Carbon Offset Provision with Guilt-Ridden Consumers

Transcription

1 University of Toronto From the SelectedWorks of Joshua S Gans March, 2009 Carbon Offset Provision with Guilt-Ridden Consumers Joshua S Gans Vivienne Groves Available at:

2 Carbon Offset Provision with Guilt-Ridden Consumers * by Joshua S. Gans and Vivienne S. Groves University of Melbourne First Version: March 2007 This Version: 30 th March, 2009 Consumers who wish to mitigate their emissions can purchase carbon offsets. In a model where consumer guilt drives the demand for such offsets, it is shown that offsets are complements to dirty consumption and the introduction of an offset market can cause dirty consumption to increase. Net emissions are shown generally to decline, however, regardless of whether electricity prices are regulated or chosen strategically or whether offset prices are exogenously or endogenously determined. We find two exceptions to this rule. It is demonstrated, that when there is no latent demand for offsets, the introduction of offsets can potentially cause a rise in net emissions when dirty producers have market power. Similarly, emissions can rise if dirty producers can engage in pre-emptive strategic commitments to deter investment in offset markets. Journal of Economic Literature Classification Numbers: L94, Q42, Q58. Keywords: carbon offsets, guilt, greenhouse gases, electricity markets, strategic behavior. * Thanks to Stephen King, Michael Ryall, two anonymous referees and a co-editor for helpful comments. Responsibility for all errors and omissions are our own. The latest version of this paper is available at: All correspondence to: J.Gans@unimelb.edu.au.

3 1. Introduction Carbon offsets allow individuals, households and firms to mitigate their carbon emissions. A common use for such offsets is to invest in trees and forests that remove carbon from the atmosphere. 1 Another example is green power. In this situation, consumers pay a premium to subsidize investment in clean electricity generation (usually, wind or solar power). At a first pass, such offsets would seemingly do no harm. Households purchasing them would receive a warm glow or reduction in guilt, 2 and emissions would be reduced and welfare increased. However, there are suspicions that offsets may not actually be inconsequential. 3 Specifically, concerns were raised when it was revealed that environmentalist and former US Vice President, Al Gore s household consumed 20 times more electricity than the average in the US. Gore countered that the quantity was not an issue as he purchased offsets to reduce his carbon footprint to zero. But still, there were concerns about whether the presence of an offset market might actually increase electricity consumption (notably, from dirty sources) due to their impact on electricity market structure. 4 1 Kotchen (2008) documents 97 nonprofit and commercial organizations offering offsets of various types. He notes that the market size has increased by more than 200 percent since 2002, totaling around $330m spent on offsets in However, the total amount of emissions reduced by such schemes is a small fraction of the level of emissions being generated. In addition, many airlines now offer offset options for travelers. These are, however, part of a bundled strategy. In this paper our focus is on unbundled or independent offset options. 2 Both intuitively and empirically, the idea that guilt might drive consumer purchases is an appealing one. Kahn (2007) describes how identification as a green consumer alters behavior, although the mechanism might be more complex than simply being driven by guilt. Andreoni (1990) discusses impure altruism in which individuals are motivated to contribute to public goods not only because they are altruistic, but also because they benefit from a warm glow the private benefit an individual receives from making a personal contribution to a public good. In this paper, it is assumed that each consumer s contribution to carbon emissions is negligible; consumers are motivated to reduce their electricity consumption only by guilt and expenditure on electricity consumption. Hence, this model is an application of Andreoni s model of purely egoistic individuals and guilt can be thought of as a negative warm glow. 3 See, for example, Tyler Cowen or The Economist blog. 4 The set of concerns here is distinct from other issues raised about voluntary offsets. For instance, we do not attempt to answer questions such as: do purchased offsets actually generate the promised reductions in emissions?

