An Economic Analysis of Regulation by Conditional Permits

An Economic Analysis of Regulation

by

Conditional Permits

Erik Lenntorp

Linköping Studies in Arts and Science No. 345 Linköping Studies in Management and Economics No. 68

Linköpings universitet, Ekonomiska Institutionen Linköping 2006

Linköping Studies in Arts and Science • No. 345

Vid filosofiska fakulteten vid Linköpings universitet bedrivs forskning och ges forskarutbildning med utgångspunkt från breda problemområden. Forskningen är organiserad i mångvetenskapliga forskningsmiljöer och forskarutbildningen huvudsakligen i forskar-skolor. Gemensamt ger de ut serien Linköping Studies in Arts and Science. Denna avhandling kommer från Nationalekonomi vid Ekonomiska institutionen. Distribueras av: Ekonomiska Institutionen Linköpings universitet 581 83 Linköping Erik Lenntorp

An Economic Analysis of Regulation by Conditional Permits Upplaga 1:1 ISBN 91-85497-08-8 ISSN 0282-9800 ISSN 0347-8920 ©Erik Lenntorp Ekonomiska Institutionen

Acknowledgements

I am sincerely grateful for the advice that I have received from Göran Skogh (supervisor), Fredrik Andersson, and Thomas Sonesson.

The research has been carried out within the Centre for Education and Research on Economic Crime and Economic Crisis (CEREC) at Linköping University. CEREC is a multidisciplinary centre - law, economics, history and ethics - complementing traditional research on economic crime. The research within CEREC was financed by the Bank of Sweden Tercentenary Foundation (Riksbankens Jubileumsfond). Financial support has also been given by Torsten och Ragnar Söderbergs Stiftelser.

Linköping, December 2005 Erik Lenntorp

Contents

1. Introduction and Summary

₁

2. Conditional Permits and Information

₉

3. Bargaining Power, Political Pressures and Information

₅₁

4. Regulatory Response to Violation of Permit

₈₇

5. Violation and Information

₁₀₉

6. The Benefit of a Big Stick – The Sanction of Permit Revocation

₁₄₅

1. Introduction and Summary

1.1 Introduction

Public law regulating industry often contains general principles or goals, such as; sustainable development, the polluter pays principle, and the precautionary principle in environment law. Such vague principles typically guide a regulatory agency (regulator) in balancing the benefits of the industry and the harms it creates. The implementation requires some powers of the regulator. A widely used regulatory technique is a conditional permit.1 _{That is, a permit}

granting a right to produce, which is valuable to the firm. At the same time the permit contains conditions to limit harm, which are costly for the firm.

For example, a firm wants to construct a pulp mill. Pulp mills pollute, and by law the firm needs a permit to operate the mill. Given that the permit is granted, the permit may contain conditions limiting pulp production, inputs, discharges, and also a requirement to install a treatment facility. Conditional permits are not only used in environmental law. Permits may be required for operating a taxi-business, for production causing occupational hazards, and even for a private homeowner building a fence in the backyard.

The literature on e.g. environmental law suggests that permits have contributed to fulfilling the goals of law, but there has been slippage.2 _{Slippage is termed by Farber (1999) meaning a}

discrepancy between what the law proscribes and what is the actual outcome of legislation. This can be illustrated by the case of Swedish sulphate pulp mills. Environmental law often requires permit conditions to be based on principles like Best Available Techniques (BAT). The Figure 1.1 compares discharges of COD [Chemical Oxygen Demand] and process sulphur in 1981 and 2000 to the discharges determined as BAT in 1992. Even though the BAT-levels are only recommendations in Swedish law some mills had not reached them even in the year 2000. However, the figure also reveals that despite suspected slippage, considerable progress has been made over the time-period.

Figure 1.1 1992 recommended Best Available Techniques (BAT) discharges for sulphur and COD per

tonnes pulp produce, compared to discharges in 1981 and 2000 from Swedish sulphate pulp mills.

Source: Gustafsson & Hellberg (2002).

