Guilt Markets 08-01-10

Carbon Offset Provision with Guilt-Ridden Consumers* by

Joshua S. Gans University of Melbourne 11th January, 2008

Carbon offsets can be purchased by consumers who wish to mitigate their emissions. In a model where the demand for such offsets is driven by consumers who feel guilt about their emissions, it is shown that the introduction of offsets are complements to existing „dirty‟ consumption and can cause such consumption to increase. Net emissions are shown generally to decline, however, regardless of whether prices are regulated, chosen strategically or offset prices are endogenous. It is demonstrated, however, that when there is no latent demand for offsets, the introduction of them can potentially cause a rise in net emissions when „dirty‟ producers have market power. One special case is illustrated whereby emissions might rise if „dirty‟ producers can engage in strategic commitments to impact on offset markets. Journal of Economic Literature Classification Numbers: L94, Q42, Q58. Keywords: carbon offsets, greenhouse gases, electricity markets, strategic behaviour.

*

Thanks to Stephen King and Michael Ryall for helpful comments. Responsibility for all errors and omissions is my own. The latest version of this paper is available at: www.mbs.edu/jgans. All correspondence to: [email protected].

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1.

Introduction Carbon offsets allow individuals, households and firms to cause activities to be taken that

mitigate their carbon emissions. A common use for such offsets is to invest in trees and forests that remove carbon from the atmosphere. Another example is „green power.‟ In this situation, consumers pay a premium to subsidise 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 as I will term here reduction in „guilt,‟ emissions would be reduced and welfare increased. There have been suspicions raised that offsets may not actually be inconsequential.1 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). This paper provides a formal treatment to evaluate such claims. The novelty of the model introduced here is that consumers feel „guilt‟ with regard to the level of greenhouse gas emissions that they generate. Notice that this is distinct from any disutility they might suffer due to the global level of emissions. Specifically, it provides a rationale for voluntary changes in their behaviour to mitigate those emissions. This is critical as it allows for an analysis of their demand for offsets and how this interacts with their consumption of ordinary goods such as electricity.

1

See, for example, Tyler Cowen or The Economist blog.

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Both intuitively and also empirically, the idea that „guilt‟ might drive consumer purchases is an appealing one. Kahn (2007) examines consumer choices based on their registration as Green Party members. He finds that „green‟ consumers are, in fact, more likely to use public transportation, purchase hybrids and reduce petrol consumption than others. This is not the first paper to model individuals who internalise some of their social negative externalities. Andreoni (1990) deals with „warm glow‟ effects. His applications are 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 behaviour can emerge. 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 the impact of environmental policies (such as minimum emissions targets) in such markets. 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 both a private good and 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 does not include much of the pricing and strategic implications that I will consider here.2 Finally, in a paper written contemporaneously with this one, Kotchen (2007) 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,

2

Kotchen (2005) expands on this model while Ferraro, Uchida and Conrad (2005) explore some empirical aspects of a similar model.

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the 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 ultimately their impact on social welfare. In contrast, my concern here is on industrial organization aspects of offset programs and whether, once possible strategic behavior is taken into account, offset programs actually serve their desired ends; namely, reducing net emissions. The paper proceeds as follows. In Section 2, I introduce the model of demand for electricity (although it could equally apply to any greenhouse gas emitting good or set of goods). The presence of guilt mitigates consumers‟ demand for carbon emitting or „dirty‟ electricity. This also means that if consumers can purchase offsets, they will do so and they will purchase more offsets as their price falls. The first result from this analysis is that purchases of offsets and consumption of electricity are complements. The cheaper are offsets, the more are consumed but this stimulates consumption of electricity as consumers‟ net emissions and hence, guilt falls. That analysis holds prices as given. The remaining sections endogenise them. Section 3 provides a model of the electricity market. It is show that the introduction of offsets when an electricity generator has some market power causes them to lower the electricity prices (as offsets are a complement) but, nonetheless, net emissions are reduced even though electricity consumption is higher. Interestingly, when there are consumers present in the market who are guilt-free rather than guilt-ridden, net emissions still fall. While the guilt-free receive price reductions, the presence of the guilt-ridden mitigates the extent of these and so net emissions are always reduced by carbon offsets being available. In that section I also demonstrate that it is possible that providing the possibility of offsets could actually lead to higher net emissions. The critical driver of this possibility is a situation

