Tailored regulation: will voluntary site-specific environmental performance standards improve welfare?

1. Introduction

There is a growing consensus among policymakers that command-and-control environmental regulation stifles efficiency and innovation by requiring heterogeneous plants to adopt similar abatement strategies. While market-based instruments such as tradable permits and emissions fees address this problem, there are a variety of political and economic barriers to their immediate and widespread application. As a result, the last decade has witnessed a number of efforts to modify existing regulations to give individual plants more control over pollution abatement. Chief among these efforts at limited reform is Project XL, the flagship of the Environmental Protection Agency's (EPA) regulatory reinvention initiative. Participating plants are allowed to develop pollution control strategies that "replace or modify specific regulatory requirements" on the condition that these strategies improve their environmental performance (Federal Register 1995). In essence, Project XL defines voluntary site-specific performance stand ards that are more stringent than the de facto standards implied by current regulation and gives plants "regulatory flexibility" to meet these standards in unconventional ways.

Blackman and Mazurek (2001) provide detailed descriptions of the first eight XL projects to be implemented. Half of these projects involve replacing complex technology standards that require a plant to obtain new air permits whenever its production process changes with a single plantwide emissions cap that leaves the plant free to reconfigure its production and abatement process as long as total emissions do not exceed a predetermined limit. The plants implementing these four XL projects are in sectors where production processes change continuously and existing technology standards and permit requirements are particularly costly. (1)

Project XL has had a troubled history, in large part because of administrative problems at the EPA (Caballero 1998). Nevertheless, it will almost certainly emerge as a prototype for similar efforts. President Clinton touted it as a "regulatory blueprint for the future," a characterization that has pervaded analysis of the project (Phillips 1995). (2) Such characterizations appear increasingly credible. In the last several years, a number of influential policy reports have called upon Congress to replace command-and-control regulation with a performance-based system (National Academy of Public Administration 1997, 2000; Enterprise for the Environment 1998). Toward that end, the Second Generation of Environmental Improvement Act has been introduced in Congress to provide the legislative underpinnings for a broad-based Project XL-like program (Inside EPA Weekly Report 1999; Inside EPA 's Environmental Policy Alert 2001b). Recent pronouncements by Bush administration environmental officials affirm the continued i mportance of Project XL and similar regulatory initiatives (Inside EPA's Environmental Policy Alert 2001a; Whitman 2001). (3) A number of such programs have already been adopted at the state level (Larsen 1998; Inside EPA's Environmental Policy Alert 2000).

All of these programs-which we refer to as tailored regulation (TR) programs-have common characteristics that we have alluded to above: They are voluntary (i.e., plants choose whether or not to participate), they entail a shift away from technology and process standards and toward more flexible performance standards, and they require participating plants to demonstrate "superior environmental performance." (4) In addition, TR programs have two characteristics we have not yet touched upon. First, they require firms to pay a fixed cost to participate. This cost is for negotiating a performance standard with regulators, developing monitoring procedures, and (in some cases) investing in new types of pollution control equipment. For example, Blackman and Mazurek (2001) found that the average fixed cost of putting Project XL agreements in place is approximately $325,000 per firm, not counting the costs of new pollution control equipment. Second, TR programs emphasize the diffusion of "regulatory innovations" develo ped at participating plants to nonparticipating plants. The EPA claims that diffusion is the principal aim of Project XL. The Second Generation legislation also stresses transfer of the benefits of plant-specific agreements. (5)

From the point of view of firms, the main attraction of TR is the significant cost savings that can arise from being allowed to circumvent "one size fits all" command-and-control regulations. While TR requires an improvement in environmental performance that would raise costs, all other things being equal, and that could theoretically completely offset cost savings from regulatory flexibility, the net impact of TR is always to reduce a participant's marginal production costs, that is, to shift the participant's marginal cost curve down. The reason for this is simply that TR is voluntary, and a plant will choose to pay a fixed participation cost only if marginal costs fall. The experience of Project XL participants confirms this logic. For example, a pulp-manufacturing plant that was allowed to substitute plantwide caps on air, water, and hazardous waste emissions for conventional technology and effluent standards reported savings of $200,000 in materials costs in the first year of the project and predicted ov er $10 million in savings during the 15-year term of the agreement. Several other XL participants have reported cost savings of similar magnitudes (U.S. Environmental Protection Agency 1999b). (6) It is important to note that TR participants do not necessarily achieve cost savings because they adopt innovations that enable them to produce both "cheaper and cleaner." Rather, their costs fall because they are able to circumvent inefficient command-and-control regulations.

There are at least two reasons to believe that TR will enhance welfare. First, as just noted, TR can generate significant cost savings for industry. In addition, the superior-environmental-performance rule ensures that environmental quality will not deteriorate. Notwithstanding these benefits, one troubling feature of TR is that it enables participating firms to operate under a different set of guidelines than their competitors. Therefore, TR could have detrimental welfare impacts by providing cost savings--and hence a competitive advantage--to selected firms. Stakeholders increasingly recognize that site-specific regulatory flexibility can have competitive impacts (Inside EPA 2001a).

In this paper, we analyze whether and how TR, compared with a command-and-control regime, can reduce social welfare, and we develop policy prescriptions aimed at avoiding undesirable outcomes. Using a simple model of competitive interaction, we find that TR can reduce welfare in oligo-polistic markets. Although TR always has a positive impact on consumers' surplus (because output prices fall) and on environmental quality (because of the superior-environmental-performance rule), it can reduce producers' surplus by lowering the production costs of relatively inefficient firms, thereby helping these firms "steal" market share from more efficient firms. We also find that regulators' efforts to diffuse the benefits of TR agreements among nonparticipating firms dampen incentives for firms to participate for the same reason that incentives to invest in conventional research and development are dampened when firms are able to free-ride on their competitors' investments.

A brief survey of the relevant literature is presented in section 2. In section 3, a generic modeling framework is developed. Using this framework, the properties of TR assuming monopoly and duopoly are examined in sections 4 and 5, respectively. A summary and conclusions are presented in section 6.

2. Literature

To our knowledge, this is the first economic analysis of voluntary site-specific performance standards. However, it contributes to a growing literature on the economics of voluntary regulation.

The literature has focused on three types of explanations for firms' willingness to enter into voluntary regulatory agreements. The first explanation is that in undertaking voluntary agreements, firms seek either to preempt future regulation and enforcement or to encourage more stringent de facto regulation in order to raise rivals' costs. For example, Segerson and Miceli (1998) suggest that a "background legislative threat" motivates participation in a voluntary agreement (along with government abatement cost subsidies and the promise of lower compliance and transaction costs).

A second explanation for participation in voluntary agreements is that firms seek to capture consumers willingness to pay for goods produced in an environmentally friendly manner. For example, using a vertical product quality model, Arora and Gangopadhyay (1995) show that firms may voluntarily overcomply with regulatory standards in order to attract high-income green consumers.

