Substitution between biofuels and fossil fuels: Is there a green paradox?

Abstract

We show that (i) subsidies for renewable energy policies with the intention of encouraging substitution away from fossil fuels may accentuate climate change damages by hastening fossil fuel extraction, and that (ii) the opposite result holds under some specified conditions. We focus on the case of subsidies for renewable resources produced under increasing marginal costs, and assume that both the renewable resources and the fossil fuels are currently in use. Such subsidies have a direct effect and an indirect effect working in opposite directions. The direct effect is the reduction in demand for fossil fuels at any given price. The indirect effect is the reduction in the current equilibrium price for fossil fuels, which tends to increase the amount of fossil fuels demanded. Whether the sum of the two effects will actually result in an earlier or later date of exhaustion of the stock of fossil fuels depends on the curvature of the demand curve for energy and of the supply curve for the renewable substitute.

Introduction

The need to reduce CO₂ emissions to combat climate change is widely acknowledged. According to standard economic theory the first best measure would be a carbon tax, and, as [27] succinctly stated, “at any time, the optimal price of carbon emissions should be equal to the present value of all future climate costs caused by present emissions, often called the social cost of carbon.” In the real world, however, policy makers are faced with many constraints on the choice of policy instruments and their levels, and consequently first best policies cannot be implemented. Governments, in particular, face political opposition to the introduction of efficient carbon taxes.

A more politically acceptable time path of carbon taxes would be of the “ramp” variety: a government starts with a low tax rate, but commits to raise the tax to efficient levels in the future. As has been demonstrated (e.g. [41]), such time paths of carbon tax may induce profit-maximizing fossil resource owners to hasten the extraction of their resources, thus increasing carbon emissions in the near term.¹ Such an outcome has been termed a “Green Paradox” [42], [43]. Sinn's message is that in designing policies one must take into account supply responses by owners of fossil fuels.

The link between climate change and the behavior of firms extracting fossil-fuel resources was explored by [39], [40], [47], [28], [46]. Sinclair [39] was among the first economists to explicitly consider climate change policies that would influence the extraction path of fossil fuels, stressing that “the key decision of those lucky enough to own oil-wells is not so much how much to produce as when to extract it.” Strand [45] showed that a technological agreement that makes carbon redundant in the future may increase current emissions. As pointed out by [25], prior to 2008, there is little work making the link between climate policies and exhaustible resources when policies are non-optimal or international agreements are incomplete.² Recent dynamic models that depict the adverse response of resource extracting firms to anticipation of taxes or substitute production include [41], [42], [25], [11], [17], [12]. Hoel [25] assumes that carbon resources remain cheaper than the substitute and analyses the situation where different countries have climate policies of different ambition levels. He shows that, in the absence of an efficient global climate agreement, climate costs may increase as a consequence of improved technology of substitute production. Hoel [26], [27] uses a two-period model where firms invest in capacity for producing a substitute. A number of key parameters are considered in his model (e.g. a parameter to capture how rapidly extraction costs increase with increasing total extraction, and a parameter affecting the time profile of the returns to investments in the substitute). Whether an investment subsidy results in greater environmental damages (a Green Paradox) depends on the relationship among these parameters.

Gerlagh [18] considers a model where extraction cost is constant, and a backstop technology can produce an unlimited amount of a renewable substitute, at a constant cost per unit. He defines a Weak Green Paradox as an increase in the current emissions in response to an improvement in the backstop technology, and a Strong Green Paradox when the net present value of damages increases as a result of an improvement in the backstop technology. Ploeg and Withagen (2012, accepted in this issue) focus on the case where marginal extraction costs of the exhaustible resource depend on the existing stock. They assume that the substitute is available in unlimited supply at a constant marginal cost. After characterizing the social optimum, they turn to the case where first-best policies are not feasible, and show that the Green Paradox prevails if the cost of backstop decreases, provided that the backstop remains expensive such that the non-renewable resource stock is eventually exhausted. By contrast, if the backstop becomes so cheap that physical exhaustion will not take place, the Green Paradox no longer holds.

The bulk of the theoretical literature on substitute production assumes that a renewable substitute can be produced under constant marginal cost. In that setting, assuming also a constant cost of extraction of fossil fuels, the Green Paradox outcome is inevitable. The intuition behind this inevitability of the Green Paradox is that subsidies on the backstop technology leads to a lower peak price for fossil fuels, whose fixed stock must be exhausted before the renewable is produced. This implies that the whole time path of the fossil fuel price is shifted downward, resulting in greater consumption of fossil fuels earlier on.³ It is important to emphasize that in such models fuel consumption has two distinct phases: in the first phase, only the exhaustible resource is used, and in the second phase, only the renewable substitute is used. By construction, there is no phase where both resources are consumed simultaneously. The key assumption which is responsible for the absence of simultaneous use is that the renewable substitute is produced at constant unit cost.

