Green Paradox or Green Unorthodoxy? Robert D. Cairns. Department of Economics and Cireq. McGill University, Montreal. and. James L.

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1 Green Paradox or Green Unorthodoxy? by Robert D. Cairns Department of Economics and Cireq McGill University, Montreal and James L. Smith Edwin L. Cox School of Business Southern Methodist University, Dallas 7 November 2014 Abstract. The green paradox is an effect by which an increasing tax per unit on oil production, aimed at tracking damages from CO2 emissions, induces an increase in aggregate oil production and a decrease in price in the near term. A subsidiary prediction is that a decreasing royalty induces a decrease in oil production in the short term. The predictions are based on rational responses in a Hotelling exhaustible-resource model. The present paper simulates the decisions of a price-taking producer in response to a royalty of various shapes. In contrast to a Hotelling model, the technology of production is specified as involving sunk costs of exploration and development. A developed reserve yields output that is subject to natural decline at an exogenous rate. Given a price path, the time path of the royalty affects the level of development and initial production, but almost any form of royalty causes a reduction in initial production. Later investments in secondary recovery and total lifetime production are also affected. Any form of royalty induces large deadweight losses. Frequently, a royalty does not pass a cost-benefit test. In general, decisions are far more complicated, and results far subtler, than in Hotelling models. An attempt to understand some general-equilibrium effects explores a firm s incentives when there is a rate of price change consonant with predictions of the paradox. The green paradox does not arise at the firm level, at which decisions are made, and its predictions are inconsistent with other observed price effects. Key words: green paradox, natural decline, exploration and development, sunk cost, Hotelling model Thanks to Chris Barrington-Leigh and Jason Stevens for helpful comments. 1

2 Green Paradox or Green Unorthodoxy? 1. Introduction Damages from emissions of greenhouse gases, especially carbon dioxide, are expected to increase over time (to be a convex function of the total stock in the atmosphere). Nordhaus (2007) proposes an increasing tax on emissions as the preferred way to mitigate climate change. However, Sinclair (1992), Ulph and Ulph (1994) and Sinn (2008), among others, argue that an increasing tax on oil and other hydrocarbons, the main sources of emissions, may result in an increase in output and consumption in the near term, rather than a reduction. An increase in consumption would exacerbate the near-term damages. The projected increase in emissions resulting from a tax on their source is called the green paradox. 1 The green paradox is a prediction of the effects of a dynamic tax imposed on each unit of oil produced. It is based on an analysis of dynamic equilibrium in the oil market styled on a famous paper by Hotelling (1931). Hotelling s model is the foundation of orthodox thinking in nonrenewable-resource economics. In it, equilibrium prices and quantities are determined so as to equate discounted net price (price net of marginal cost) at each future time. The imposition of an increasing tax would reduce discounted net prices more in the future than in the present. Producers would be induced to minimize the effect of the tax by tilting the production profile toward the less taxed present. The new equilibrium path would exhibit a higher quantity produced at earlier dates and a lower price, as well as higher emissions. Although the change is a response by optimizing producers to the imposition of a tax, and for that reason unremarkable, the result was surprising to many and disconcerting to others because of the near-term increase in emissions when the objective of the tax was to reduce them. Some have proposed an initially high tax that would decrease through time as a possible means of shifting output and emissions toward the future. 1 Sinn reasons that a carbon tax is not the only policy that is subject to a green paradox. A subsidy to oil-conserving technologies or to greener (renewable, mainly) forms of energy, for example, would also reduce margins to oil producers in the future and a similar tendency to increase production in the present. 2