A third explanation is that firms enter into voluntary agreements to reduce their production costs. This is the motivation for firms to participate in TR in our model: The regulatory flexibility TR confers lowers firms' production costs. By contrast, almost all existing analyses concern voluntary agreements that raise production costs (Brau and Carraro 1999).

Our model is also distinguished from the bulk of the literature on voluntary regulation by its focus on competition. We adopt this focus because as a firm-specific cost-saving regulatory option, TR clearly can have competitive impacts. Few other papers have focused explicitly on the link between voluntary regulation and competition. However, Brau and Carraro (1999) survey related literature to draw some preliminary conclusions. Like us, Brau and Carraro find that there may be a tradeoff between the environmental benefits of voluntary regulation and the economic costs, although they reach these conclusions for different reasons. (7)

Aside from its implications for voluntary regulation, our paper is also relevant to the literature on asymmetric cost effects in oligopolistic markets. It draws upon Carraro and Soubeyran's (1996) and (especially) Dung's (1993) analyses of how firm-specific taxes affect welfare in a Cournot oligopoly with asymmetric costs. A firm-specific subsidy in these models is similar to a cost-reducing TR agreement in our model. However, in our model, firms must pay a fixed cost to get a "subsidy" and are able to freely choose whether or not to get subsidies, a feature that results in a market equilibrium with properties different from those of standard Cournot models. Our analysis also resembles models of cost-saving technological innovation in an oligopoly (e.g., Lahiri and Ono 1988) and models of merger in an oligopoly (e.g., Farrell and Shapiro 1990). The counterintuitive insight from these papers is that in an oligopoly, lowering the production costs of relatively inefficient firms can reduce welfare by shifting ma rket share away from efficient firms.

3. Generic Model

In this section, we develop a generic modeling framework to be used to analyze TR in two different types of markets: a monopoly and a duopoly. In essence, we model TR as a reduction in variable production costs that firms may "purchase" for a fixed participation cost. In this section, as in those that follow, we relegate proofs to the Appendix.

We assume there are three types of agents: an environmental regulator, firms indexed by i, and a representative consumer. The regulator offers selected firms a choice between two regulatory regimes: command-and-control (C) and TR (T). The two regimes are indexed by r [member of] (C, T). Each regime is defined by three variables: [t.sup.ir], the fixed costs paid by firm i to participate in regime r; [e.sup.ir], firm i's environmental performance standard under regime r ([e.sup.iC] is the de facto performance standard implied by command-and-control regulation); and [x.sup.ir], an index of firm i's marginal costs under regime r. (8) As discussed below in more detail, [x.sup.ir] indexes firm i's marginal costs net of the marginal costs of meeting the environmental performance standard. To keep the exposition simple, we normalize the command-and-control parameters to zero, that is, [t.sup.iC] = [e.sup.iC] = [x.sup.iC] = 0, and we assume that [x.sup.iT] is negatively correlated with marginal costs, that is, the lar ger [x.sup.iT] is, the lower marginal costs are for every level of output. The fixed costs are exogenous, that is, independent of the regulator's specific choice of [x.sup.iT]. We make the following assumption about TR.

ASSUMPTION 1. Relative to command-and-control, TR entails a more stringent environmental performance standard, lower marginal production costs for every level of output, and a higher fixed participation cost, that is, [e.sup.iT] [greater than or equal to] 0, [x.sup.iT] > 0, and [t.sup.iT] > 0.

This assumption formalizes the description of TR in the introduction. To briefly reiterate the intuition for the effect on marginal costs, TR always has countervailing impacts on a participant's marginal cost curve. Requiring the firm to meet a more stringent environmental performance standard shifts the curve up, but allowing it to circumvent restrictive command-and-control regulations shifts the curve down. The second effect always dominates the first. The reason for this is that TR is voluntary and also entails significant fixed costs. As a result, a firm will never choose to participate unless the net effect of TR is to reduce marginal costs. (9) Thus, [x.sup.iT] indexes TR's net negative effect on marginal costs. Graphically, [x.sup.iT] measures the downward shift of the finn's marginal cost curve. To keep the exposition simple, we assume that TR's impact on marginal costs is invariant to output; that is, [x.sup.iT] is independent of [q.sup.iT]. For convenience, we refer to [x.sup.iT] as the "cost savin gs" TR provides to firm i.

The regulator offers selected firms a take-it-or-leave-it choice between [x.sup.iC] and [x.sup.iT] given [t.sup.iC] and [t.sup.iT]. Firms choose r and a level of output, [q.sup.ir], to maximize profit given the regulator's TR offer. That is, firms solve

[max.sub.(r,[q.sup.i])] [[pi].sup.ir] ([q.sup.ir] \ [x.sup.ir], [t.sup.ir]) = p(Q)[q.sup.ir] - [c.sup.i]([q.sup.ir] \ [x.sup.ir]) - [t.sup.ir], (1)

where [[pi].sup.ir] is profit, p(*) is an inverse demand function, Q = [[SIGMA].sub.i] [q.sup.ir] is the total market quantity, and [c.sup.i](*) is a variable cost function. We make the following assumptions about the demand and cost functions (we use subscripts to denote partial derivatives and primes to denote derivatives of functions with one argument).

ASSUMPTION 2. The inverse demand function

(i) is decreasing in market quantity (p' < 0) and

(ii) satisfies [q.sup.i]p" + p' < 0.

Part (ii) is the standard stability condition for Cournot oligopoly. (10) Intuitively, it implies that the marginal revenue curve is steeper than the market demand curve.

ASSUMPTION 3. The cost function has the following characteristics:

(i) variable costs are increasing and convex in [q.sup.ir] ([c.sub.q] > 0 and [c.sub.qq] > 0),

(ii) variable costs are decreasing and convex in [x.sup.iT] ([c.sub.x] < 0, [c.sub.xx] > 0),

(iii) marginal costs are decreasing in [x.sup.iT] ([c.sub.qx] < 0), and

(iv) the effect of [x.sup.iT] on marginal costs is invariant to [q.sup.iT] ([c.sub.qxq] = 0).

Firms can be thought to solve Equation 1 by first determining the profit-maximizing output for each regime, [q.sup.[iC.sub.*]] and [q.sup.[iT.sub.*]], and then comparing the maximized levels of profit for each regime, [[pi].sup.[iC.sub.*]] and [[pi].sup.[iT.sub.*]] to choose [r.sup.*]. Firm i's first-order condition for the choice of [q.sup.[ir.sub.*]] is

p + [q.sup.ir]p' - [c.sup.ir.sub.q] = 0. (2)

Assumption 2(ii) is sufficient to guarantee that the second-order condition is met. Firm i will choose [r.sup.*] = T, that is, it will participate in TR, if and only if

[[pi].sup.[iT.sub.*]] ([q.sup.[iT.sub.*]] \ [x.sup.iT], [t.sup.iT]) - [[pi].sup.[iC.sub.*]]([q.sup.[iC.sub.*]] \ 0,0) [greater than or equal to] 0. (3)

The following result will prove useful in examining the welfare impacts of TR under monopoly and duopoly.