In practice the regulator and the permit applicant may negotiate conditional permits. This includes both negotiations of the original permit and the enforcement response.3 _{There are}

several reasons why the regulator negotiates permits, like uncertainty about the benefits and the costs of regulation, political controversy, insufficient agency resources, bureaucratic incentives and elements of capture. However, two general reasons for negotiations, which result in slippage, are:

(i) The regulator depends on the firm for information to implement the law. Empirical research has shown that regulators may overcome asymmetric information by negotiating conditional permits, but the lack of information results in slippage.4

(ii) Enforcement is costly for the regulator. Regulators typically adopt a cooperative enforcement style, largely due to the enforcement costs.5 _{Cooperative enforcement usually}

aims at consent on performance, rather than to deter or punish. Consent is often reached by a reduction in stringency of regulation.6 _{The enforcement style is thus a source of slippage.}

The purpose of this thesis is to increase the understanding of how conditional permits implement law. More specifically, the purpose is to explain how commands are transformed

COD Kg/tonnes pulp sulphur Kg/tonnes pulp

BAT sulphur BAT COD 1981 2000 25 50 75 100 125 150 175 200 3 1 5

into negotiated commands, or slippage. Throughout this thesis conditional permits are exemplified by the case of environmental law.

This thesis extends the economic analysis of regulation by studying conditional permits.7

Basically, the analytical idea is to view the permit as a fully contingent (or complete) contract in a principal-agent setting. This framework has previously been applied to regulation. However, the connection to permits has not been made. In particular, this means that the payment to the agent in the permit is the right to produce, and the effort is related to the conditions imposed. In the previous literature the payment typically involves monetary transfers.

1.2 Summary

Chapter 2 focuses on how information can be revealed in permit negotiations. The problem is that the firm has private (hidden) information that the regulator needs to implement law. A model is constructed to study information revelation in conditional permits. Simplifying assumptions are:

Permitting is case-by-case regulation. In the model there is one regulator and one firm, whose production causes harm.

The value of the permit for a firm is the right to produce.

The firm can reduce harm from production at a cost. The harm thus depends on output and effort to reduce harm. The combination of an output level and reduction effort is denoted a precaution. The firm may be one of two types, depending on the costs of harm reduction is high or low.

Law stipulates that the regulator shall deny a permit if harm exceeds some critical level. Law stipulates that if harm is less than this critical level, the permit should be granted. If the permit is granted law stipulates that permit conditions should

The analysis first examines permit design without the problem of private, or asymmetric information. In this benchmark model, conditional permits perfectly implement law, or, more formally, the first best level of harm. Thereafter is the problem of asymmetric information introduced. The firm’s entitlement to earn a normal profit implies that the regulator depends on the firm for information. The principal-agent model with hidden information is used to analyse this type of situation. The basic idea is that the principal (the regulator) through the permit controls the agent’s (the firm’s) surplus. By properly designing the permit, the agent’s private information may truthfully be revealed.

The major result is:

It is possible for the regulator to use permits to reveal the firm’s private information. However, the “second best” permits imply that the firm is allowed to incur more harm than under symmetric information. Asymmetric information can thus explain slippage. However, the negotiated commands in the “second best” permits result in less harm, i.e. a better legal goal fulfilment, than if the regulator instead tried to command the “first best” precautions. Empirical research supports the model that private information may be revealed in the permit process, and that private information causes slippage.

Chapter 3 examines the consequences of bargaining power and political pressures under both symmetric and asymmetric information. The regulator and the firm negotiate conditional permits in a complex process. Relative bargaining strength is important. Bargaining power and political pressure are related to asymmetric information. The firm may exploit the regulator’s lack of information by exaggerating the consequences of regulation. In the permit negotiation firms also mobilize support from industry associations, labour unions, and even local governments to assert pressure on the regulator.8

The model in this chapter builds on the model in chapter 2. Bargaining power is modelled as a struggle for the profit earned by production.9 _{This includes both the scale of production (i.e.}

the size of profit), and the fraction of profit that is used for harm reduction. Political pressures are modelled as the regulator benefiting from profits above the normal level.

The major results are:

Bargaining power, political pressures, and asymmetric information sometimes interact. Political pressures only affect the outcome if the firm has some bargaining power, or information is asymmetric. Perhaps the most striking result is that asymmetric information has no effect when bargaining power is equally divided between the regulator and the firm. The interaction corresponds to conclusions from empirical research. Hucke (1982) claims that the primary arguments of firms are that the burden of regulation is unreasonable, possibly causing dismissal of workers or even shutdown. Hucke then adds that such arguments are also effective in mobilizing the support from trade unions and local governments to influence regulation.

Bargaining power, political pressures, and asymmetric information result generally in slippage, i.e. these phenomena explain how commands end up as negotiated commands. Are negotiated commands also preferable in such cases? The answer is both yes and no. If bargaining power is a struggle for profit, then negotiated commands only increase harm. However, if commands are negotiated to reveal information, then negotiated commands decrease harm.