3 In the study of non-renewable resources, a unit tax is called a royalty. In the present paper, the paradox is considered to be the prediction of a tilt of output toward the present resulting from the imposition of an increasing royalty, as compared to the situation without a royalty. A subsidiary effect is the difference between increasing and decreasing royalties, namely, that an increasing royalty may increase production and current emissions and that a decreasing royalty may decrease them. A Hotelling model abstracts from producers individual decisions in deriving the sectorial equilibrium directly. In contrast, the present model stresses the incentives of a dynamic royalty for a producer s decisions in maximizing the net present value of an oil reserve. Technological and geological features of production are at the heart of the analysis. Decisions are simulated using a model developed by Smith (2012). A distinguishing feature of the model is a break from the stress placed on continuing decisions in Hotelling analyses of oil production. Oil occurs in separate, heterogeneous reserves. In order to discover reserves, exploration wells must be drilled. The model allows for a drilling a sequence of such wells until either a discovery is made or the effort is abandoned. If a reserve is discovered, a discrete, sunk development investment must be made to prepare it for production. If conditions warrant, a further investment in enhanced recovery may be sunk at an endogenous future date. Exploration, development and enhancement are all affected by policy. In dynamic simulations of the world oil market, McGlade (2013) and Bauer et al. (2013) find wide variations in the paths of price and output as a result of climate policy. Complexity of the oil market forces them (as well as other modelers) to make strong assumptions about the nature of the future equilibrium path. We follow them in assuming that the time path of the price is given to the producer. Each producer responds similarly, but the discreteness of decisions in partial equilibrium renders aggregation over reserves difficult in an extension to general equilibrium. Our proposals about the nature of the market equilibrium and the effects of the various forms of royalty are not definitive. Still, we argue that they are more representative than the proposals emanating from 3

4 Hotelling models. 2 Pindyck (2013) argues forcefully and authoritatively that the assumptions of all integrated-assessment (general-equilibrium) models are so flawed as to make them useless for policy analysis. Our findings complement his in indicating that the widespread assumption of Hotelling s rule is not a valid description of equilibrium for an oil producer or for the oil market. In basic Hotelling models, including several that have been used to illustrate the green paradox, the reserve is assumed to be known and to consist of a single aggregate. Accordingly, the first results presented herein are for a reserve that has already been discovered and is being developed. In contrast to the Hotelling models, development of (irreversible investment in) a reserve yields a production pattern through time that is constrained by natural features. The tilt of production follows a natural decline which is determined by the geology of the reserve and is not affected by the royalty. The effect of a royalty, increasing at rates up to five percent, is to reduce investment and hence initial output. In comparison, the rate of increase of damages due to emissions is predicted to be about 1.5 percent (Nordhaus 2007). The subsidiary prediction of the green paradox fares better: the incentive to avoid the tax leads producers to invest less if the royalty falls than if it rises. However, considerably more is ultimately produced from a given reserve if the royalty decreases, largely because of later investments in enhancing reserves. Further results incorporate effects of the royalty on exploration, including the number of exploratory wells drilled. 2. Development and Extraction According to Smith (2012), the level of development of the reserve, K, determines an initial level of output at time t = 0, q 0, that is proportional to the initial investment. Output q t, t > 0, is 2 Bauer et al. (2014) observe that a tax reduces the quasi-rents to oil-using investments. An important question is whether oil users are locked into decisions or have flexibility in adapting to a rise in the carbon price. A decrease in their prospective rents leads to a decrease in demand for oil-using investments and a persisting inward shift of the demand curve for oil. Like that of other supply-side models, our focus on oil producers decisions abstracts from this phenomenon, which also affects the green paradox. 4