4 3 This paper provides a formal treatment to evaluate such claims. The aim is to study a number of market structures to determine whether the claim that the introduction of offset markets can increase carbon dioxide emissions is indeed true. Key to driving the demand for offset purchases literally a voluntary contribution to a global public good is the presence of guilt in the utility function of consumers; specifically, with reference to greenhouse gas emissions. However, as we will demonstrate, the presence of offset markets can impact on the optimal set of strategies for providers of dirty products if they possess market power. Hence, throughout much of the paper, we consider a monopolist provider of such products in order to highlight this. The paper proceeds as follows. In Section 2, we introduce a model of electricity markets in which consumers are able to mitigate their guilt from contributing to global warming by purchasing carbon offsets, and the price of electricity is determined exogenously. We begin with the case where offset purchases are used to fund activities (such as carbon sequestration) that are unrelated to the local electricity industry. At a certain level of electricity consumption individuals will find it more beneficial to purchase offsets than to incur additional guilt. So, as the price of offsets fall consumers will purchase more offsets. The first result from this analysis is that purchases of offsets and consumption of electricity are complements. The lower the price of offsets, the more offsets are consumed; this stimulates consumption of electricity as consumers net emissions and hence, guilt falls. We then endogenize the price of electricity examining what happens when electricity is produced by a monopolist. It is shown that the introduction of offsets causes the dirty producer to expand output (as offsets are a complement). Nonetheless, net emissions are generally reduced Are offsets provided by firms for their own emissions not themselves being reversed by higher emissions by the firm in other product markets? And is the implied price of carbon too low? See Kotchen (2008) for a discussion of these.

5 4 even though electricity consumption is higher. We demonstrate, however, that it is possible that allowing consumers to purchase offsets could actually lead to higher net emissions. The critical driver of this possibility is a situation where, prior to becoming available, there is no latent demand for offsets; that is, consumers would not purchase offsets at their current consumption levels. The presence of a sufficiently low cost offset market, however, can allow a dirty producer with market power to take advantage of it by lowering prices of electricity and stimulating demand to a point where consumers are willing to purchase offsets. This higher consumption in turn fuels offset trading to the detriment of causing higher net emissions but also higher profits for the electricity provider, who takes advantage of consumers outward shift in demand resulting from the introduction of an offset market. Section 3 then turns to consider purchases of offsets related to electricity generation: namely, investment in clean generating capacity such as wind or solar power. Regardless of whether clean generation is supplied in a strategic or non-strategic manner, it is demonstrated that the presence of an offset market reduces net emissions. This is despite the fact that competition reduces electricity prices and causes an increase in the consumption of electricity. Net emissions fall because the volume of dirty electricity consumed falls. That said, we also examine the possibility of strategic commitment by dirty electricity generators. It is shown that dirty generators can squeeze the demand for offsets and competition from clean generators by pre-emptively committing to a high quantity. By increasing output, the relative premium consumers pay to purchase green power over generic electricity rises, causing fewer offsets to be sold as a result of this pre-emptive action. This is not the first paper to model individuals who internalize some of their social negative externalities. Andreoni (1990) deals with warm glow effects. His applications are

6 5 focused on charitable giving and do not involve the introduction of green or similar products per se. More recently, Benabou and Tirole (2006) have examined various means by which socially oriented behavior can emerge. In a paper written contemporaneously with this one, Kotchen (2009) studies markets for environmental offsets in detail. To understand the demand for offsets, he uses a similar motivation to that dealt with here. However, his research agenda is different. Specifically, his paper deals with how wealth and preference issues drive the demand for offsets. This is part of providing a general analysis of what factors will impact on volumes observed in offset markets and what their impact is on social welfare. Most closely related to our set-up here is a stream of research that examines markets in which firms can profit from consumers increased willingness to pay for environmentally friendly products. In particular, Moraga-Gonzalez and Fumero (2002) look at competition between firms for consumers, some of whom prefer environmentally friendly goods. Their analysis does not consider offsets but instead considers the impact of environmental policies (such as minimum emissions targets). Bagnoli and Watts (2003) consider a model in which firms can engage in strategic corporate social responsibility an attempt to increase profit by linking the provision of private goods to the provision of public goods, either explicitly or implicitly. They demonstrate that more competition can lead to less provision of the public good. Their results differ from ours, however, in that the public good is always provided although the level of provision may be inefficiently high or low. In contrast, we focus on independent offsetting (as opposed to offset provision by a firm) and examine whether the public good is provided or not. Finally, Toolsema (2007) considers a duopoly model of vertical differentiation and applies it to the market for green and non-green electricity. She determines the inter- and intra-firm switching costs necessary for a consumer to change to renewable energy sources. Toolsema