Chapter 4 considers various regulatory responses to violation of permit conditions. After a permit has been issued the firm may violate the permit conditions. For such an event law typically contains various enforcement actions, like a compliance order, a monetary penalty, permit suspension, and permit revocation. The enforcement problem has been the subject of an extensive theoretical and empirical literature.10 _{This chapter extends the economic analysis}

by considering regulatory response to permit violations.

In this chapter the only obstacle for the regulator to implement the “first best” precaution is the possibility for the firm to breach permit conditions. A tribunal, e.g. an external judge, levies a fixed fine on the firm. However, for any sanctions to be imposed, the regulator must (i) verify that a violation has occurred, and then (ii) refer the case to the tribunal. Verification and referral are costly for the regulator.

Somewhat fictitiously the regulator may employ two different enforcement styles in response to a violation. The first enforcement style is “deterrence-based”, meaning that the regulator police and punish violations. The other style is “cooperation-based”, in which the regulator basically negotiates compliance with the firm. There is an ongoing policy debate over the relative merits of these styles (see e.g. Rectschaffen & Markell (2003)). Nevertheless, there is a widespread consensus in the literature that regulators in practice have adopted a cooperative enforcement style.11 _{Typically, cooperative enforcement involves a settlement, like a permit}

modification or a consent decree. Permit modifications and consent decrees often reduce the stringency of some permit condition. Often, the fine is set low or rescinded to not destroy the possibilities for a settlement. Clearly, cooperative enforcement results in slippage.

More specifically, this chapter studies in a “permitting context” when the regulator is more likely to resort to cooperation-based enforcement, and when it is more likely to rely on deterrence-based enforcement.

The major result is:

Generally, the best response to non-compliance includes some slippage. The regulator is likely to rely on cooperation-based enforcement when the costs of enforcement are large. Detection expenditure can be saved by cooperative behaviour, but the harm is increased. Negotiated commands achieve some balance of the harm and the cost of enforcement, which may be advantageous.

Chapter 5 studies the effect of both non-compliance and asymmetric information on the stringency of permit conditions. The regulator often depends on the firm for information, and the enforcement of permit conditions is costly for the regulator. Both these facts may independently explain why regulators engage in negotiations. This chapter considers both these aspects, and how they may interact.

The major result is:

Information can be revealed despite the problem of non-compliance. An additional implication of considering asymmetric information and non-compliance simultaneously is that information revelation may become more costly, compared with the analysis in chapter 2.

Chapter 6 studies the effect on the incentives to comply, when the regulator may as a sanction withdraw the permit (permit revocation). An empirical anomaly that has received considerable attention is that firm’s comply with regulation despite the fact that gain of violation is larger than the expected sanction (see e.g. Heyes (2000)). In the economic literature this anomaly is termed the Harrington-paradox.12 _{One explanation is the claim that}

the regulatory enforcement situation is a repeated prisoner’s dilemma, with the outcome that firms comply despite being under-deterred (Scholz (1984a), (1984b)). To induce cooperation in the prisoner’s dilemma Ayres & Braithwaite (1992) argue that the threat of permit revocation is useful for escalating deterrence.

This chapter examines the effect of adding permit revocation to the situation when only a fine can be imposed. An important assumption here is that the regulator revokes the permit, when harm is unacceptable. The firm’s decides whether (i) to violate the permit, but not so much that the permits are at risk, or (ii) to violate and risk to have the permit revoked. Permit revocation in the model here can thus also be seen as a case of escalating deterrence.

The major result is:

The combination of a fine and permit revocation, improves the regulator’s outcome in terms of harm and enforcement costs. Note that, the expected fine alone may not deter the firm, but recognizing the additional threat of permit revocation explains why firms still choose to comply. This contributes to the explanation of the Harrington-paradox.

Notes to Chapter 1

1 _{OECD ((1999a), (1999b), (1999c)) surveys the use of environmental permits in the OECD countries. Davies} (2001) presents a survey of environmental permitting mainly in the U.S. focused on problems and reforms. 2 _{That permits has contributed to reduction in harms, see Gustafsson & Hellberg (2002), Hildén et al (2002),} Mickwitz (2003), and Gunnigham et al (2003), but that there has been slippage, see e.g. Latin (1991), Flatt (1997), Farber (1999), Harrington (2003).