5 subject to natural decline: the level of production decreases from q 0 at an exogenous rate that depends on the geology of the reserve. Production is abandoned when the avoidable cost (including the fixed cost), VC, exceeds the revenues from production, pq. 3 Reserves are assumed to be homogeneous. A widely observed regularity is that production is constrained by natural decline, so that in practice q at t = q 0 e. Whenever such a constraint binds a producer, it has a positive shadow value ν(t), notionally what the producer would be willing to pay to relax the constraint for an instant. Aggregating the petroleum reserves of Texas into a single entity subject to natural drive, Anderson, Kellogg and Salant (2014) argue that the shadow value of the constraint was positive throughout , a period of strong fluctuations in the market price. The reason for the positive shadow value, ν(t), is that, at the margin, the sunk investment in productive capacity (in development) must be paid back over the producing lifetime of the reserve. If PK is the value invested in development capital K at the initial date t = 0, a necessary condition of optimality is that P = T v( t) e rt dt (Cairns 2001). The shadow value is a component 0 of the price net of marginal cost. Under mild assumptions it is positive throughout the productive life [0,T] (cf. the findings of Anderson et al.). It can remain positive even if the rate of increase of the net price (price net of marginal cost) is greater than at the rate of interest, r, for short periods of time (Cairns and Davis 2007). 4 In addition to being recovered at the margin, the total investment cost PK must be recoverable from anticipated discounted net revenues, so that discounted net cash flow is non-negative. Moreover, net cash flow (revenue net of avoidable cost) must be non-negative at any time. 3 Although closing costs may be substantial (Muehlenbachs 2014), herein they are assumed to be zero. In a more complete model, they would constitute yet another form of lumpy, specific investment that would qualitatively distinguish the model from a Hotelling model. They would be covered as if by a sinking fund from the net revenues from production. Muehlbachs finds that they provide an incentive to postpone closure. 4 Occasionally reserves are shut in (q = 0 and thus v = 0 for a short time). Often wells are shut in for maintenance, for which there is some flexibility of timing. 5

6 There is also a possibility of investing in increasing or enhancing the recovery of the reserve at a future date chosen by the producer. For simplicity, the investment cost is assumed herein to be the same per initial daily barrel as for development investment. It increases the reserves that remain at the time of the investment by a factor λ > 1. The fundamental decisions by a producer pertain to sunk levels of development, initial and enhanced, that constrain production for significant periods of time. The model is a simplification of the problem faced by an oil producer. It is used to illustrate the effects of technology (irreversible investment) and geology (natural decline). The initial parameters assumed for the analysis are shown in Table 1. Table 1. Basic Parameters of the Model Variable Symbol Value Price p $100/bl Output q Capital Cost K $40,000 per initial daily barrel Avoidable Cost VC $20Q K Reserve R 100 mm bbl Interest rate r 8% Enhancement factor λ 2.5 Carbon content ½ tonne/bl The comparisons made in discussions of the green paradox, in the context of a producing firm s decisions, require that some features of exploitation vary as the dynamic royalty is varied. Because the predictions about effects on production current and cumulative and its timing are the essence of the paradox, these include initial extraction, the productive life of the reserve and the total, ultimate level of recovery. Since the firm is motivated by the present value of its rents, this value must be allowed to vary as well. The effects on timing are subtle and specific to a reserve. 6

7 Clearly, the properties of the initial reserve must be held fixed. To make valid comparisons, it is also necessary to hold a measure of inter-temporal tax effort fixed. The present value of the royalties is held fixed at fifty percent of the gross discounted social value (gross of the social cost or damages of emissions) available before imposition of the new royalty regime. The model is sketched in Appendix 1. A royalty may decrease fast enough to induce a firm to delay investment. The delay can be interpreted as consistent with the subsidiary prediction of the green paradox. But the delay affords reduced royalties over the producing lifetime. The first spreadsheet shows that the imposition of a royalty in any form has a strong effect on the output from the reserve. A pertinent comparison is between scenario 1 (no royalty) and scenario 2a (or 3a or 4a). When a constant royalty of 33.9% ($33.90/bl) is imposed, the initial development investment K decreases by twenty percent. As a result, initial production q 0 decreases from 7.5 (0.075 R) to 6.0 mm bbl. Moreover, investment in enhanced recovery is delayed from year 10 to year 16. As a result of these changes in investment and the consequent slowing of production, the life of the reserve is extended from 44 to 54 years. Both the present value of the producer s rents and the ultimate recovery are reduced. Scenarios 2 (b) and (c), 3 (b) and (c) and 4 (b) and (c) compare the results when there are increases or decreases of the royalty at rates of one, three and five percent per year, while still providing the same present value to the government. As compared to the case of no royalty (Scenario 1), in all cases but one (discussed below) a royalty results in a decrease in investment and thus in initial production, including in two cases of an increasing royalty 2(b) and 3(b). This prediction is contrary to the main prediction of the green paradox. With an increasing royalty there is higher initial investment than with a decreasing royalty. This comparison is consistent with the subsidiary prediction of the green paradox. However, only with a steep, five percent, rate of increase of the royalty in Scenario 4(b) does the initial production attain the initial level when there is no royalty. (An informal calculation based on a graph by Nordhaus (2007) suggests that damages are predicted to rise at approximately 1.5 percent. Nordhaus (2014) models damages as rising at three percent per year through A Pigovian tax would be expected to track the path of damages.) With the steep royalty, however, enhanced 7