LEMMA 1. To induce a firm to participate, the regulator must offer an [x.sup.T] such that variable cost savings from the TR agreement are at least as great as the fixed participation cost.

It will also prove useful to define [x.sup.T] to be the critical value of [x.sup.T] such that Equation 3 holds as an equality. That is,

[[pi].sup.[iT.sub.*]] ([q.sup.[iT.sub.*]] \ [x.sup.T], [t.sup.iT]) - [[pi].sup.[iC.sub.*]] ([q.sup.[iC.sub.*]] \ 0, 0) = 0. (4)

Thus, [x.sup.T] is the cost savings that makes the firm indifferent to participation given the fixed participation costs.

4. Monopoly

To assess the effect of TR on welfare in a monopoly, we first derive the following result.

LEMMA 2. In a monopoly, participation in TR increases equilibrium output.

The intuition for this lemma is simply that TR reduces marginal costs, thereby making it profitable to increase output.

To analyze the effect of TR on welfare, we assume a representative consumer who maximizes a utility function, u(q, e), that is increasing and concave in both q and e ([u.sub.q] > 0, [u.sub.qq] < 0, [u.sub.e] > 0, [u.sub.ee] < 0).

PROPORTION 1. In a monopoly, participation in TR unambiguously increases welfare.

The intuition for this proposition is straightforward. The impact of TR on welfare in a monopoly can be broken down into the agreement's impacts on environmental quality, producers' surplus, and consumers' surplus. The environmental impact is always positive because of the superior-environmental-performance constraint. The impact on producers' surplus is always positive because of the participation constraint, which ensures that TR increases the monopolist's profit. The impact on consumers' surplus is positive since TR reduces marginal costs and therefore increases equilibrium output.

Finally, we examine a monopolist's incentives to participate in TR.

LEMMA 3. In a monopoly, [x.sup.T], the reservation level of the TR cost savings, is increasing in t, the fixed participation cost.

Thus, to the extent that the regulator is able to reduce the fixed participation cost, t, it can offer a lower cost savings, [x.sup.T], and still induce participation.

5. Duopoly

In this section, we assume the regulator introduces TR into a Cournot duopoly. Each duopolist's objective function is given by Equation 1, except now Q = [[SIGMA].sub.i] [q.sup.ir]. In this version of the model, each firm's output and participation decisions depend on its rival's decisions. In addition, these decisions depend on the regulator's policies regarding the administration of TR: whether one or both firms are offered TR agreements and whether or not TR agreements "diffuse," that is, whether firms can appropriate the cost-reducing features of their competitor's agreements without paying a fixed cost (we define diffusion more precisely below). Regardless of how TR is administered, only a limited number of "outcomes" are possible: either zero, one, or two firms participate, and either zero, one, or two firms pay fixed costs to participate. Therefore, to make the exposition more concise, we first examine the welfare implications of each of these outcomes. Then, we examine how different administrative pol ices generate the different outcomes. This approach avoids having to repeat the derivation of welfare results for each policy scenario.

This section is organized as follows. The first subsection analyzes the welfare consequences of the various outcomes. The remaining subsections consider various TR policy regimes. The second subsection considers a TR regime in which the regulator arbitrarily selects one of the two duopolists to participate and does not allow TR agreements to diffuse. The third subsection considers a TR regime in which the regulator arbitrarily selects one of the two duopolists to participate and does allow TR agreements to diffuse. Finally, the last subsection examines a TR regime in which the regulator offers both firms TR agreements.

Welfare Properties of TR in Duopoly (11)

In a heterogeneous Cournot duopoly, firms' market shares depend on their marginal costs. Hence, TR agreements that reduce marginal costs also affect market share. For example, if firm f participates in TR but firm j does not, then firm f's market share will increase and firm j's will decrease. This is illustrated in Figure 1. Equilibrium is given by the intersection of the two reaction functions. Graphically, all other things being equal, a cost-reducing TR agreement changes the slope of a participant's reaction function so as to increase its market share. When both duopolists participate in TR, the net effect on market share will depend on the specifics of the two TR agreements.

In order to derive welfare results, we first need to establish the impact of TR on total market output and individual firms' outputs. Regarding the former, we need to know whether the introduction of asymmetric cost-reducing TR agreements into a Cournot duopoly can reduce total market output. Is it possible that the reduction in output due to one firm's loss of market share swamps the increase in output due to its rival's gain? The answer is no.

PROPOSITION 2. In a Cournot duopoly, if either or both firms participate in TR, industry output increases.

Next, we consider the impact of TR on a firm's own output.

PROPOSITION 3. In a Cournot duopoly, firm f's output will increase under TR if and only if (i) firm f participates but firm j does not or (ii) both firms participate and [x.sup.f] is sufficiently large relative to [x.sup.j].

The intuition for the proposition is as follows. As Figure 1 makes clear, when only one firm participates, its marginal costs fall relative to its competitor's, and its market share and output rise. When both firms participate, both firms' marginal costs fall. However, if the ratio of the two firms' marginal costs changes sufficiently, the firm whose costs rise relative to its competitor's costs will lose market share. In this case, the direct positive effect of the reduction in marginal costs on output may be swamped by the indirect negative effect of the loss of market share. As a result, the firm's output may fall.

Given Propositions 2 and 3, we may now consider how TR affects welfare.

PROPOSITION 4. In a Cournot duopoly, TR may reduce welfare if either one or both firms participate.

The intuition for Proposition 4 is as follows. As in the monopoly case, the impact of TR on welfare can be broken down into its impacts on environmental quality, producers' surplus, and consumers' surplus. TR's environmental impact is always positive because of the superior-environmental-performance constraint. TR's impact on consumers' surplus is also always positive since Proposition 2 guarantees that TR always increases market output and therefore lowers market price. However, TR's impact on producers' surplus--the sum of the profits of the two firms--can be either positive or negative. If the impact on producers' surplus is sufficiently negative, net welfare can fall.

How can TR reduce producers' surplus? Recall that TR affects duopolists' market shares. TR reduces producers' surplus when the market share loser's reduction in profit outweighs the market share winner's increase in profit. This happens when the winner has higher initial marginal costs--and therefore a lower profit margin--than the loser. In short, TR will reduce producers' surplus when it shifts production from an efficient firm to an inefficient firm. For example, when only one firm participates, that firm gains market share at its rival's expense. As a result, the participants' profits rise, while the nonparticipant's profits fall. If the participant is less efficient than the nonparticipant, the reduction in the nonparticipant's profits can outweigh the increase in the participant's profits, and producers' surplus can fall. For a numerical example in which market stealing generates a welfare loss, see Blackman and Boyd (2002).