7 6 analyses the effects of potential government policies on the degree of monopoly pricing in electricity, but does not consider whether promotion of green products will lead to better environmental outcomes. 5 In contrast to Bagnoli and Watts (2003) and Toolsema (2007) our paper s contribution is to consider the net benefits for the environment from the introduction of offset markets both unrelated and related that arise independently of firm actions or promotional efforts. Thus, it analyses a distinct market environment from the existing literature. 2. Unrelated offsetting We begin with the case where carbon offsetting occurs in a market far removed from the consumption activity of the individuals purchasing offsets. A good example of this is carbon sequestration. The cost of offsetting is independent of the activity which gives rise to the consumer s guilt. As we demonstrate, the value of such offsets is to directly mitigate the level of guilt that consumers internalize over the emissions from their consumption activity. We consider first, a situation where the price of the consumption activity (i.e., electricity) is exogenous either regulated or cost-based and driven by competition. We then turn to consider the case where the price of electricity is endogenous and set by a firm with market power. 5 Kotchen (2006) analyses markets for green products and identifies potential counter-intuitive impacts. His analysis looks at self-interested individuals who care about a public good and have a discrete impact on it. He examines how they react to the emergence of green products that produce a private good and also contribute to the public good. Such products can cause individuals to reduce their effective public good consumption by substituting away from direct contributions to indirect ones. Kotchen s concerns are with the technical characteristics of such goods and do not include much of the pricing and strategic implications that we will consider here. Kotchen (2005) expands on this model while Ferraro, Uchida and Conrad (2005) explore some empirical aspects of a similar model.

8 7 Exogenous price setting Suppose that a representative consumer has utility, u(q) g(q) pq where q is both the quantity of electricity consumed and the quantity of emissions, 6 p is the price of electricity and u(.) and g(.) are continuously differentiable functions with,,, and for all q. 7 g represents guilt on the part of the consumer. As individuals consume more electricity they become more guilt-ridden since this creates more emissions. It is also assumed that the marginal level of guilt rises with net emissions. That is, consumers do not feel as guilty about adding emissions to the atmosphere when their consumption is low as they do when their consumption is high. The consumer solves:. The first order condition is: (1) Notice that the presence of guilt reduces the total consumption of electricity. We define as the base case quantity demanded when offsets are not available (satisfying (1)). Now suppose that a voluntary carbon offsets scheme becomes available. An offset permit costs t and the consumer chooses f such permits. 8 This impacts on the guilt component, which is now written. The consumer now solves:. In this case, the consumer s first order conditions become: (2) (3) 6 This assumption is made for convenience. The analysis below would hold for a more general emissions function that was an increasing function of electricity consumption. 7 The assumption of strict concavity of u is not necessary for all propositions below some of which only require that u is log-concave. However, for expositional simplicity we impose the stronger assumption throughout. 8 It is assumed here that t is set at cost and so is exogenous. Note that all the results here would continue to hold if t was an upward sloping function, t(q), with.

9 where the second condition holds with equality for t sufficiently small. 9 Let 8 be the quantity demanded when offsets are available (satisfying (2) and (3) with equality). This leads to a first proposition. Proposition 1. Suppose that, then. In addition consumption,, and offsets purchased,, increase as t falls. However, net emissions,, decreases as t falls with. PROOF: Note, first, that, as, g is submodular in (q, f) and, thus, is supermodular in and (it is trivial to show that it) has increasing differences in. Theorem from Topkis (1998) implies that the that satisfies (2) is strictly increasing in f. implies that and (3) holds with equality. Thus,. In addition, by the supermodularity of the consumer s objective function in, applying Theorem from Topkis (1998) proves that is strictly decreasing in t. Thus, combining this with the first result of the proposition, is strictly decreasing in t. Note that or, rearranging, that. As and u is strictly concave, the left hand side of this equation is positive. Thus, as it must be the case that. Lastly, since (3) holds with equality and, as falls, so does. The proof demonstrates that the consumer s choice of consumption and offset purchases are complements. 10 Thus, reducing offset prices increases both consumption of offsets and electricity. Intuitively, having the option to purchase offsets allows consumers to minimise the total cost of consumption, for any given q. Offsets, however, will only be purchased if there exists some f > 0 such that, ; something that is guaranteed by the assumption that. 11 This 9 When the price is sufficiently low consumers incur less disutility from buying offsets than from suffering guilt. 10 Indeed, if consumer s total utility was a general function U(q, g(q-f)) where U qg < 0 and U gg > 0 but g was still strictly convex, the propositions throughout the paper would be unchanged. 11 If this did not hold then the introduction of offsets would not have an effect.