8 recovery is never undertaken and ultimate recovery is reduced by more than half. More gently rising royalties in Scenarios 2(b) and 3(b) still induce a reduction in investment as compared to the benchmark of no-royalty. The timing of investment in enhanced recovery is also of interest for the green paradox. In general, any royalty induces a substantial delay of enhanced production, from about ten years to the mid-teens of years (or else it is never undertaken). The delay is longest for an increasing and least for a decreasing royalty. An increasing royalty, then, has a strongly negative effect on both timing and levels of investment in enhanced recovery. When the royalty is initially high but decreasing, the initial extraction rate is further reduced from the benchmark of no royalty. The early reduction is in line with the subsidiary prediction of the green paradox. Investment in enhanced recovery is delayed a few years. The life of the reserve is lengthened. Ultimate recovery is increased for the royalties declining at three and five percent as compared with the no-royalty scenario. The increase in recovery from a reserve of constant quality, with an increase in emissions in the long term, is subtler than a stock effect and is not foreseen in Hotelling models of the green paradox. There is a significantly higher loss of discounted rent to the producing company for both increasing and decreasing royalties as compared to a constant royalty or no royalty. (Recall that the present value of the government s revenue is held fixed.) The rising royalty induces the greatest decrease in a producer s returns. The reason is not a decrease in quality as the reserve is depleted, as in the stock effect, but of the timing and level of investment in enhanced recovery, if any. The present value of ultimate recovery measures the discounted physical volume of production, not its monetary value. It is a rough indicator of timing of production. All royalty scenarios have similar values of between 42 and 47, about ¾ of the level without a royalty. The cost per barrel of reduced recovery and per barrel equivalent in columns 16 and 17 suggest that a royalty, especially a rising royalty, is a costly way to reduce carbon emissions. According to column 17, the least costly royalty is the constant royalty. 8

9 The second spreadsheet shows the same types of comparison for reserves with higher development and variable costs. These reserves are close to being marginal. As such they have special relevance to those who model the stock effect in Hotelling models. To leave fifty percent of the social value in the government s hands, royalty rates must be lower. 5 For any type of royalty, initial production never attains that of the no-royalty scenario. As compared to a decreasing royalty, an increasing royalty exhibits higher initial production, lower ultimate recovery and a shorter life (with no enhanced recovery) than a decreasing royalty but a slightly higher net present value to the company. The third spreadsheet depicts a different comparison, with the total rent kept (close to) fixed over the different forms of royalty. There is greater investment when the royalty is increasing (at 3%), in keeping with the main prediction of the green paradox, but a substantially lower ultimate recovery. Two important features of oil markets are neglected in the results above. First, exploration is neglected. Second, price is assumed constant at $100/bl. These features are addressed in the fourth and fifth spreadsheets. Effects on timing and level of enhanced recovery are similar to those in the scenarios without exploration. 3. Exploration Exploration consists of drilling of a series of wells aimed at revealing the presence and size of a reserve (Smith 2012). Successful exploration provides a reserve of uncertain size that can be exploited at a profit. The size of such a reserve is assumed to take values of (i) 25 million barrels with probability 0.5, (ii) 100 mm bbl w.p. 0.35, or (iii) 750 mm bbl w.p If dry holes are drilled (w.p for the first hole), the probability that there is a reserve is revised using Bayes s rule. As more dry holes are drilled, the probability of a find decreases until ultimately the 5 For the case studied ($60,000 development cost per initial barrel of production and avoidable costs of $40 per unit plus two percent of development cost), a royalty of just over one quarter is used rather than nearly one third. 9