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where, prior to offset becoming available, there is no latent demand for them; that is, consumers would not purchase offsets at their current consumption levels. However, the presence of a relatively high cost offset market can allow a firm with market power to take advantage of it with lower prices and higher consumption. That higher consumption in turns fuels offset trading to the detriment of net emissions but higher profits for the firm. Section 4 then considers what happens when offsets are invested in competing „clean‟ electricity capacity such as wind power. It is assumed that the amount of offsets purchased determines the supply quantity of such alternative electricity and that this supply is „nonstrategic‟ and not withheld through the exercise of market power. Again it is demonstrated that the presence of offsets reduce net emissions. This is despite the fact that competition reduces electricity prices and causes more consumption overall. The volume of „dirty‟ electricity purchased falls. Section 5 examines the possibility of strategic commitment by „dirty‟ electricity generators that pre-emptively impact the offset market. It is show that when offset prices are fixed or regulated, the „dirty‟ generator sets electricity prices high so as to deter the purchase of offsets (in this model all the way to zero). However, this reduces emissions as production must be curtailed to achieve this. When offset prices themselves are endogenous, the motives of the „dirty‟ generator are reversed. In this situation, flooding the market with „dirty‟ capacity depresses electricity prices but raises offset prices. I demonstrate that when the capital costs of „clean‟ generation are high, this might mean more emissions in equilibrium with offsets than without them. Finally, in Section 6, I examine whether a market where clean producers were not subsidised but acted strategically could actually lead to less emissions than a subsidised/non-

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strategic situation. Of course, with regulated offset pricing, that price can be adjusted so that this is never the case. But with endogenous offset pricing, I show that if clean generation is cheap enough, then an unsubsidised model is preferable. Put simply, while the clean generator withholds capacity to increase profits, the dirty generator‟s consumers are constrained by guilt and so favour clean generation in any case.

2.

The Demand Model Suppose that a representative consumer has utility, u(q) – g(q) – pq where q is the

quantity of electricity consumed, p is its price and u  0 and g  0 . (It is also assumed that

u  g  0 ). g represents guilt on the part of the consumer. As they consume more electricity they become more guilt-ridden as this creates more emissions. The consumer solves: max q u(q)  g (q)  pq . The first order condition is:

u(q)  g(q)  p

(1)

Notice that the presence of guilt reduces the total consumption of electricity. Now suppose that a voluntary carbon offsets scheme becomes available. An offset permit costs t and the consumer chooses o such permits.3 This impacts on the „guilt‟ component which is now written g (q  o) . The consumer now solves: max ( q,o ) u(q)  g (q  o)  pq  to . In this case, the consumer‟s first order conditions become:

u(q)  g(q  o)  p

(2)

g(q  o)  t

(3)

where the second condition holds with equality for t sufficiently low. To simplify exposition, I assume the following: 3

It is assumed here that t is set at cost and so is exogenous. Note here that the results below will continue to hold if t was an upward sloping function, t(q), with t   g  all of the results here would continue to hold.

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(A1) The demand for offsets is downward sloping. That is, g   0 for o > 0. The idea here is that as the price of offsets fall, the consumer purchases more. This requires that as a consumer emits more, their guilt rises in greater proportion than their emissions.4 It could be argued that the reverse might be the case. A consumer might be less concerned as they emit more and more but experience a large jump in guilt as they move from zero to a little emissions. However, this could still be accommodated but assuming that

g (0)  0. In this situation, if t falls low enough, q = o. Let q0* be the quantity demanded when offsets are not available (satisfying (1)) and qo* , quantity demanded when they are (satisfying (2) and (3) with equality). To consider an interesting case, it is assumed that: (A2) The offset price is sufficiently low that there is latent demand for offsets when they are unavailable; that is, g (q0* )  t . This assumption 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 of 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. This leads to a first proposition.