10 9 assumption requires that the offset price be sufficiently low such that there is latent demand for offsets in the absence of a carbon-offset market. It implies that (3) holds with equality when offsets are not available or purchased. 12 This result is illustrated in Figure 1. Notice that as t falls, electricity consumption will increase as will offset purchases. However, the net level of emissions falls. Moreover, note that when, and there is no latent demand for offsets, an introduction of an offset market does not change anything as. Figure 1: Offsets and electricity demand g t u - p Quantity This has a number of testable implications in not only understanding electricity demand but also the behavior of electricity companies (or indeed any suppliers of dirty consumer 12 This is a reasonable starting point as those introducing offset markets would likely assess it as being worthwhile only if, at current consumption levels, guilt costs are sufficiently high that people would purchase offsets at a price t. It is shown below that, when electricity prices are exogenously determined this assumption merely serves to guarantee that an introduction of offsets has some effect (otherwise, there is no effect). However, when electricity prices are endogenous, this assumption is more critical and qualitative conclusions may change if it does not hold.

11 10 goods; e.g., automobiles). Those companies will have an interest in promoting carbon offset plans; at least to the extent that they do not compete directly with their operations. On Figure 1, observe that as t falls to a level where, the consumer chooses to go carbon neutral. Notice that, at this point, their electricity consumption is higher than would be the case without offsets. So when it comes to Al Gore, this analysis suggests that while his carbon footprint may be zero, his electricity consumption would have increased as a result of taking those actions. It is useful at this point to state the following corollary to Proposition 1. Corollary 1. Consider any change to long as consumer. such that electricity consumption increases. Then so prior to the change, any increased consumption will be completely offset by the PROOF: From (2) we have that. implies that (3) holds with equality. Thus, is constant since t is exogenous. Hence, a shift in will lead to an increase in, but no change in, and so the change in electricity demanded will be completely offset. This result can also be seen from Figure 1. Any change in the curve does not impact upon the net emission choice,, of the consumer. In particular, this invariance result would apply for a shift in p. 13 Endogenous price setting The above analysis takes the price of electricity (the dirty good) as given. This may be appropriate if p is determined in a competitive market or by regulation (as is often the case with electricity). However, it is useful to consider what happens when p is endogenous, in particular, 13 Corollary 1 also applies to decreases in electricity consumption where offsets are still purchased following the reduction.

12 11 if it is chosen by a monopolist. Here we conduct that analysis. For simplicity we will assume that in supplying electricity, the monopolist s only costs are unit costs of c. How does the presence of offsets change the demand curve faced by the monopolist? From (1), we have the inverse demand curve when offsets are not present. Also, assuming an interior solution for offset purchases, substituting (3) into (2) gives, the inverse demand curve when offsets are available. Thus, the inverse demand curve facing a monopolist is: (4) The fact that implies that there exists a such that for all such that,. Thus, as price falls, consumption eventually rises to a point where offsets are purchased. From Proposition 1 we know that when,. p Figure 2: Demand for Electricity With offsets Without offsets q Figure 2 illustrates the resulting demand curve. Observe that it has a kink in it at whereby the slope of the inverse demand curve becomes less steep as. What this means is that the marginal revenue curve of the monopolist has a discontinuity (with upward jump) at