10 prospect is abandoned. Two scenarios are represented with different relative weights placed on prior geological knowledge and on experience from drilling. Because anticipated rents provide the firm s incentive to explore, the institution of a royalty reduces exploration. Although the effect is muted by the fact that exploration expenditure is a discrete variable, it can be discerned in the results. In Scenario A, a royalty with any tilt reduces the maximum number of wells a firm is willing to drill from four to three, except if price decreases at two percent, when there is no change. In Scenario B, in which more stress is placed on geological knowledge, the effect is more pronounced. The assumptions we have made imply that the rents anticipated by the firm are proportional to the initial investment, K, and hence of initial output q0 and the initial size of the discovery R. The effects on initial output and ultimate recovery, conditional on a discovery, are broadly similar to those reported above, without exploration. Conditional on a discovery, the decision of the firm is changed only to the extent that the expected size of the field is used rather than the 100 mm bbl assumed earlier. 4. Price The presentation herein is a faithful, if highly simplified, rendering of the decisions made by a typical oil producer with respect to a single reserve. The strength of the analysis is also its weakness. It is set in a partial equilibrium: the path of oil prices is given to the firm and is not endogenous to the model. Even if one maintains that all firms are price takers, as is customary in work on the paradox, a royalty imposed following an international climate agreement would change all firms choices and thereby the path of prices. A Hotelling model melds decisions and effects: sectorial results are derived from decisions applied to aggregated reserves rather than to distinct reserves. As a result, some properties of a competitive equilibrium can be characterized. Anderson et al. (2014) propose a bridge between conventional Hotelling models and technologically and geologically based models of individual reserves with natural decline (e.g. Adelman 1990). Anderson et al. examine price determination under the assumption that the resource (undeveloped prospects) and the reserve (developed 10

11 prospects) are each consolidated into single entities. The undeveloped resource and developed reserve are homogeneous. Output from the developed reserve is subject to natural, exponential decline. Exploration and development (which are combined into drilling) and production are continuous. The only cost is drilling cost, the aggregate of which over all producers is continuous through time. Even given their strong, simplifying assumptions, the authors analysis is much more complicated than a standard, Hotelling model as used to study the green paradox. Anderson et al. provide a qualitative equilibrium, using a phase diagram. With some further simplifying assumptions, they are able to simulate the response of a competitive industry to an unanticipated event; one can interpret the imposition of a royalty as such an event. Although the assumptions render their results only suggestive, the authors do find that a negative event leads to a reduction in drilling and, contrary to the green paradox, a decrease in aggregate output: Fewer new properties are developed and all producing properties are subject to the exogenous decline path. A model of price determination that would incorporate discrete exploration and development expenditures, avoidable fixed and variable costs of production, heterogeneity of reserves, a dynamic equilibrium among producers involving the choice of entry dates and levels according to physical properties of the reserves, would be extremely complicated. Results would be highly dependent on strong assumptions about properties of discovered and undiscovered reserves and on other simplifications. 6 To do justice to the myriad micro decisions that are made in the industry would require a simulation beyond the capabilities of the present model or of the most sophisticated integrated assessment models. In a Hotelling-style competitive model the green paradox predicts that when a rising royalty is introduced, in the short term more aggregate output is produced (output is tilted toward the present, producing more emissions) and that the price drops. Thereafter, the price is predicted to rise more quickly than in the original equilibrium. Other students of climatic change also presume that the price of oil will increase through time. The reason that they give is a resort to costlier sources of supply through the stock effect. The two effects are not the same. Empirically, then, the green paradox would be hard to discern using data on price. 6 Compare Pindyck s (2013) dismissal of integrated assessment models of climatic change. 11