The results below do not need as a strong a condition as this on demand. Indeed, so long as u(0)  g (0) and there exists a finite q so that u(q)  g (q) , the comparative statics results will hold. 4

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Proposition 1. Under (A1) and (A2), qo*  q0* and the choice of consumption, qo* , and offsets purchased, o* , increases as t falls. However, total emissions qo*  o* decreases as t falls with

qo*  o*  q0* . It suffices to prove this graphically. In Figure 1, without offsets, total consumption is determined by the intersection between u(q)  p and g (q) , the point depicted above q0* . When the consumer can purchase offsets at a price of t, if that price is too high – that is, (A2) did not hold and t  g (qo* ) – no offsets are purchased and nothing changes. However, if, as depicted in Figure 1, g (0)  t  g (q0* ) , then offsets are purchased up to the point where g (qo*  o* )  t . Consumption is, however, determined not by guilt but by the offset price at a point where

u(qo* )  p  t .

Figure 1: Offsets and electricity demand

g’

t u’ - p

qo*  o*

q0*

qo*

Quantity

As can be seen from Figure 1, the presence of offsets increases electricity consumption. Notice also that as t falls, electricity consumption will increase as will offset purchases. However, the net level of emissions falls.

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As t falls to a level where g(0)  t , 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 also indicates that consumers who myopically purchase offsets based on their current consumption levels will find themselves purchasing more offsets in future years as their consumption grows. It is useful at this point to state the following corollary to Proposition 1. Corollary 1. Consider any change to u  p such that electricity consumption increased. Then so long as o*  0 prior to the change any increased consumption will be completely offset by the consumer. This can be seen again from Figure 1 and (3). Notice there that any change in the u  p curve does not impact upon the net emission choice qo*  o* choice of the consumer. It is determined by (3) and so any change in electricity consumption will necessarily lead to an offsetting change in offsets purchased. In particular, this invariance result would apply for a shift in p.5 Put simply, offsets and electricity consumption are complements. Those with higher intrinsic demand for electricity purchase offsets and a reduction in the offset price causes more electricity consumption. This has a number of testable implications in understanding electricity demand but also the behaviour of electricity companies (or indeed any suppliers of „dirty‟ consumer 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.

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Corollary 1 also applies to decreases in electricity consumption where offsets are still purchased following the reduction.

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3.

Pricing response 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, if it is chosen by a price-setting monopolist. For simplicity, it is assumed that the monopolist has a constant marginal cost, c, of producing electricity. From (1), we have the inverse demand curve facing a monopolist when offsets are not present and, assuming an interior solution for offset purchases, substituting (3) into (2) gives

p  u(q)  t ; the inverse demand curve when offsets are available. In effect, that demand curve coincides with the one when offsets are not present for high t and than at some t becomes distinct (lying above it as depicted in Figure 2). Figure 2: Demand for Electricity p

With offsets

Without offsets q

(A2) guarantees that the monopolist is operating in the relevant range where the two demand curves are distinct. For that reason, the monopolist‟s marginal revenue curve will shift

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outwards when offsets are available and hence, it will supply more electricity. Formally, when offsets are available, the monopolist chooses a quantity ( qo* ) that satisfies:

u(qo* )qo*  u(qo* )  t . In comparison, the quantity when offsets are not available ( q0* ) is determined by:

u(q0* )q0*  u(q0* )  g (q0* )  g (q0* )q0* . Thus, so long as g (q0* )  g (q0* )q0*  t , qo*  q0* . What happens to net emissions? The answer depends on what happens to electricity prices. It is possible that the introduction of offsets could make the demand for electricity more elastic. In this case, the monopolist could lower electricity prices. Here, however, Corollary 1 applies and net emissions are price independent – determined solely by (3). By (A2), these must be less than total emissions without offsets. Hence, net emissions fall. It is also possible that the higher demand with offsets could cause prices to rise. Thus, it is possible that the „guilt free‟ component of demand may shift inwards. Again, by Corollary 1, this has no impact on net emissions until price rises to a point where g (qo*  o* )  t in which case, (3) will be violated and there would be no offset purchases. By revealed preference (they could have chosen that high a price without offsets), choosing a price such that this occurred would never be optimal for the monopolist. Thus, net emissions will always fall. Example: To illustrate this, it is instructive to utilise a simple linear demand specification. Suppose that linear demand set-up with u (q )  aq  bq 2 and g (q  o)  12 (q  o)2 . Then without offsets being available, inverse demand is p  a  (b  1)q and so the monopoly quantity chosen is q0* 

a c 2( b 1)

and price is po*  a 2 c . Profits are

( a  c )2 4( b 1)

. When offsets are available, inverse demand

is p  a  bq  t . When demand for offsets is expected to be positive, qo*  a2cbt and po* 

a  c t 2

.

