non-renewable resource extraction

Tax brackets are a common feature of non-renewable resource taxes. Although the introduction of brackets would seem to be an innocuous way of approximating a non-linear tax system, the dynamic effects are surprising. This paper shows that the presence of tax brackets in both a severance tax system and a profits tax system can induce the extractive firm to depart from the well-known monotonically declining extraction profile and to choose instead a profile which has constant extraction rates over some interval of time.     

Discounting,inequality and economic convergence

The aim of this paper is to examine the impact of inequalities and economic convergence on the efficient discount rate when international credit and risk-sharing markets are inefficient. We consider an economy in which initial consumption levels and growth expectations are heterogeneous. In the benchmark case in which relative inequalities are permanent and relative risk aversion is constant, inequalities do not affect the discount rate. We derive necessary and sufficient conditions under which permanent inequalities reduce the discount rate. We also show that the anticipation of economic convergence raises the efficient discount rate when relative prudence is larger than unity.