12 Although the equilibrium price changes cannot be obtained, changes in price can be imposed as parameters and their effects on a price-taking producer s decisions can be simulated. The changes are set at 1% intervals between -2% and 2% per year. The results of spreadsheet 4 remain comparable to those from the simulations with a constant price and without exploration, in spreadsheets 1, 2 and 3: A royalty increasing at three percent results in a higher initial production than one falling at three percent. It also results in a lower ultimate recovery and a shorter reserve life. A falling royalty leads to greater ultimate output than a rising royalty. Total rent is higher for the increasing royalty. 7 Since price is given, the simulations compare situations in which aggregate supply from other sources is assumed not to change as the royalty is varied. Even under such a restrictive and unrealistic assumption, the exercise points out some of the complexity of the effects of the tax. Output for the firm at any time is reduced under any royalty; thus, emissions and their present value are unambiguously reduced. A further key effect is on the investment in enhanced recovery. The rising royalty has a greater disincentive to enhanced recovery, which is a lowmargin investment. While enhanced recovery produces the same emissions per unit output, it is obtained in the future and is heavily discounted. Because of the timing of the reductions, the increasing royalty has lower costs per unit reduction in emissions than the decreasing royalty. It also provides higher discounted rent to the firm: Given predictions of rising damages, an increasing royalty is closer to the Pigovian ideal. Given a price path, a firm prefers the increasing royalty to a decreasing royalty. These results are for firms contemplating investment in exploration and development at the time of the introduction of the royalty. Contrary to the Hotelling model and the green paradox, output by firms that are currently exploiting their reserves is not affected: their levels of output are fixed by earlier choices of the level of development. The decision about whether and when to invest in enhanced recovery in the future, however, is affected. Imposition of a royalty discourages such investment, more so for an increasing royalty. 7 The higher rent contrasts with the lower rent for an increasing royalty noted in Section 2, when price is constant at $100/bl. There is a reversal in the ratio of the two rents close to the scenario for a constant price. For an increasing or decreasing price, the increasing royalty leaves a greater rent to the firm. 12

13 Given these partial-equilibrium results, the presumed drop in price of the green paradox in general equilibrium has to be explained in some way other than through the extrapolation of decisions by price-taking firms in partial equilibrium. Since firms cut back on investment with the introduction of a royalty, realization of the green paradox (an initial fall in price and rise in aggregate output) requires that other firms hasten their investments in current development and perhaps in current exploration. The effect of a rush to bring already discovered reserves to earlier development would have to overcome the depressing effects of the royalty on investments by firms that were already entering in the original equilibrium (with no royalty). An early decrease in price is a further disincentive to exploration and development. Suppose, however, that, in accordance with the green paradox, there is new investment in development that causes a fall in the oil price. The new investment requires renting additional rigs. Available, excess capacity tends to be older rigs that are less efficient. The supposition implies, then, that drilling costs must rise as the price of oil falls. Anderson, Kellogg and Salant (2014: 14-15), however, document that rental rates for rigs are strongly positively correlated with the price of oil, so that there tend to be sharp decreases in rental rates for drilling rigs when the price of oil falls. Ceteris paribus, an increase in the rental costs of rigs reduces net present value and discourages development. Expanding exploration to find new reserves also requires renting scarce drilling capacity. Successes at marginal prospects decline because of the use of older, less effective rigs. This effect is not explicitly modeled herein but is implicit in the simulations of exploration with higher costs as well as development with higher investment costs. Scenario 6 in spreadsheet 5 is calculated using price-change parameters with the qualitative properties predicted by the green paradox. It examines regimes with constant, increasing and decreasing royalties. The benchmark rate of increase of the oil price, assumed for the scenarios with no royalty and a constant royalty (36.1%), is 1.5% per year. According to the green paradox an increasing royalty causes the initial price to be lower and initial output to be higher than when there is no royalty; over time the equilibrium price increases more quickly. In keeping with this prediction, a 3% increase in the royalty is assumed to induce a rate of price rise of 2%. The opposite holds for a royalty decreasing at 3%: output increases early 13