The next three subsections explore firms' incentives to participate in three TR policy regimes defined by different assumptions about which of the firms are offered TR agreements and whether TR agreements diffuse. We use the results derived in the present subsection to analyze the welfare impacts of TR in these three regimes.

Duopoly with Arbitrary Selection and No Diffusion

In this section, we assume that the regulator offers only one of the two duopolists, say, firm an opportunity to participate in TR. This assumption is meant to approximate a TR regime in which certain firms are more or less arbitrarily selected to participate and little effort is made to ensure that the "regulatory innovations" developed under the program are diffused to other firms. Note that the political and legal practicality of such a regime (beyond a pilot stage) is questionable. This section is primarily meant as a benchmark for following sections.

Firm f's participation decision in this scenario is straightforward. The regulator must offer firm f an agreement [x.sup.T] > [x.sup.T] in order to induce participation (Eqn. 4). As in the monopoly case, [x.sup.T] is increasing in t. As for social welfare, Proposition 3 dictates that firm f participates, its output will increase. The proof of Proposition 4 in the Appendix shows that welfare will fall when the ratio of firm f's marginal costs to firm f's marginal costs is sufficiently large, that is, when firm f is sufficiently inefficient compared with firm j.

Duopoly with Arbitrary Selection and Costless Diffusion

In this section, we assume that the regulator selects one of the two duopolists, say, firm f, to participate in TR but also ensures that the same TR agreement costlessly diffuses to firm j. In other words, the regulator grants both firms the same regulatory flexibility and holds both to the same more-stringent environmental standard. However, the regulator does not require firm j to pay the fixed participation cost, [t.sup.fT]. (12) This regulatory scenario is meant to capture TR programs like Project XL in which the regulator makes a determined effort to ensure that "regulatory innovations" developed by participants are diffused throughout the industry.

It is important to note that costless diffusion will not necessarily confer the same cost benefits ([x.sup.jT]) on firm j and firm f, even though both firms receive the same regulatory flexibility and both are held to the same more-stringent environmental standard. The reason for this is that the two firms have different cost functions. This heterogeneity reflects, among other things, differences in human and physical capital as well as differences in the way these and other inputs are used to abate polluting emissions and to innovate to achieve cost reductions. Hence, given diffusion, [x.sup.jT] = [lambda][x.sup.fT], where [lambda] is a positive parameter that may be greater than, equal to, or less than unity. We first show that costless diffusion dampens incentives to participate.

PROPOSITION 5. In a TR regime with arbitrary selection and costless diffusion, (i) the regulator must offer a higher [x.sup.T] than when diffusion does not occur, and (ii) for some parameterizations of the model, the regulator may not be able to induce any participation.

Thus, firm f's incentives to participate in TR are dampened when firm j is able to appropriate the cost savings, since the appropriation erodes firm f's market share and profits. From a policy perspective, this implies that the regulator may want to limit the diffusion of TR agreements in order to encourage participation. There is a clear analogy to patents that strengthen firms' incentives to invest in research and development by limiting the ability of competing firms to free-ride on such investments.

Next, we consider welfare.

PROPOSITION 6. A TR regime with arbitrary selection and costless diffusion may reduce welfare.

The intuition for Proposition 6 is the same as that for Proposition 4: TR can reduce producers' surplus, and therefore welfare, when it changes the two firms' marginal costs in a way that enables an inefficient firm to steal market share from an efficient firm. (13)

Happily, however, the fact that TR is voluntary ensures that welfare losses in an arbitrary selection/costless diffusion regime are possible only if the regulator selects the inefficient firm to participate. TR reduces welfare when it shifts market share from an efficient firm to an inefficient one. Efficient firms will never voluntarily participate in TR programs that have this effect.

Duopoly with Industrywide Offers

In this section, we assume that TR agreements are simultaneously offered to both competitors. Given this assumption, the participation decision is game-theoretic: each firm's participation decision affects its rival's decision. (14) In what follows, we first describe the pure-strategy Nash equilibrium in the "participation game" and show how it depends on the terms of the TR offers, ([x.sup.fT], [t.sup.fT]) and ([x.sup.jT], [t.sup.jT]). Next, we consider the impact of costless diffusion. Finally, we discuss welfare.

To simplify the exposition, we use [[pi].sup.fr]([x.sup.fr] [x.sup.jr], [t.sup.fr]) to represent firm f's profits under each regime. The idea is to convey in a concise manner that firm f's profits depend on whether or not firm f participates ([x.sup.fT] > 0 vs. [x.sup.fC] = 0), given firm j's decision to participate or not ([x.sup.jT] > 0 vs. [x.sup.jC] = 0) and given the exogenous fixed participation cost associated with the regulatory regime firm f chooses ([t.sup.fT] > 0 vs. [t.sup.fC] = 0). Using this notation, the payoffs in the participation game are represented in Figure 2.

Given these payoffs, we may characterize the pure-strategy Nash equilibria as a function of [x.sup.fT] and [x.sup.jT], holding constant the fixed participation costs for both firms, [t.sup.fT] and [t.sup.jT]. To keep the analysis simple, we do not explore mixed-strategy equilibria or equilibria in which side payments between firms are allowed. The intuition for the equilibrium is that when the [x.sup.iT] values are small, neither firm will participate, since small [x.sup.iT] values will not compensate the firms for the fixed costs of participation, [t.sup.iT]. By contrast, when the [x.sup.iT] values are large, one or both of the firms may choose to participate.

More formally, it is useful to first define two critical levels of [x.sup.iT], which we will call [x.sup.iT.sub.L] and [x.sup.iT.sub.H] (where the subscripted L and H indicate low and high, respectively). Let [x.sup.iT.sub.L] be the [x.sup.iT] such that

[[pi].sup.i]([x.sup.iT] \ 0, [t.sup.iT]) = [[pi].sup.i](0 \ 0,0) (5)

for a given fixed participation cost paid by firm i ([t.sup.iT]). In other words, [x.sup.iT.sub.L] is the cost savings that makes firm i indifferent to participating given that its rival does not participate. Note that [x.sup.iT.sub.L] is equal to [x.sup.T], defined in the second subsection above. Similarly, let [x.sup.iT.sub.H] be the [x.sub.iT] such that

[[pi].sup.i] ([x.sup.iT] \ [x.sup.g[not equal to]iT], [t.sup.iT]) = [[pi].sup.i](0 \ [x.sup.g[not equal to]iT], 0). (6)

In other words, [x.sup.iT.sub.H] is the cost savings that makes firm i indifferent to participation given that its rival does participate. We assume that [t.sup.iT] is small enough that an [x.sup.iT.sub.H] exists. With these definitions we can show the following.

LEMMA 4. In an industrywide-offers TR regime, firms require a larger cost savings to induce them to participate when their rival also participates, that is, [x.sup.iT.sub.L] < [x.sup.iT.sub.H].