3 _{To exemplify, the literature dealing with environmental permits is unanimous that permits are negotiated, see} e.g. Richardson (1982), Ullman (1982), Hucke (1982), Downing (1982, 1983), Ayres & Braithwaite (1992), Ogus (1994), Hunter & Waterman (1996), Mehta & Hawkins (1998), Fineman (1998), OECD (1999a), Lange (1999), Aoki et al (2000), Welles & Engel (2000), Dwyer et al (2000), Davies (2001), Sunding and Zilberman (2002), Sorrell (2002), Similä (2002), Hildén et al (2002), Gunningham et al (2003), Rechtschaffen & Markell (2003), and Bengtsson (2004).

4 _{Lehmann (2000), Sorrell (2002), and Hildén et al (2002).}

5 _{see e.g. Richardson (1982), Ullman (1982), Hucke (1982), Downing (1982, 1983), Langbein & Kerwin (1985),} Ayres & Braithwaite (1992), Hunter & Waterman (1996), Mehta & Hawkins (1998), Fineman (1998), Shapiro & Rabinowitz (2000), Gunningham et al (2003), Ogus (2004), Rechtschaffen & Markell (2003), and Bengtsson (2004)).

6 _{Downing (1982), Hucke (1982), Hunter & Waterman (1996), Flatt (1997), Oljaca et al (1998), Davies (2001).} 7 _{Although permitting often is mentioned it rarely is in the analytical focus. Lehmann (2000) applies a Rubinstein} bargaining model based on an incomplete contract environment in a permitting context to analyze in particular the effect rules on standing and judicial review have on discretionary administrative acts. In Lehmann’s model the agency may collude with the firm (the agency receives a bribe from the firm) in order to implement less stringent regulation than the one implied by uniform regulation set by the legislative. Environmental organizations may play the role of watchdogs contesting susceptible standards. Lehmann’s problem is more one of delegation and controlling agency discretion than analyzing the process of standard setting itself. Bargaining in Lehmann’s model is informal and bargaining is not a part of the formal instrument of permitting. Sunding & Zilberman (2002) makes a cost-benefit analysis of a change in the wetland permitting program that increases the number of projects that needs to be dealt with on a individual basis. The few examples may be suspicious. The author draws some confidence in the following quote from Decker (2003): “Clearly, [permitting] plays a prominent role in environmental law…[t]o my knowledge no formal studies exist that investigate the environmental [permitting] process” [p.106].

8 _{Hucke (1982), Hunter & Waterman (1996), Sorrell (2002), and Harrison (2002).}

9 _{The framework for dealing with bargaining power is based on Inderst (2002). The analysis here differs} significantly from Inderst in (i) no monetary transfer is involved, and, (ii) countervailing incentives are possible. Countervailing incentives is when an agent is tempted to claim to have lower costs than it really has.

10 _{Surveys are Cohen (1998), Heyes (2000) and Faure & Visser (2004). The literature is also related to general} economic analysis of crime based on Becker (1968), and surveyed in Garoupa (1997) and Shavell & Polinsky (2000).

11 _{Exceptions to the cooperative style are violations resulting in large and tangible harm, for which punishment} may be sought immediately, and when the firm refuses to enter into a settlement.

2. Conditional Permits and Information

2.1 Introduction

Firms causing harm are typically regulated by a requirement to hold a conditional permit. For example if a firm wants to build a pulp mill - pulp mills pollute - by law the firm needs a permit to operate the mill. The permit, if granted, may permit x tonnes of pulp production per year, restrict input use (e.g. use of bleaching input), and limit discharges (e.g. tonnes COD per day).1 _{The regulator may also require the installation of a specific treatment facility. The}

conditional permit thus grants the firm a right to produce, which makes the permit valuable to the firm. At the same time the permit contains costly duties, or conditions, for the firm to reduce harm.

The law often delegates the right to issue a conditional permit to a regulator. Typically, the regulator’s task when issuing a conditional permit is to transform rather vague goals and principles of law, such as sustainable development, polluter pays principle, and the precautionary principle in environmental law, into enforceable permit conditions. Schematically, the implementation chain can be construed as:

Goals, principles of law → permitting → permit condition

The step from e.g. sustainable development to a mandate to install a treatment facility may be quite long. However, this also implies that conditional permits, when applicable, are crucial to understanding how the law is implemented.