14 on and price rises faster, at an assumed rate of 1%. The response of the firm is shown after column 5. For comparability of tax effort (meaning that the present values of the government s receipts are approximately equal) the increasing royalty must start lower and the decreasing royalty higher. As in the other scenarios, the number of drilling attempts is lower than when there is no royalty and the initial rate of extraction (level of development) is lower. The oil company prefers the rising royalty. Scenarios 6 and 7 attempt to hold constant some variables in order to make valid comparisons, but there are several divergences in rents and consequently in incentives, in damages, etc. They display some instances of a strong green paradox, defined as a greater present value of emissions with a royalty than without. These strongly paradoxical effects are concentrated at the low rate of discount, viz. the 1.4% recommended in the Stern (2006) Review and for the decreasing royalty. Paradoxically, the strong paradox arises in the discounting regime that would be preferred by environmentalists. The reason is that there is greater recovery under the decreasing royalty, almost as much as with no royalty but well into the future, which, at 1.4%, is only lightly discounted. Effects of an enhanced recovery remain qualitatively the same: any royalty induces a delay in and a reduction in investment. Both are greatest for an increasing royalty. A general feature of a royalty is that it produces high deadweight losses. Only for a few scenarios, namely, for a rising royalty with damages evaluated at low discount rates, does any policy pass a cost-benefit test. The decreasing and constant royalties do not pass a cost-benefit test in any instance. 5. Conclusion Contrary to the underlying vision of the green paradox, the tilt of output from an oil reservoir (and hence in the aggregate) does not depend on whether there is a royalty or whether the royalty itself has an increasing, constant or decreasing tilt. Instead, the tilt of production is exogenous in all cases: it is equal to the rate of natural decline of the reserve. 14

15 Also contrary to the vision of the green paradox is the fact that exhaustibility is not the only constraint facing an oil producer. Producers cannot increase their production at will. They produce at a capacity determined by investment and by geology. An increase in production requires a further investment. Producers evaluate how much investment to sink and when to make it. The incremental, discounted net cash flows must pay back that investment. Even though marginal considerations play a role in decisions, a purely marginal analysis is an oversimplification. Royalties reduce net cash flows. A royalty tends to lead to a reduction in the level of development, and hence of production throughout the reserve s lifetime, because the present value of the net cash flow is reduced. Any form of royalty has qualitatively similar, strong effects on extraction and timing of extraction, namely, lower investment and initial production, delays and reductions in enhanced recovery, reduced rents, and, in most cases but with some exceptions, reduced discounted carbon damages and reduced overall recovery. Changes in the tilt of the royalty increasing or decreasing induce less striking but still notable variations in these effects. The incentive to reduce initial investment tends to be stronger for a decreasing royalty than an increasing royalty. On the other hand, an increasing royalty discourages and may preclude investment in enhanced production, thereby reducing the total level of output from the reserve as well as the length of production. For predictions of the green paradox to be realized, the depressing effect of the royalty on sunk investments in exploration and development would have to be overcome through earlier development of known but undeveloped reserves. Ultimate production from all reserves would be unambiguously lower. Even though different potential price paths can be simulated, with some guidance from the predictions of the paradox, the present analysis is limited to a partial equilibrium of a single reserve. The single reserve is the locus of decisions for the production of oil, the decisions that are supposed to give rise to the paradox. The sectorial equilibrium involves the outcomes of decisions at tens of thousands of heterogeneous developed and undeveloped properties and undiscovered resources. There is no set of parameters among the many background variables that can be held fixed in order to make all scenarios comparable. Simulating the equilibrium would involve heroic assumptions about 15