We may now characterize the Nash equilibria of the participation game as a function of the [x.sup.iT] values offered to the firms and of [t.sup.iT] values associated with participation.

PROPOSITION 7. There are three general types of pure-strategy Nash equilibria in an industrywide-offers TR regime. Which equilibrium obtains depends on the [x.sup.iT] values as follows:

(i) when [x.sup.fT] < [x.sup.fT.sub.L] and [x.sup.jT] < [x.sup.fT.sub.L], neither firm participates,

(ii) when [x.sup.fT] > [x.sup.fT.sub.H] and [x.sup.jT] > [x.sup.jT.sub.H], > both firms participate, and

(iii) in all other cases, only one of the two firms participates.

The specifics of the various cases in which only one of the two firms participates (part (iii) of the Proposition 7) are detailed in the proof in the Appendix.

Next, we consider how the fixed participation costs, [t.sup.fT] and [t.sup.jT], affect the equilibria. First, note that the fact that [[pi].sup.iT] is decreasing in [t.sup.iT] implies that both [x.sup.iT.sub.L] and [x.sup.iT.sub.H] are increasing in [t.sup.iT]. Given this result and Lemmas 1 and 4, we can graphically illustrate the relationship between cost savings, [x.sup.iT], and participation costs, [t.sup.iT], holding constant the terms of the TR agreement ([x.sup.g[not equal to]iT]) offered to the other firm (Figure 3). From Lemma 4 and the result just noted, we know that when [x.sup.iT.sub.L] and [x.sup.iT.sub.H] are drawn as functions of [t.sup.iT], both are increasing in [t.sup.iT], and [x.sup.iT.sub.L]([t.sup.iT]) lies below [x.sup.iT.sub.H]([t.sup.iT]). In addition, Lemma 1 implies that both functions intersect the origin.

Figure 3 illustrates that low values of [x.sup.iT] combined with high values of [t.sup.iT] will produce equilibria in which neither firm participates; high values of [x.sup.iT] combined with low values of [t.sup.iT] will produce equilibria in which both firms participate; and intermediate values of [x.sup.iT] and [t.sup.iT] will produce equilibria in which only one firm participates. In sum, the lower the fixed participation costs, the less (privately) desirable an agreement has to be in order to induce participation.

Next, consider the participation game equilibrium when the regulator allows costless diffusion. In this case, both firms are offered a TR agreement, but if one firm participates (i.e., pays the fixed participation cost), its rival can costlessly appropriate the cost savings. There will clearly never be a Nash equilibrium in which both firms pay the fixed participation cost, since one of the firms can always increase its profits by not paying. Hence, this scenario is substantively equivalent to that described in the preceding subsection in which only one firm is offered a TR agreement but the other firm can costlessly appropriate the benefits. The effect of diffusion is the same: It dampens incentives to participate.

Finally, consider the effect of an industrywide-offers TR regime on social welfare. Proposition 4 dictates that welfare losses may occur when an inefficient firm steals market share from an efficient firm. This can happen when the inefficient firm participates in TR by itself and also when it participates along with its more efficient rival. Proposition 7 and Figure 3 indicate what types of TR agreements generate equilibria in which one or both firms participate.

Note that in an industrywide-offers regime, firms may participate in TR even though participation makes them worse off than they would be under command-and-control. This can happen when one firm, say, firm f, is offered a significantly larger cost reduction than its rival, firm j. In such cases, firm f will always participate, and firm j will lose market share whether it participates or not. However, firm j will minimize its losses if it participates. In other words, TR can generate prisoners'-dilemma-type situations in which firms would be better off if TR were never introduced but nevertheless have a dominant strategy to participate. (15)

6. Conclusion

We have shown that voluntary site-specific performance standards (TR) can reduce social welfare in certain market settings. In a monopoly, TR always improves welfare: it has a positive impact on the environment, on consumers' surplus, and on producers' surplus. However, in a Cournot duopoly, TR can reduce welfare. It has a positive impact on the environment and on consumers' surplus. However, TR can reduce producers' surplus by helping relatively inefficient firms steal market share from more efficient competitors. More precisely, TR lowers participating firms' marginal costs and therefore affects their market share. In general, one firm will lose market share and its rival will gain. Producers' surplus--the sum of the firms' profits--can decline if the loser's loss outweighs the winner's gain. This occurs when the loser has relatively low marginal costs and therefore a relatively large profit margin compared with the winner.

Regulators can try to ensure that TR attracts participants and enhances welfare by carefully choosing which firms participate, the cost savings ([x.sup.iT]) offered to each firm, and the extent to which TR agreements are allowed to diffuse to nonparticipating firms. With regard to the selection of firms and the terms of the agreement, we have shown that the regulator can avoid welfare losses by ensuring that relatively inefficient firms are not singled out for participation or particularly advantageous agreements. This is more easily done in an arbitrary selection regime than in an industrywide-offers regime. However, even if this strategy can be successfully implemented, it has an important drawback: It implies that regulators should provide cost breaks to market leaders, a policy that smacks of inequity and would likely run into stiff political opposition. Moreover, such a policy could result in increased market concentration and the exit of smaller firms. In this paper, we have abstracted from exit in orde r to focus on adverse welfare impacts from market stealing. Nevertheless, undesirable exit is a valid concern, and intuition suggests that while TR administrators should ensure that inefficient firms are not the principal beneficiaries of the TR regime, they should also ensure that efficient firms are not helped to such an extent that their competitors are forced to exit.

Happily, in practice, even if regulators do not actively select relatively efficient firms to participate, political-economic considerations are likely to favor the participation of such firms. With in-house environmental management and lobbying capabilities and relatively easy access to investment capital, large market leaders (which are presumably relatively efficient) can more easily pay the fixed cost of participation in TR. The Project XL experience thus far would appear to confirm this hypothesis. Blackman and Mazurek (2001) found that of the first eight firms to implement Project XL agreements, six were among the top three firms in their industries in terms of market share.

With regard to the regulator's policy about whether TR agreements are allowed to costlessly diffuse among nonparticipating firms, we have demonstrated that the voluntary nature of TR ensures that diffusion cannot lead to welfare losses by enabling inefficient nonparticipating firms to steal market share from more efficient participants. However, diffusion clearly dampens firms' incentives to participate. In fact, we have shown that in some situations, when diffusion is costless, it may not be possible to induce participation no matter how attractive the terms of the TR agreement are. (16) Therefore, the regulator may want to limit diffusion in order to generate formal participation, along with its attendant benefits, including improved environmental quality (assuming that performance standards under TR are in fact significantly more stringent than those under command-and-control).

However, diffusion of TR agreements clearly has economic benefits as well. It reduces firms' marginal costs and thereby enhances consumers' surplus. This benefit may be sufficient to offset any potential loss in producers' surplus. Hence, in setting a diffusion policy, the regulator must balance potential welfare benefits against costs. This calculation is likely to vary across industries.