13 12. Consequently, if the quantity chosen by the monopolist without offsets is less than, when offsets are introduced there may be two quantities for which marginal revenue equals marginal cost. If, prior to the introduction of offsets, there is latent demand for them, then p must be such that. Consequently, when offsets are introduced, this avoids the potential multiple local optima. Utilizing this we can demonstrate that Proposition 1 translates over to the endogenous price environment. Proposition 2. When prices are set endogenously, all the results of Proposition 1 hold. Namely, suppose that, then. Also, and, increase as t falls. However, decreases as t falls with. PROOF: The monopolist chooses q to maximize profits, offsets,, is determined by: In contrast, when offsets are introduced,, is determined by:. When there are no Note that the left hand side of (5) and (6) is decreasing in and, respectively, if u is log-concave (Vives, 1999, Theorem 2.7). The assumption that u is strictly concave guarantees that it is log-concave. Notice that and imply that. Consequently, the right hand side of (5) exceeds that of (6) so by Milgrom and Roberts (1994, Theorem 1), which permits upward jumps in first-order conditions,. Note also from (6) that a reduction in t causes an increase in. Similarly, is determined by which by implies that is increasing in t. That (3) holds with equality implies that is increasing in. Finally, note that and imply that which by gives the final result of the proposition. Intuitively, the introduction of offsets causes consumer demand for electricity and the monopolist s marginal revenue to increase. Consequently, the monopolist chooses a higher level of output. (5) (6)

14 13 But what happens to net emissions if the monopolist changes price? From Figure 2 we see that a rise in quantity may lead to either an increase or a decrease in price. But notice that holding electricity consumption constant, any change in p causes the guilt free component of demand,, to shift. By Corollary 1, this has no impact on net emissions unless p was chosen to be so high that no offsets are purchased, that is, when. Such a price could have been chosen by the monopolist prior to the introduction of offsets, but by we know that it was not optimal. Hence, by revealed preference, it is not profitable to choose such a high price after the introduction of an offset market either. So the resulting change in price has no effect on net emissions. Thus, when there is latent demand for offsets, from Proposition 2, net emissions will always fall. What happens if there is no such latent demand (i.e., )? Recall that in the exogenous price case the introduction of offsets would have no effect, as consumers would not choose to purchase them. For the endogenous price case, it is possible to prove the following. Proposition 3. Suppose that (i.e., net emissions rise).. Then it is possible that, in equilibrium, PROOF: We prove this proposition by example. Suppose that and. Then without offsets being available, inverse demand is and so the monopoly quantity chosen is and price is. Profits are. implies that. When offsets are available and demand for offsets is expected to be positive, inverse demand is. Then,,, and profits are. This expectation will be met if. Net emissions are equal to t (since and implies ), which by assumption are greater than. Thus, for both and, which is a feasible parameter range. Of course, it needs to be demonstrated that the monopolist s profits are higher by choosing a quantity that accommodates offset purchases even when there is no latent

15 14 demand. This involves comparing two local optima for the relevant parameter range. Profits that accommodate offset purchases will be higher than profits that do not if. The right hand side of this exceeds and so for, profits will be higher when offsets are accommodated and hence equilibrium net emissions will rise with the introduction of offsets. Apart from as a necessary condition, a complete characterization of when net emissions will rise with the introduction of offsets is not possible. However, the example in the proposition suggests that when the elasticity of guilt free demand for electricity is sufficiently high, the conditions by which net emissions rise will be met. Intuitively, when there are no offsets, the monopolist prices high as a result of the cost of guilt to consumers of expanding output. Offsets remove this guilt. Hence prices only fall slightly as output expands, and so the monopolist drops price and targets a very high level of output. Figure 3 illustrates why net emissions can rise when an offset market is introduced. Assume the monopolist lowers price from to p. In this situation, net emissions rise as the availability of offsets as well as lower price fuels sufficient demand such that offset purchases are less than the demand increase. What is interesting is that, in the absence of offsets, there is no latent demand for them. However, if offsets are priced sufficiently high, but not too high, the monopolist can take advantage of their presence by pricing low and fuelling electricity demand. That, in turn, creates a demand for offsets where none existed and can lead to a situation where net emissions actually rise as a result of the presence of an offset option.

16 15 Figure 3: Net emissions ( ) g t u p u - p Quantity Interestingly, as a consequence of selection amongst local optima, the creation of an offset option always increases the monopolist s profits. Put simply, it expands the range of demand. Hence, the monopolist has an incentive to facilitate the introduction of such markets. What is demonstrated here is that, in situations where offsets are relatively expensive, the monopolist may have an incentive to encourage them even in situations where net emissions might rise as a result. Consequently, there is a potential mismatch between social and private goals in this regard Related offsetting We now turn to consider offsets that are directly related to the consumption activity. For example, suppose that the offsets are not used to plant trees (an unrelated industry) but instead 14 Of course, a complete welfare analysis would require a consideration of consumer surplus as well and a balancing of various price and emission effects beyond simply the consumers in any one market.