16 governmental decisions and about the properties of undiscovered reserves. (Furthermore, if the sectorial analysis were to be relevant to policy rather than a theoretic exercise, it would also have to include behavioral assumptions about the prevalent state-owned oil companies, whose motivations are subtler than the maximization of discounted profit and likely changing over time.) It is clear from the analysis that the common simplifying assumptions, such as that marginal costs are equalized across reserves, that all discovered reserves are in production and that all resources can be aggregated into discovered and undiscovered reserves, can be expected to mislead. Hotelling models are oversimplified for policy applications. There is inertia in the production from currently active reserves and a reduction in new investment and production from reserves that enter in the equilibrium without a royalty. Can hastening entry of other reserves overcome this reduction? Are the firms willing to make these investments? Are firms prepared to ramp up exploration to realize the predictions of the green paradox over the near future? Assumptions, simulations and predictions can always be improved. The results are not definitive but they do pinpoint what needs to be explained about effects of carbon taxes on emissions. Additional scenarios involving an exogenous price path may be the indicated next series of steps. There appears to be little reason to believe that the green paradox would be the outcome of a tax on carbon producers. A strong objection to the royalty, unobserved in analyses of the green paradox, is the high cost, in terms of natural resources, of the environmental policy. The deadweight losses of the instrument render it in many cases a socially inefficient way to reduce carbon emissions. Among royalties, the best bet for society may be the rising royalty, in terms of both the social efficiency in the use of a scarce resource and for reasonably accounting for the negative effects of carbon emissions on the producers side of the market. 16

17 Appendix. Simplified Symbolic Representation of the Model As an indication of the complexity of the model as compared to the Hotelling model, this appendix indicates the main considerations of the model, abstracting from the possibility of enhanced recovery. The following assumptions are maintained in the model, for time t > 0: 1. The interest rate is denoted by r. 2. Price is denoted by p(t) and rises or falls at rate π. 3. Output is denoted by q(t) in barrels (bbl) and falls through time at rate a. 4. The royalty is denoted by τ(t) and rises or falls at rate ρ. 5. The damages of carbon emissions are denoted by d(t) per tonne and rise at rate γ. Carbon content is ½ tonne per barrel. 6. The capital cost is sunk and is denoted by K = 40,000 q(0). 7. The avoidable cost of output is denoted by c(t) = 20q(t) K = 20q(t) + 800q(0), comprising fixed and variable components. 8. Exploration expenditures are denoted by E 0. In scenarios where exploration is considered, the realized exploration expenditure depends on the number of holes drilled until exploration is abandoned without success or a reserve, R, which may take one of three values, is discovered. Given (expected) exploration investment of E 0 and development investment K > 0, the (expected) net present value to the firm is given by T V ( K, T ) = E K + { p( t) q( t) [20q( t) + 800q(0)] )} t= 1 rt t ( t) q( t e. The net present value, V(K,T), depends on the level of exploration and the success of exploration at stated probabilities. If exploration is unsuccessful, development does not take place. Given discovery of a reserve, the expression for V(K,T) is simplified and maximized with respect to K (or to q(0)) and T, subject to the resource constraint that q ( t) R. Carbon damages are given by D T rt ( K, T ) = d( t) q( t) e. t= 1 When the royalty is positive (when τ(0) > 0), the present value of royalties obtained by the government is given by Θ T rt ( K, T ) = t ( t) q( t) e. t= 1 The value Θ(K,T) is held fixed across different values of τ(0) and ρ for comparisons of the effects of increasing, decreasing and constant royalties. 17

18 The imposition of a royalty changes the willingness of the firm to engage in exploration and causes a change in K and hence q(0) for discovered reserves. If there is a development investment (K > 0), the imposition of a royalty induces a change from the neutral value V(K,T) (with τ(0) = 0) to V(K,T ) + Θ(K,T ). The change in net social value is denoted by Γ = V(K,T ) + Θ(K,T ) V(K,T) and the change in the damages is given by Δ = D(K,T ) D(K,T). The cost per unit change in damages is given by Γ/Δ. In addition, the firm may invest in enhanced recovery. The timing and cost of that investment are endogenous to the solution and increase the available reserve at that time by the factor λ > 1. 18

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