Finally, our findings highlight the desirability of minimizing the fixed costs of participation in TR. Given that TR agreements must reduce marginal costs in order to induce participation, there is clearly a tradeoff between the amount of cost-reducing regulatory flexibility an agreement entails and the amount of environmental benefit it requires ([e.sup.iT]). However, we have seen that lower participation costs imply that regulators can induce participation with less attractive offers (lower [x.sup.iT] values). Therefore, one means of allowing for more of each type of benefit is to find ways of reducing fixed participation costs. Although we have modeled fixed participation costs as exogenous, in practice, regulators have some control over them. For example, in the case of Project XL, empirical research has indicated that management problems at the EPA and uncertainty about the statutory foundation of the initiative are key contributors to participation costs. Accordingly, management and legal reforms that reduce participation costs have the potential to generate more participation and to improve environmental performance.

Appendix: Proofs of Lemmas and Propositions

PROOF OF LEMMA, 1. The participation constraint (Eqn. 3) may be written as

[[integral].sup.[x.sup.T].sub.0] d[pi]*/dx dx [greater than or equal to] [t.sup.T].

Using the envelope theorem,

[[integral].sup.[x.sup.T].sub.0] [-C.sub.x] dx [greater than or equal to] [t.sup.T]. (A1)

QED.

PROOF OF LEMMA 2, Totally differenting the first-order condition (Eqn. 2) yields

dq*/dx = [C.sub.qx]/(p' + qp" + p' - [C.sub.qq]) > 0,

since the numerator is negative by Assumption 3 and the denominator (the second-order condition) is negative by Assumption 2. QED.

PROOF OF PROPOSITION 1. Given a representative consumer and a monopolistic producer, welfare (w) is given by

w = u(q,e) - c(q\[x.sup.T]) - [t.sup.T].

We differentiate totally to indicate the direction in which welfare moves as a result of increases in x, e, and t associated with participation in TR. Using [u.sub.q] = y yields

dw = [u.sub.e]de + dq*/dx (p - [c.sub.q])dx - [c.sub.x]dx - dt. (A2)

The total impact of a TR agreement is given by

[[integral].sup.[e.sup.T].sub.0] [u.sub.e]de + [[integral].sup.[x.sup.T].sub.0] dq*/dx (p - [c.sub.q])dx - [[integral].sup.[x.sup.T].sub.0] [c.sub.x]dx -[[integral].sup.[t.sup.T].sub.0] dt. (A2')

The first term is nonnegative by Assumption 1. The second term is positive, since dq*/d[x.sup.T] is positive by Lemma 2 and since the expression in parentheses-the markup of price over marginal cost-is clearly positive. The third term is positive by Assumption 3. Lemma 1 ensures that the sun of the third and fourth terms is positive. Thus, the total effect of TR is to increase welfare. QED.

PROOF OF LEMMA 3. We can be certain that there is only one such value of [x.sup.T], since [[pi].sup.T] (.) is strictly increasing in [x.sup.T] while [[pi].sup.C](.) is constant in [x.sub.T]. Taking the total derivative of Equation 4 and using the envelope theorem yields

d[x.sup.T]/dt = -1/[c.sub.x]>0.

QED.

PROOF OF PROPOSITION 2. Totally differentiating the first order conditions (Epn. 2) for each firm yields

[[alpha].sup.f] [summation over (i)]d[q.sup.i] + d[q.sup.f] - [[beta].sup.f]d[x.sup.f] = 0 (A3)

[[alpha].sup.j] [summation over (i)]d[q.sup.i] + d[q.sup.j] - [[beta].sup.j]d[x.sub.j] = 0, (A3')

where

[[alpha].sup.i] = [q.sup.i]q" + p'/p' - [c.sup.i.sub.qq] > 0 (A4)

by Assumptions 2 and 3. Also,

[[beta].sup.i] = [c.sup.i.sub.qx]/p' - [c.sup.i.sub.qq]>0 (A5)

by Assumptions 2 and 3. Summing these total differentials over both firms yields

[summation over (i)][[alpha].sup.i] [summation over (i)]d[q.sup.i] + [summation over (i)][[beta].sup.i]d[x.sup.i] = 0.

Rearranging,

[summation over (i)]d[q.sup.i] = [summation over (i)][[beta].sup.i]d[x.sup.i]/[DELTA] >0, (A6)

where

[DELTA] = [summation over (i)][[alpha].sup.i] + 1.

The sum of the differentials in Equation A6 is positive, since [[alpha].sup.i], [[beta].sup.I]. and d[x.sup.i] are all positive. QED.

PROOF OF PROPOSITION 3. Subsitutiong Equation A6 into Equation A6 into Equation A3 and solving for d[q.sup.f] yields

d[q.sup.f] = [[beta].sup.f]d[x.sup.f] -[[alpha].sup.f] [summation over (i)][[beta].sup.i]d[x.sup.i]/[DELTA]. (A7)

If only firm f participates, then

d[q.sup.f]/d[x.sup.f] = [[beta].sup.f] ([[alpha].sup.j] + 1)/[DELTA]>0. (A8)

If both firms participate, then Equation A7 implies that d[q.sup.f] [greater than or equal to] 0 if and only if

d[x.sup.f]/d[x.sup.j] [greater than or equal to] [[alpha] .sup.f][[beta].sup.j]/[[beta].sup.f]([[alpha].sup.j] + 1).

QED.

PROOF OF PROPOSITION 4. Welfare is given by

w = u ([summation over (i)] [q.sup.i],[e.sup.f],[e.sup.j]) - [summation over (i)] {[c.sup.i]([q.sup.i]\[x.sup.i]\) + [t.sup.i]}.

Differentiating totally and using [u.sub.Q] = p yields

dw = ([u.sub.e][de.sup.f] +[u.sub.e][de.sup.j]) + (p - [c.sup.f.sub.q])[dq.sup.f] - [c.sup.f.sub.x][dx.sup.f] -[dt.sup.f] + (p-[c.sup.j.sub.q])[dq.sup.j] - [c.sup.j.sub.x][dx.sup.j] - [dt.sup.j]. (A9)

Using Equation A7 to substitute out [dq.sup.i] yields

[FORMULA NOT REPRODUCIBLE IN ASCII] (A10)

If only firm f participates then [dx.sup.j] = [dt.sup.j] = 0, and this expression reduces to

[FORMULA NOT REPRODUCIBLE IN ASCII] (A11)

The total impact of TR on welfare is given by the integral of Equation A11 over the ranges x [member of] [0, [x.sup.T]], t [member of] [0, [x.sup.T]], and e [member of] [0, [e.sup.T]], (i.e., the analog of Eqn. A2'). The superior-environmental-performance constraint (Assumption 1) ensures that the integral of the first term is positive. The participation constraint (Eqn. 4) ensures that the sum of the integrals of the last two terms is positive. A sufficient condition for the integral of the second term to be positive is

(p - [c.sup.f.sub.q]) > [[alpha].sub.j] ([c.sup.f.sub.q] - [c.sup.j.sub.q] [for all] [x.sup.f] [member of] [0, [x.sup.fT]]. (A12)

Thus, we can certain that TR enhances welfare when firm f has lower marginal costs than firm j at [x.sup.fT] = 0 (i.e., before firm f participates in TR). TR can enhance welfare even when firm f's marginal costs are higher than firm j's for some or even all values of [x.sup.f] [member of] [0, [x.sup.fT]], as long as the marginal cost differential between the two firms is not too great. However, when the cost differential between the two firms is sufficiently large, the integral of the second term in Equation All can be negative. If both firms particpate, then from Equation A10, the net impact on welfare depends on both the ratio of the marginal costs of the two firms and the ratio of the cost savings ([x.sup.fT]] and [x.sup.jT] that the firms receive. QED.