Notice that q  q  t  ab1c which always holds when offset demand is positive (that is, t  q which implies that t  2abc1  ab1c ). Note also that electricity prices fall. Net emissions when offsets * o

* 0

are present equal t. Thus, they will fall if t  q0* which is guaranteed by (A2).

* o

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‘Guilt free’ consumers The above model assumes that all consumers are identical or, at the very least, have a guilt ridden component to their utility. In reality, there is consumer heterogeneity. Moreover, if guilt ridden consumers cause the monopolist to reduce prices (as it did in the last example), this will cause consumption by the guilt free to arise without an offsets on emissions. Could overall emissions rise in this case? To consider this, suppose that there were two types of consumers in this market. One set of consumers – the guilt-ridden – have utility functions as specified above. The other set – the guilt-free – have g(.) = 0 for all q – o. It is assumed that there is a unit mass of consumers, a fraction,  of which are guilt-ridden. In this situation, the monopolist prices to take into account the preferences of the guiltfree and guilt-ridden. When the latter can purchase offsets, their demand increases. This may lead to price increases or prices falls depending upon specific utility functions. If price increases, net emissions will clearly fall. But if price decreases, while the net emissions of the guilt-ridden will fall, overall emissions may rise. Of course, this depends on the share of each type of consumer. It is difficult to evaluate this without specific functional forms. Thus, I return to our running example to see how the effects balance out in that case. Example (continued with heterogeneous consumers): Without offsets, guilt does not factor into price and so p*  a 2 c . However, it does matter for quantity with q*  ( a 2cb)(( bb1)1 ) . With offsets, however, po*  ac2 t , q0*  a 2cbt and qo*  a c 2tb( 2) . Thus, an offset market reduces price and increases quantity. However, net emissions become (1 )( a c )  t (2b 1) a c t * * *  (qo  o )  (1   )qo   t  (1   ) 2b  . This is lower than the ‘without offset’ 2b level of a c 2( b 1)



( a  c )( b 1 ) 2 b ( b 1)

( a c )b ( b 1)(2 b 1 )

.

if t 

( a c )b ( b 1)(2 b 1 )

which must hold under (A2) as this requires t 

a c 2( b 1)

where

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So even with heterogeneous customers, net emissions fall when offsets are introduced. Put simply, the extent of the price fall is contingent on the number of guilt-ridden customers purchasing offsets. As the share of these expands, the price fall is larger but so is the share of consumption offset. This latter effect dominates for the functional form assumptions here.

What if there is no latent offset demand? The running examples above show that the introduction of offsets may reduce electricity prices. For this reason, it is useful to consider what happens when (A2) does not hold. In this situation, there is no latent demand for offsets at electricity prices when they are not available. However, should those prices fall when they are available, it is possible that consumption could rise to such an extent that there is demand for offsets under those new pricing conditions. If this were to occur, then the outcome as depicted in Figure 3 could arise. 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. Figure 3: Net emissions when (A2) does not hold (p‟ < p)

g’

t u’ – p’ u’ - p

q0*

qo*  o*

qo*

Quantity

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Example: Recall that net emissions with offsets equal qo*  o*  t and without offsets equal qo* . (A2) does not hold if t  q0*  2(abc1) ; thus, under these functional forms, by definition, net emissions are higher when offsets are available. The question is whether, if (A2) does not hold, the demand for offsets will be positive if they are available. The condition for this is: t  qo*  a2cbt . This condition and t  q0* can hold simultaneously as offset availability raises demand. In the running example, there exist parameters such that for monopoly electricity prices, it can simultaneously be the case that t  g (qo* ) (A2 does not hold) and t  g (q0* ) (the demand for offsets are positive). Hence, the situation depicted in Figure 3 can occur. What is interesting is that, in the absence of offsets, there is no latent demand for them. However, if they are priced sufficiently high, but not too high, the monopolist finds it advantageous to 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. Interestingly, 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. However, 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.6

4.

Supply Response Suppose that the offsets are not used to plant trees (an unrelated industry) but instead are

used to purchase cleaner (non-emitting) sources of electricity (e.g,. wind or solar power). For 6

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.