17 16 are used to purchase cleaner (non-emitting) sources of electricity (e.g., wind or solar power). The difference between such offsets and unrelated offsetting are two fold. First, the purchase of offsets by the consumer constitutes a substitute consumption activity that does not generate emissions, and consequently, guilt. Thus, such offsets directly reduce emissions. Second, the supply of such offsets competes with the supply of dirty electricity. This will have an impact on the demand curve facing dirty suppliers as well as their pricing behavior. Of course, the outcome of this competition will depend upon the constraints facing clean producers. In Australian electricity markets, for instance, consumer purchases of green electricity do not result in a direct procurement of electricity from those sources; instead it funds investments in generating capacity with little or no emissions. Under the rules of most wholesale electricity markets around the world, green producers bid capacity into electricity pools. It may be that their bidding behavior in order to be directly marketed as offsetting dirty generation of electricity is committed or regulated to be based on marginal cost. 15 For solar or wind power, this means that such generation will ordinarily be dispatched first. Alternatively, it may be that customer purchases of green power, while funding investment, do not involve contracts that constrain such generators to bid at marginal cost. Thus, we examine both the non-strategic and strategic clean generator cases. 16 Non-Strategic Clean Generation As before, let q be the consumption of dirty electricity. Related offsetting, f, is now also of consumption value but unlike q does not impact on guilt as it is assumed to involve no 15 This is achieved by vesting green generators with contracts that cover the level of demand from purchasers of green power. Consequently, as is well-known, generators holding those contracts will bid into electricity pools at marginal cost and will not be strategic bidders (Gilbert and Newbery, 1992). 16 Of course, for the non-strategic case, considering clean generators as being made up of a competitive fringe would also lead to marginal cost bidding.

18 emissions. Thus, the consumer s total electricity consumption is 17 and as it is traded in an electricity market consumers pay p per unit generated regardless of its source. Consumers, however, to generate f, must also purchase offsets at an additional unit price of t. It is assumed that those clean generators receive p + t per unit of electricity generated and that this, in any equilibrium, covers the unit rental cost of capacity, which is exogenously set at. In effect, consumers pay a premium for electricity generated from clean sources. Thus, the consumer solves:. In this case, the consumer s first order conditions become: (7) (8) where the second condition holds with equality for t sufficiently low. As before, we assume that the dirty producer is a monopolist. It is also assumed that the dirty generator s choice of q and the consumers choice of f occur simultaneously. To be consistent with the assumption of non-strategic clean generation, we also assume that f translates directly into capacity; that is, a purchase of offset units is equivalent to units of electricity generating capacity. In this situation, (7) will determine the dirty generator s demand function, which will shift inwards as f increases. Consequently, as a result of the consumer s alternative electricity option, demand for dirty electricity is reduced. Let and be defined as before, namely, the quantity of dirty electricity consumed in the base case and in the case where offsets (i.e., green generation) are available. Then we can prove the following. Proposition 4. With a non-strategic clean generator, and.

19 18 PROOF: is defined by the first order condition: Suppose that, then as, consumers will not find it worthwhile to substitute green consumption for dirty consumption and and. Now suppose that. In this case, is determined by (8) while the dirty producer chooses its output holding f as given: (10) Because u is log-concave (implied by the assumption that u is strictly concave) the left hand side of (10) is decreasing in f (Vives, 1999, Theorem 2.7). Thus, compared with (9), the dirty generator s marginal benefit from expanding quantity is lower. Hence,. (9) Note that and. As and., which, as u is log-concave, implies that The intuition for this proposition is straightforward. So long as t is low enough, green generation provides an attractive substitute for some of the consumer s dirty consumption. 17 Consequently, the dirty generator faces a decrease in demand which decreases the quantity they supply. This leads to a fall in emissions. This competition also decreases the price of electricity as well as reducing the marginal cost of guilt to the consumer. Hence, total consumption of electricity rises. Note that, unlike the case with unrelated offsets, there is no potential, even with a dirty producer with market power, for there to be an increase in emissions. When there is no latent 17 This argument relies on the fact that the monopolist does not benefit from the introduction of the offset market, and hence their optimal pricing schedule will not change. By revealed preference, the monopolist will not increase its prices, since this will only serve to make consumers even less likely to purchase dirty energy. Alternatively, it is not incomprehensible that, under certain conditions, as in Proposition 3, the monopolist can benefit from lowering its prices, encouraging offset consumption, and fueling further demand for dirty consumption. If this were the case, a lower p, call this, would lead to an increase in q, call this. If were sufficiently low then a case might arise in which. The flaw in this argument, however, lies in the fact that this would then encourage consumers to exchange some of their current dirty consumption for clean consumption, until. The end result is that the monopolist receives a price,, and a quantity,, which is less than the quantity,, it would receive if it charged a price in a market without offsets. Since is not optimal, then neither is. Hence, the introduction of a related offset market in which clean producers are non-strategic does not lead to any change in the dirty monopolist s pricing behavior.