In reality, renewable substitutes such as biofuels are produced under conditions of increasing marginal cost. As pointed out in Chakravorty et al. [7], increased use of biofuel may, by moving up the supply curve of land, increase the unit cost of the renewable resource. Using a dynamic empirical model firmly grounded on the Hotelling framework, they estimated the effect of biofuel mandates on food prices. They did not address the issue of the Green Paradox. With a few exceptions, the bulk of the existing literature on biofuel subsidies uses static analysis. Many authors have found, in the static context, mechanisms for increased carbon emissions (a Green Paradox outcome) with biofuel subsidies.⁴ It has also been pointed out that the production process of biofuels is not “green” because it involves the use of many inputs with high carbon contents. Moreover, because the first generation of biofuels displace land for food production it may increase food prices.

Our paper complements the existing literature with a dynamic mechanism. The contribution is a much richer understanding of the Green Paradox, delimiting cases when it occurs and when it does not, and shedding light on the inter-temporal consequences of biofuels subsidies.⁵ While models without a phase of simultaneous consumption are useful devices to illustrate principles, it is also important to consider situations where there is a phase in which exhaustible resources and renewable substitutes are simultaneously consumed in varying proportions. Such situations occur when the renewable substitute is produced under increasing marginal cost. This corresponds to the case of first generation biofuels based on conventional crops such as sugar cane, corn and vegetable oils (soy, canola, etc.). This is because the gradual expansion of biofuels output, at least for first generation biofuels, necessitates the increasing use of less productive land with inevitable diminishing returns.⁶

Using a framework where both types of fuels are simultaneously consumed in the first phase, we find conditions under which a Green Paradox outcome will not occur, as well as conditions under which it will occur. We focus on the effect of a biofuel subsidy on the time path of extraction of the fossil fuel resources. A striking result of our paper is that in the case of a linear demand for energy, together with (i) zero extraction cost for fossil fuels and (ii) an upward-sloping linear marginal cost of biofuels, a biofuel subsidy will have no effect on the amount of fossil fuels extracted at each point of time, even though the subsidy does result in a lowering of the price of both fuels at each point of time, and in a higher quantity of energy demanded at each point of time. Under the stated assumptions we show that the increase in quantity of fuel demanded is exactly matched by an increased output of biofuels, leaving the extraction rate unchanged. Thus, the time at which the stock of fossil fuels is exhausted is unchanged, irrespective of the rate of subsidy. This result stands in contrast to the inevitable Green Paradox in the model of Hoel [25] where the supply curve of the renewable resource is horizontal. We stress that the Green Paradox does not arise in our model in the presence of a linear and increasing marginal cost of the renewable substitute to fossil fuels.

A second and important result of our paper is that when the assumption of zero extraction cost of the fossil fuel is replaced by the assumption of a positive and constant marginal extraction cost, a biofuel subsidy will result in a longer time over which the fossil fuel stock is exhausted. In this second case the Green Paradox does not arise. Indeed, there is no paradox at all: the subsidy works as intended because it extends the extraction period.

A third setting to investigate the possibility of a Green Paradox is when the marginal cost of biofuels increases at an increasing, or a decreasing rate as biofuels supply increases. In particular, we consider the case where the marginal cost of biofuel production is strictly increasing and strictly concave. In this situation along the equilibrium price path, as the price of energy rises gradually along the optimal extraction path of fossil fuels, biofuel output will increase over time, but the rate of the supply increase (per dollar increase in energy price) is greater when the price is higher. Consequently, fossil fuel firms, in anticipation of this greater expansion of the substitute in the later stage, respond by increasing their extraction at an earlier date. In this case, a Green Paradox outcome results.

In summary there are multiple cases when the Green Paradox does, and does not hold. The purpose of our analysis is to provide necessary and sufficient conditions for the Green Paradox to hold. We decompose the effect of a biofuel subsidy and show, for the first time, a direct effect of the subsidy (which is “pro-Green”) and an indirect effect (which is “anti-Green”). Further, we show that a Green Paradox occurs if and only if the indirect effect outweights the direct effect. The analytical condition is general, but it can be hard to interpret without numerical examples. For this reason, we have supplied and commented on some simulation results.

Our model is consistent with the current state of play in terms of biofuel production. The main producing countries for transport biofuels are the U.S., Brazil and the EU. Brazil and the U.S. combined produced 55% and 35%, respectively, of the world's ethanol in 2009 while the EU produced 60% of the total biodiesel output. The main stimulus to the use of biofuels are policies that encourage the substitution from fossil fuels, especially for road transportation. Government mandates for blending biofuels into vehicle fuels have also been enacted in at least 17 countries, and many states and provinces within these countries. Typical mandates require blending 10% to 15% ethanol with gasoline or blending 2% to 5% biodiesel with diesel fuel. Recent targets have encouraged higher levels of biofuel use in various countries [48, pp. 15–16].

The range of policies that have stimulated biofuel demand by setting targets and blending quotas has been aided by supporting mechanisms, such as subsidies and tax exemptions. In the US, the total biofuels support encompasses the total value of all government supports to the biofuels industry, including consumption mandates, tax credits, import barriers, investment subsidies and general support to the sector such as public research investment. A report by Koplow [31, pp. 29, 31] for the Global Subsidies Initiative indicates that the total support estimates for the US alone, in 2008, was between $9.2 and 11.07 billion.

What do our results imply for biofuel subsidy policies? Our analysis indicates that the effects of proposed policies can only be gauged by using empirical models that are firmly grounded on dynamic theory that takes into account intertemporal behavior of resource extraction firms.