PROOF OF PROPOSITION 5. Part (i): totally differentiating Equation 4, the equation that defines [x.sup.T], yields

d[[pi].sup.fT] = (p - [c.sup.f.sub.q])[dq.sup.f] + [q.sup.f]dp-[c.sup.f.sub.x][dx.sup.f]-[dt.sup.f] = 0, (A13)

since d[[pi].sup.fC] = 0 if firm f does not participate. Using Equation 2 to substitute out p, dp = p'dQ along with Equation A6 to substitute out dp, and Equation A7 to substitute out [dq.sup.f] and setting [dt.sup.f] = 0 yields

[-[c.sup.f.sub.x] - [q.sup.f]p'[[beta].sup.f][[alpha].sup.j]]/[DELTA]][dx.sup.f] + [q.sup.f]p'[[beta].sup.j] ([[alpha].sup.f] + 1)/[DELTA]][dx.sup.j] = 0.

Hence,

[dx.sup.f]/[dx.sup.j]\[pi]= -[[q.sup.f]p'[[beta].sup.j] ([[alpha].sup.f] + 1)/[DELTA]]/ [-[c.sup.f.sub.x] - ([q.sup.f]p'[[beta].sup.f][[alpha].sup.j]/[DELTA] > 0

by Assumption 2 and 3 and by Equations A4 and A5. QED.

Part (ii): Beginning with d[[pi].sup.fT] given in Equation A13 and using Equation 2 to substitute out p, dp = p'dQ along with Equation A6 to substitute out dp, and Equation A7 to substitute out [dq.sup.f] and assuming that [dx.sup.j] = [lambda][dx.sup.f] yields

d[[pi].sup.f]/[dx.sup.f] = -[DELTA][c.sup.f.sub.x]-[q.sup.f]p'[[beta].sup.f](1+[[alpha].sup.j]+1 +[lambda] [q.sup.f]p'[[beta].sup.j]([[alpha].sup.f] + 1))/[DELTA].

The sign of this term is ambiguous, so for certain parameterizations of the model, it may be negative. QED.

PROOF OF PROPOSITION 6. We show that welfare may fall even when the TR cost savings for both firms are the same. Starting with Equation A9 and setting [dx.sup.f] = [dx.sup.j] and [t.sup.j] = 0 yields

dw = ([u.sub.e][de.sup.f] +[u.sub.e][de.sub.j]) + (p - [c.sup.f.sub.q])[dq.sup.f] - [c.sup.f.sub.x][dx.sup.f] -[dt.sup.f] + (p-[c.sup.j.sub.q])[dq.sup.j] - [c.sup.j.sub.x][dx.sup.f].

Using Equation A7 to substitute out [dq.sup.i] yields

dw = ([u.sub.e][de.sup.f] + [u.sub.e][de.sup.j]) + [dx.sup.f]/[DELTA] {[summation over (i)] [[beta].sup.i] (p - [c.sup.i.sub.q]) - [[gamma].sup.f] ([c.sup.f.sub.q] - [c.sup.j.sub.q])} - [c.sup.f.sub.x][dx.sup.f] - [dt.sup.f] - [c.sup.j.sub.x][dx.sup.f],

where, [[gamma].sup.f] [equivalent to] ([[alpha].sup.j][[beta].sup.f] - [[alpha].sup.f][[beta].sup.j] = -[[gamma].sup.j]. The total impact of TR on welfare is given by the integral of this expression over the ranges x [member of] [0, [x.sup.T], t [member of] [0, [t.sup.T], and e [member of] [0, [e.sup.T] (i.e., the analog of Eqn. A2'). The superior-environmental-performance constraint (Assumption 1) ensures that the integral of the first term in parentheses is positive. The participant constraint (Eqn. 4 ensures that the sum of the integrals of the terms is positive. The integral of the second term in curly brackets will be positive if

[summation over (i)] [[beta].sup.i] (p - [c.sup.i.sub.q]) > [[gamma].sup.f] ([c.sup.f.sub.q] - [c.sup.j.sub.q]) [for all] [x.sup.f] [member of] [0, [x.sup.T].

This condition requires that the sum of the [beta]-weighted markups is larger than the [gamma]-weighted difference between the two firms' marginal costs. Note that since the sign of [[gamma].sup.f] may be negative, this condition can fail even when [c.sup.f.sub.q] < [c.sup.j.sub.q] over the rel qevant range of x values, that is, even when the firm that formally participates (firm 1) is more efficient than the finn that does not (firm j). In fact, in a similar model, Dung (1993) shows that, assuming linear demand and constant (but not identical) marginal costs, when finn f is more efficient than firm j, [[gamma].sup.f] will always be negative. QED.

PROOF OF LEMMA 4. Since [x.sup.iT.sub.L] is equal to [x.sup.T] (used in the second subsection of Section 5), this proposition follows directly from the proof of Proposition 5(i), which showed that firm f's [x.sup.T] is higher when firm j participates than when firm j does not participate.

PROOF OF PROPOSITION 7. The proof follows directly from the definitions of [x.sup.iT.sub.L] and [x.sup.iT.sub.H].

Part (i): [x.sup.iT] < [x.sup.iT.sub.L], we know that [[pi].sup.i]([x.sup.iT]\0, [t.sup.iT]) < [[pi].sup.i](0\0, 0). This follows from Equation 5, the definition of [x.sup.iT.sub.L], and the fact that [[pi].sup.i]([x.sup.iT]\0, [t.sup.iT]) is increasing in [x.sup.iT]. In addition, since [x.sup.iT] < [x.sup.iT.sub.H], we know that [[pi].sup.i]([x.sup.iT]\[x.sup.g[not equal to]iT], [t.sup.iT]) < [[pi].sup.i](0\[x.sup.iT], 0). In other words, each firm's dominant strategy is to not participate. Thus, symmetric nonparticipation is the unique, pure-strategy Nash equilibrium.