20 19 demand for offsets, their availability is inconsequential and the dirty producer s behavior is unchanged. This is because, unlike the unrelated offset case, for the dirty producer offset availability is no longer a strategic complement to its own production. Strategic Clean Generation We now consider whether Proposition 4 continues to hold when the clean generator bids strategically. In this situation, the clean generator is assumed to choose its quantity, f, at the same time that the dirty generator chooses. Thus, the clean and dirty generators are Cournot duopolists. The difference is that for the clean generator, rather than increasing guilt, additional quantity imposes a premium, t, on consumer s electricity price. When clean generators act strategically we see that Proposition 4 continues to hold: Proposition 5. With a strategic clean generator, and. PROOF: is defined by (9) from the Proof of Proposition 4. If, then as, consumers will not be willing to purchase offsets even if production is available and so the clean generator will not choose a positive quantity and the introduction of offsets will result in no change. There are two other broad cases to examine in which. First, suppose is the equilibrium quantity of the dirty generator when the clean generator invests its equilibrium quantity, f *, and expects to sell offsets for a premium of t for that entire amount. The clean generator solves, whereas the dirty generator solves where p is given by (7). This results in the first order conditions: (12) As in Proposition 4, (12) is decreasing in f, and compared with (9), the dirty generator s marginal benefit from expanding quantity is lower. Hence,. Then if, the clean generator s expectations will be met and this will be an equilibrium outcome. Note also that this implies that the left hand side of (12) is less than that of (9) and, because u is log-concave,. (11)

21 20 Second, suppose that, then the clean generator cannot sell offsets to the level of f *. In this case, its first order condition becomes: (13) where takes on a value of 1 if and 0 otherwise. Notice that as f > 0 and f and q are strategic substitutes, the equilibrium choice of dirty output will be no greater than the equilibrium output when f = 0. So. In addition, it is easy to show that as g is log-convex (see (Vives, 1999, Theorem 2.7). Hence, the conclusions of the proposition hold. Thus, the result that the introduction of offsets creates competition in generation and causes emissions to fall, holds even when clean generators are able to invest strategically. The intuition is essentially the same as before since such investment necessarily causes the dirty generator to invest in less capacity. Pre-emptive Quantity Commitments This discussion naturally leads to the question of what happens if the dirty generator can move first and pre-emptively choose its capacity prior to clean generation becoming an option for consumers. Suppose that the monopolist sets q prior to consumers choosing their offset purchases. In this case, we can demonstrate the following. Proposition 6. Suppose that the clean generator is non-strategic and the dirty generator can choose its quantity prior to any other decisions being made. Then, and. PROOF: Note that when, there is no clean generation entry and there is no change in the dirty generator s output. Alternatively, if, the dirty generator cannot sell a quantity greater than that implied by as consumers purchase offsets to allow the residual amount to be produced by clean generation. This implies that since. By revealed preference, the monopolist will not produce less than the quantity implied by. So. This implies that.