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example, investments in wind power might be subsidised by the offset program. This means that the introduction of offsets lead to an expansion in capacity for generation that competes with current generation. Regardless of how p is set (monopolistically, oligopolistically or competitively), subsidies of this kind in competing capacity can cause p to fall. Consumers will take p as given. However, their decision without offsets will now look like Figure 4 where p  p . This results in a shift along their demand curve for „dirty‟ electricity and hence an expansion in their consumption of that. This situation is akin to Corollary 1. In situations where offsets are purchased (that is, t is sufficiently low), the expansion in consumption of „dirty‟ electricity is completely offset. So net emissions are invariant to the competitive response. Net emissions are solely a function of t and not p. What this implies is that, at a base level, concerns that a supply response will cause net emissions to rise are false.

Figure 4:Impact of a price change

g’

t u’ – p’ u’ - p

qo*  o*

q*

qo*

Quantity

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While this illustrates a rationale as to why a supply response would not cause any unusual patterns in net emissions following the introduction of offsets, it is somewhat incomplete in that the mechanism by which offsets translate into a supply response is unmodeled. In addition, when prices are formed endogenously, strategic issues may come into play. Suppose that offsets are translated directly into the output of a competing electricity supplier. It is often the case that green power markets operate in this way. Offsets are used to subsidise wind farms which then are required to bid into electricity pools in a non-strategic manner (i.e., at marginal cost which is usually assumed to be zero). The offsets themselves are used to fund investments in generating capacity. In such a situation, o becomes the quantity choice of the competing electricity supplier. What this means is that a consumer‟s guilt will now be a function solely of q and not depend on o directly. This is because offsets are now direct consumption rather than mitigating offsets caused by dirty consumption (they are perfect substitutes for electricity in u(.)); so net emissions are simply q. Thus, the consumer‟s problem becomes: Now the consumer solves:

max ( q,o) u(q  o)  g (q)  p(q  o)  to ; where offsets are purchased (at a premium) to be consumed directly. In this case, the consumer‟s first order conditions become:

u(q  o)  p  g (q)

(4)

u(q  o)  p  t

(5)

where the second condition holds with equality for t sufficiently low. It is assumed that the monopolist‟s7 choice of q and the consumers‟ choice of o occur simultaneously.8 In this situation, (4) will determine the monopolist‟s demand function which will shift inwards as o increases. Consequently, as a result of the consumer‟s alternative

7 8

I will continue to refer to the producer of dirty electricity as the monopolist. That is, the monopolist cannot commit to q; an assumption that will be relaxed in the next section.

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electricity option, demand for „dirty‟ electricity is reduced as is the monopolist‟s supply of it. Note that these results do not depend on (A2) holding per se, as, in this case, consumers would not purchase „green‟ electricity if (A2) did not hold. Example: Utilising our previous functional form assumptions, from (5), o*  a bp t  q . The first order condition for the monopolist is then: a  2(b  1)qo*  bo  c . This gives qo* 

a  c bo 2( b 1)

and

b ) t and qo*  t . po*  a c2bo . Substituting in o* and solving gives: po*  c  (1  b)t , o*  ac2(1 b

Notice that so long as t is low enough that o*  0 , then qo*  q* and emissions strictly decrease as a result of offsets being available.

5.

Strategic commitments One feature of offset programs that create alternative sources of electricity generation is

that the subsidised plants are invariably required to be non-strategic; bidding in their capacity at cost rather than to maximise profits. To be consistent with that, the analysis here has maintained that assumption. But it has also been assumed that the strategic „dirty‟ generator of electricity has taken consumer and, hence, clean generator behaviour as given. A natural question to ask, however, is what would the impact on emissions be if the monopolist were to act strategically and commit to certain actions to influence that consumer behaviour? In this section, we address this question looking at the cases of exogenous and endogenous offset prices in turn.

Exogenous offset prices Suppose that the monopolist set p prior to consumers choosing their offset purchases. This would amount to a price commitment on the part of the monopolist. This is something that they could achieve in electricity spot markets where clean generation is bid in at a reservation price of zero and the monopolist‟s bid sets the marginal price for the system.