Part (ii): When [x.sup.iT] > [x.sup.iT.sub.H], we know that [[pi].sup.i]([x.sup.iT]\[[x.sup.g[not equal to]iT], [t.sup.iT]) > [[pi].sup.i](0\[x.sup.iT]\[[x.sup.g[not equal to]iT], 0). This follows from Equation 6, the definition of [x.sup.iT.sub.H], and the fact that [[pi].sup.i]([x.sup.iT]\[[x.sup.g[not equal to]iT], [t.sup.iT]) is increasing in [x.sup.iT]. When [x.sup.iT] > [x.sup.iT.sub.H], it must also be the case that [[pi].sup.i]([x.sup.iT]\0, t) > [[pi].sup.i](0\0, 0). This follows from the definition of [x.sup.iT.sub.L] and the fact that [x.sup.iT.sub.L] < [x.sup.iT.sub.H]. In other words, both firms have a dominant strategy to participate. Thus, symmetric participation is the unique pure-strategy Nash equilibrium.

Part (iii): There are four scenarios in which only one of the two firms participates. Firm i participates, but firm g ([not equal to] i) does not in the following cases:

(a) [x.sup.iT.sub.L] < [x.sup.iT] < [x.sup.iT.sub.H] and [x.sup.g[not equal to]iT] < [x.sup.g[not equal to]it.sub.L]

(b) [x.sup.iT] > [x.sup.iT.sub.H] and [x.sup.g[not equal to]iT] < [x.sup.g[not equal to]iT.sub.L]

(c) [x.sup.iT] > [x.sup.iT.sub.H] and [x.sup.g[not equal to]iT.sub.L] < [x.sup.g[not equal to]iT.sub.H].

Either firm f or firm j, but not both, participates when

(d) [x.sup.fT.sub.L] < [x.sup.fT] < [x.sup.fT.sub.H] and [x.sup.jT.sub.L] < [x.sup.jT] < [x.sup.jT.sub.H].

The proofs for cases a, b, and c are similar to those for parts (i) and (ii). For case d, assume that firm f participates and firm j does not. We show that this is a pure-strategy Nash equilibrium. (By symmetry, it follows that there is an equivalent pure-strategy Nash equilibrium in which firm j participants and firm f does not). If from j does not participate, since [x.sup.fT] > [x.sup.iT.sub.L], we know that [[pi].sup.f]([x.sup.fT]\0, [t.sup.iT]) > [[pi].sup.f](0\0, 0). Thus, firm f cannot increase its profit by not participating. Correspondingly, if firm f participates, since [x.sup.jT] < [x.sup.jT.sub.H], we know that [[pi].sup.j]([x.sup.jT]\[x.sup.fT], [t.sup.jT]) < [[pi].sup.j](0\[x.sup.iT], 0). Thus, firm j cannot increase its profit by participating. Moreover, given the definitions of [x.sup.iT.sub.L] and [x.sup.iT.sub.H], neither symmetric participation nor symmetric nonparticipation can be Nash equilibria. Thus, participation by firm f is the unique pure-strategy equilibrium.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Received August 2001; accepted March 2002.

(1.) Of the remaining four projects described by Blackman and Mazurek (2001), three allow plants to use unconventional methods of treating or handling hazardous waste and one involves consolidated permitting. For a detailed description of one of the most prominent Project XL agreements, see Boyd et al. (1999).

(2.) For example, the New York Times has argued that "It is increasingly likely that the ... approaches being tested [in Project XL] will eventually evolve into a new legal framework that could profoundly change the way major industries meet the nation's environmental mandates" (Cushman 1996, p. All).

(3.) The Bush administration has set a goal of increasing the number of XL projects from the 50 in progress at the end of the Clinton administration to 1,000 (Inside EPA 200lb).

(4.) It may be argued that such programs are not entirely voluntary, given that the alternative is a compulsory command-and-control regime.

(5.) EPA's website states, "It is vital that each [XL] project tests new ideas with the potential for wide application and broad environmental benefits.... The goal is to ... apply what is learned more broadly ..." (U.S. Environmental Protection Agency 1999a). Similarly, the Second Generation initiative gives priority to projects that have "wide applicability," and requires participating plants to submit a plan for "integrating the innovations in the agreement into the Agency's standard practices to the extent practicable...." (Inside EPA Weekly Report 1999).

(6.) The EPA's sulfur dioxide permit trading program provides additional evidence that replacing command-and-control regulation with performance standards can generate significant cost savings. According to Burtraw (1996), in the first several years of the program, when the number of actual trades was limited, participants still saved millions of dollars in compliance costs simply because the program replaced technology standards with performance standards.

(7.) Brau and Carraro (1999) argue that voluntary agreements may bring about undesirable impacts on competition by increasing concentration, promoting collusive behavior, and creating barriers to entry.

(8.) In addition to [e.sup.ir], [x.sup.ir] and [t.sup.ir], the TR regime is defined by rules governing which firms are offered agreements and whether TR agreements diffuse among firms in the industry. We consider these rules in section 5.

(9.) Note that for simplicity, we assume TR has no effect on fixed production costs aside from its effect on participation costs, [t.sup.iT], so it is only reductions in marginal costs, not reductions in fixed costs, that induce firms to participate in TR.

(10.) See, for example, Farrell and Shapiro (1990).

(11.) The three propositions in this subsection, as well as Proposition 6 in a subsequent subsection, all rely on well-known findings on asymmetric cost effects in oligopolistic markets. In particular, we draw upon Dung (1993).

(12.) In practice, diffusion is never costless. However, this assumption highlights the likely disparity in the fixed costs (of acquiring the benefits of TR) borne by participants and those borne by nonparticipants. In particular, participants will pay many negotiation and transaction costs that nonparticipants will not pay.

(13.) For example, welfare can fall when TR agreements yield equal percentage reductions in both firms' marginal costs so that the relatively inefficient firm receives a larger absolute marginal cost reduction. See Blackman and Boyd (2002) for a numerical example.

(14.) See Reinganum (1981) and Jensen (1992) for related game-theoretic analyses of the adoption of cost-saving innovations in a duopoly.

(15.) See Blackman and Boyd (2002) for a numerical example.

(16.) Given that the EPA's stated policy is to diffuse the XL agreements industrywide, it is perhaps no accident that, as described in Blackman and Mazurek (2001), Project XL has had difficulty attracting participants.

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Allen Blackman * and James Boyd +

* Resources for the Future, 1616 P Street NW, Washington, DC 20036, USA; E-mail [e-mail]; corresponding author.

+ Resources for the Future, 1616 P Street NW, Washington. DC 20036, USA.

This research was funded by the Environmental Protection Agency, Office of Research and Development (grant no. R826154-0l). We are grateful to Alan Krupnick, David Simpson. the editor, and two anonymous referees for helpful comments and suggestions.