22 21 Compared with a market without offsets notice that, when there is latent demand for offsets, consumers would, if quantity did not change, purchase offsets. Indeed, they would purchase offsets such that. Consequently, the dirty generator will pre-commit to no more than this quantity. This deters clean electricity production and leaves the market with higher prices and lower emissions/consumption than is the case without offsets. The outcome here is very different from a Stackelberg or leadership with a competitive fringe outcome that would normally lead to a higher quantity commitment by the dominant firm. Here, consumers select between dirty and clean generation not on the basis of the price of electricity per se but the costs of mitigating guilt. As the offset price is fixed, it determines the maximum quantity the dirty generator can produce. Alternatively, consider what might happen if t was determined ex post. Earlier we argued that in some cases might be held constant in order to reflect the cost faced by clean generators (either due to competition or regulation), so that. Suppose instead that the dirty generator commits to quantity, after which consumers choose whether to purchase offsets or not, where t = r p. Thus, in equilibrium, clean generators break even. In this situation, the dirty generator, when setting its pre-emptive quantity, would have to forecast not only p but t also. A higher t would raise the maximum quantity it could sell. Following its quantity commitment, two factors determine t. First, the price of electricity, p, will equal. Second, t = r p. For these to hold simultaneously implies that so long as r is not too high. Since q is committed to prior to this point, this equation will determine f. Note that for every unit increase in q, a unit of f will be displaced. This insight drives the following proposition.

23 22 Proposition 7. Suppose that t is endogenous where, clean generation is non-strategic and the dirty generator can choose its quantity prior to other decisions being made. Then it is possible that. PROOF: Suppose that be negative and so offsets would cover the entire market with, then at the monopoly quantity, t would have to. In contrast, for r sufficiently high such that, the dirty generator can set its monopoly quantity and no offsets will be sold. For intermediate levels of r, the dirty generator chooses its quantity to maximise:. This yields the first order condition: Note that as,. Comparing this with (9), since, we know that if (14). This will be true if. Using the functional forms and, this inequality will hold if. Note that and that offsets will be sold if.. Thus, it is possible that The intuition for this result is that the monopolist s behavior is now driven by its role in offsetting guilt. As the only strategic producer, if the monopolist restricts quantity, this decreases the premium on offsets and hence, allows more competing production. The monopolist, therefore, has incentives to target a lower price. This results in more output being sold than if offsets are not present. Of course, this depends on r not being so low that dirty generation is driven from the market or so high that clean generation cannot enter without a subsidy. Thus, when offset price is endogenous, the strategic incentives of the monopolist are very different to the case in which is exogenous. Instead of pricing high to deter offset investment, the monopolist prices low in an attempt to soften competition from such investment. The end result is that emissions may rise.

24 23 4. Conclusion This paper has examined concerns that the voluntary purchase of carbon offsets by consumers can lead to unintended consequences that cause emissions to rise. The key feature was to recognize that consumers who curtail consumption of dirty electricity because of personal guilt over their emissions will demand offsets with a sufficiently low price. While it is true that the purchase of offsets allows individuals to alleviate their guilt and hence, consume more electricity, the presence of offset markets will, generally, cause net emissions to fall. In general, the consumption effect of offsets does not outweigh their ability to reduce emissions. Nonetheless, a situation in which offsets (used in an unrelated industry) might harm net emissions is identified. This occurs when there is no latent demand for offsets but, due to pricing behavior, such demand is, in fact, created. In some situations, the impact of the offset market may cause firms with market power to dramatically expand their supply of dirty goods; less than the supply expansion is countered by offset purchases. It was also shown that when offsets generate direct competition with the dirty good suppliers, the presence of an offset market can cause net emissions to increase. In most cases, offsets cause a reduction in the price of electricity from dirty sources. However, the quantity produced by dirty good suppliers also fell along with price. Offsets increased consumption overall but reduced total emissions. Nonetheless, in the case in which dirty producers could engage in strategic quantity commitments, the presence of an offset market could increase emissions as dirty producers moved to deter consumption from clean competitors. There are a number of empirical implications from the analysis here. Examining the link between offset markets and total consumption would be interesting, as would examining the impact between strategic behavior and offset purchases. From a policy perspective, however, the

25 24 analysis demonstrates that voluntary purchases of offsets are most likely to reduce environmental harm and should be seen as desirable alongside collective forms of emissions reduction such as emissions caps, carbon taxes and permit trading. Nonetheless, the assumed environment in this paper is one where global emission caps or carbon taxes are not in place. It is likely that the impact of voluntary offsets in those circumstances will be more complex but that is something we leave for future research.

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