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For a given q, consumer behaviour is determined by (5). Substituting this into (4) and the level of q is determined by the condition, t  g (qo* ) . This means that by increasing price, p, the monopolist will not change its own sales volume. However, a price rise will reduce offset purchases. Consequently, the monopolist will set its price so that o*  0 .9 Compared with a market without offsets notice that, when (A2) holds, consumers would, if quantity did not change, purchase offsets. It is easy to show that in this case then po*  p0* so that the introduction of offsets causes electricity prices to rise. As clean electricity production is deterred by this pricing behaviour, total electricity production must fall. Thus, when it can make a strategic commitment, the presence of the offset market constrains the monopolist. While no offsets are sold and so not actual competition arises, potential competition constrains the monopolist price. This reduces electricity consumption and emissions. Compared to the case where offsets are used in an unrelated market, both consumer and producer surplus are reduced.10

Endogenous offset prices The analysis, thusfar, takes offset prices as fixed at t. It is arguable that these should be cost based and so, in an electricity market context, this would be equal to the cost of added capacity less revenues the clean energy producer would receive. Thus, if the cost of each unit of clean capacity is r then the offset price, t  r  p (the cost premium of clean capacity in the

Using our functional form assumptions this would occur at a price of po*  a  t (1  b) and at this point, qo*  t . Note that this exceeds t and so is an equilibrium. 10 If consumers are heterogeneous this conclusion would be softened as the monopolist will factor into account the guilt-free who never purchase the more expensive offset electricity. Thus, the monopolist‟s demand curve would become less than perfectly inelastic. 9

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market). It is also assumed that r  c which is a necessary condition for clean capacity to require a subsidy. In this case, (5) now becomes:

u(q  o)  p  r  p

(6)

In this situation, when the monopolist sets price first, equilibrium consumption of „dirty‟ electricity would be determined by the condition: t  g (qo* ) or r  po  g (qo* ) . In this case, the monopolist will lose sales if it prices higher as this means that the price of offsets are lower. This then defines the (inverse) demand function facing the monopolist, i.e., po  r  g (qo ) ; with elasticity,  o 

r  g g q

. It is instructive to compare this with the (inverse) demand function that

would arise when offsets were not present. In that case, p  u(q)  g(q) and its elasticity is

   (uugg) q . Note that:

 o    urgg  ugg 



(7)

0

The left hand side is positive when prices are positive. Thus, the introduction of offsets with an endogenous subsidy makes the monopolist‟s demand more price elastic. So such competition will constrain its price to be lower. The issue is: even with this lower price, does the quantity of emissions produced fall when offsets are introduced? The following addresses this for our functional form assumptions: The following proposition addresses this Example: Here I show that when offset prices are endogenous and are used to fund competing capacity, then offsets are purchased in equilibrium if 2 a 1c(1bb )  r . In this case, the introduction of an offset market will increase total consumption but emissions will fall if and only if abbc1  r . To see this, note that, facing the new demand function, the monopolist chooses qo*  12 (r  c) . Setting r  qo*  a  b(qo*  o) we can solve for o*  2 a (b1)2bc(b1) r and po*  c 2 r . Note, however, that this is only an equilibrium (with positive offset purchases) if 2a  c  r  b(r  c) which can

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be rewritten to give the condition in the proposition. Notice also that as r  c , then po*  r and so the offset price is positive. Total electricity consumption is

2 a c r 2b

. This is less than q* 

a c 2( b 1)

if 2a  c  r  b(r  a) . If the equilibrium condition holds, it is easy to see that this must hold too. For emissions, these are now at qo* . Comparing this to q* gives the condition in the proposition. This demonstrates that if r is too high, then offset prices will be too high and the monopolist producer of dirty electricity will be unconstrained. In that case, there will be no change in behaviour from the introduction of offsets. Given the fact that electricity prices are lower when offsets are introduced, it is not surprising that total electricity consumption rises. In this respect, offsets also offset existing market power by providing a competitive electricity alternative. This raises consumer welfare. More interesting is the possibility that emissions might rise as a result of offsets. The example shows that for r  ( abbc1 , 2a 1c(1bb ) ) , the equilibrium condition holds but emissions rise compared with a situation where offsets are not present. This possibility is illustrated graphically as in Figure 4 where it is assumed that c  0 . That figure shows the demand function facing the monopolist with and without offsets; willingness to pay for dirty electricity falls. However, the monopolist prices off its „strategic‟ demand curve that takes into account offset reaction. It is off of this that a marginal revenue function drives the quantity choice is depicted. The intuition for this is that the monopolist‟s behaviour is now driven by its role in offsetting guilt. As the only strategic producer, if the monopolist increases their price, this also decreases the price of offsets and hence allows more competing production. The monopolist, therefore, has incentives to lower price but to achieve this in the face of competition sometimes requires more output than before.

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Figure 4: Emissions may increase $

Demand for dirty electricity without offsets

r

p* Demand for dirty electricity with offsets

po*

Strategic demand curve

q*

qo*

r Quantity

Thus, when offset price is endogenous, the strategic incentives of the monopolist are very different. 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 when offset price is endogenous.

6.

Should clean producers be strategic? The above analysis presumes the need for offsets to be purchased by guilt-ridden

consumers in order to subsidise clean electricity production. While it was assumed that such

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electricity had a higher long-run marginal cost than existing dirty electricity generation, the case for a subsidy would have to be made more carefully. Specifically, it is instructive to consider what happens without an offset market and whether an unsubsidised clean electricity provider – operating strategically – could result in lower levels of emissions than one that is non-strategic and subsidised through offsets. Once again, given the potential complexity, I return to our running example to analyse this case. Example: Consider a situation where a dirty and clean producer compete (Cournot) where dirty consumption reduces demand because of guilt but clean production is more expensive with r > c. Then it is easy to show the clean output will only be positive if a 2 c  r . Notice that with just a single dirty producer, p*  a 2 c . Thus, if price with a monopolist dirty producer is less than the marginal cost of clean production, that production will not enter the market. If a 2 c  r , it can be shown that qo*  a3(b2c1) r and o*  a 3cb2r . For the cases where offset prices are exogenous, whether this resulted in lower emissions would depend upon t. Specifically, recall that in those cases, emissions were equal to t and so an unsubsidised producer would lead to lower emissions if a3(b2c1)r  t . As t is presumably a policy choice, this could be achieved. More interestingly, when offset prices are endogenous, the lowest level of emissions are achieved when the monopolist acts non-strategically. In this case, the an unsubsidised clean producer will lead to lower emissions if r  a (21b)2(bb1) c . Thus, it is possible that if a clean producer is efficient enough, an unsubsidised situation would lead to better outcomes than a subsidised one. The intuition here is that when clean production is non-strategic but subsidised, consumers‟ demand for it is limited by the extent of the subsidy. With an unsubsidised model, consumers are not constrained by this but, in fact, prefer it as they do not feel guilt. Consequently, this causes the „dirty‟ producer to compete more aggressively and, in so doing, constrain the market power of clean producers. The end result can mean lower production by dirty producers compared to an offset market case.

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7.

Conclusion This paper has examined concerns that the voluntary purchase of carbon offsets by

consumers can lead to unintended consequences that actually cause emissions or net emission to rise. The key feature was to recognise that those purchasing offsets were likely to be those who were already curtailing consumption of „dirty‟ electricity and the like because of personal guilt over their emissions. While it is true that the purchase of offsets allows those people to alleviate their guilt and hence, consume more, net emissions fall. The consumption effect of offsets does not outweigh their ability to reduce emissions. The paper also examined several mechanisms by which offset purchases may have external effects that were harmful. For example, by causing demand to become more elastic for some commodities, prices might fall increasing consumption by those not purchasing offsets. However, when the proportion of guilt-free consumers is high (suggesting a large external impact), the impact on price is small, mitigating this. So on net emissions still fall. Nonetheless, a generic situation where offsets might harm net emissions is identified. This occurs when there is no latent demand for offsets but, due to pricing behaviour, 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; more than that supply expansion is countered by offset purchases. Another mechanism whereby offsets can impact on emissions was a direct one whereby offsets generated direct competition with the „dirty‟ good suppliers. Again this might cause a price reduction. However, in all but one model examined, quantity produced by „dirty‟ good suppliers also fell along with price. Offsets increased consumption overall but reduced total

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emissions. In one case where a strategic commitment was possible then it was possible that offsets could increase emissions. This suggests, however, that such instances are implausible. There are a number of empirical implications from the analysis here. Examining the link between offset markets and total consumption would be interesting as well as the impact between strategic behaviour and offset purchases. From a policy perspective, however, voluntary purchases of offsets would likely reduce environmental harm and should be seen as desirable alongside collective forms of emissions reduction such as emissions caps, carbon taxes and permit trading.

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