Empirical research into e.g. environmental permits finds that conditional permits have contributed to the fulfilment of legal goals, but not without slippage.2 _{Slippage is a}

discrepancy between what law stipulates, and the actual outcome from implementation (Farber (1999)). It is within the realm of the conditional permit that much slippage occurs. More precisely, in practice the regulator and the regulated firm negotiates the permits, and the negotiated permit entails some slippage.3

In most regulation models there are no incentives to negotiate, since the regulated party has nothing to offer the regulator in return for leniency (Amacher & Malik (1998)). Put differently, nothing prevents the regulator from “commanding”.4 _{However, a common}

difficulty for the regulator to implement the law is his dependence on the firm for information. The law generally restricts regulators to require “reasonable” precautions. To judge the reasonableness of regulation the regulator generally depends on the firm for information (e.g. Ricketts & Peacock (1986)). This is perhaps most visible in environmental permits. Typically, conditions in environmental permits are based on concepts like Best Available Techniques (BAT).5 _{In short, BAT implies that permit conditions should minimize}

harm, given that the firm is entitled to a normal profit (Førsund (1992)). The regulator must thus determine the firm’s profit, which may be hidden, or private, information. In conclusion, a reason for regulators to enter into negotiations is to overcome information asymmetries, and in the extension asymmetric information may explain slippage.6

The purpose of this thesis is to increase the understanding on how conditional permits result in slippage. More precisely, this chapter attempts to study if the regulator’s dependence on the firm for information can explain how permit conditions end up as “negotiated commands” rather than commands. The study departs from the principal-agent characteristics of the regulator/principal firm/agent interaction. The set-up draws on Ricketts & Peacock (1986) assertion that the principal-agent paradigm captures a “cooperative element” in the relationship between the regulator and the regulated firm. Meaning that information asymmetries may result in negotiation, in which the regulator and the firm struggle over the surplus of information provision. Ricketts & Peacock focus on moral hazard, while the focus here is on hidden information. Negotiations are in the model limited to the regulator giving up some surplus to reveal hidden information; hence the more cautious term “negotiated commands”. The principal-agent model with hidden information framework is previously applied to regulation in e.g. Baron & Myerson (1982), and Laffont & Tirole (2002).7 However, the literature has not made the connection with permits. The previous literature generally assumes that the regulator controls the firm via a stipulation of costly effort and a monetary transfer. The main difference to the model when applied to permits is that the regulator controls the firm through the profit generated by the permit, where no monetary transfer is involved.

The chapter is organized as follows. The next section describes the model settings. One firm is assumed to apply for a permit. The law stipulates that the regulator minimizes harm caused by the firm, given that the firm is entitled to a normal profit. Harm is a function of the firm’s precaution, which includes both the output level and harm reducing effort. As mentioned, entitlement to a normal profit is a common restraint on regulators through principles like Best Available Techniques. The section concludes by deriving the first best level of harm, i.e. the benchmark of perfectly legal goal fulfilment. The third section studies implementation when information is symmetric. A further complication studied is that the regulator must decide on a permit design, that is, how to regulate a firm’s behaviour, and whether regulation should be individual or apply for an industry. It is shown that under symmetric information both a permit limiting harm and one specifying a precaution implement the first best level of harm. In the fourth section asymmetric information is introduced. This is done by assuming that the firm can either have high or low costs of precaution, and the type of cost is private information. The analysis reveals that only a permit specifying a precaution can be used to reveal information. However, to reveal information more harm is permitted. Asymmetric information thus explains slippage. The fifth section applies the model’s results to a specific permit programme and presents some facts on the transactions costs involved with permitting. The sixth and final section offers some concluding remarks.

2.2 The model

2.2.1 The firm

A firm applies for a permit to produce a good called w in a locality. The firm has access to a production technology that by placing a facility in a particular locality can transform w of input on a one-to-one-basis to w of output. The construction of the facility imposes a fixed cost k> on the firm.0 8 _{The locality is constrained tow of input (and hence output). It is}

assumed that the firm has no competitors for the locality.9 _{The firm can neither affect the cost}

of input nor the price of output. The location-specific unit cost of input is less than the unit-price of output giving rise to a location rent m> .0 10

Production of w also incurs harm on the community. Harm from producing w may be reduced if the firm exerts costly efforts e . The firm’s cost of harm reduction effort is a convex function θi⋅c e( )with c(0) 0= , 0ce> and cee> .0 11 { , }θi∈ θ θl h is a technological

shift-parameter. Subscript l denotes low cost, and h high cost. Naturallyθ θh> > , and l 0 consequently 0c_θ > and 0ceθ > . A firm with cost-parameter θl is called efficient, and a firm

with θh is called inefficient.

The firm is assumed to be risk-neutral and its objective function, or profit function, is concave and defined by:

( ) (0, ] ( , ) 0 0 i m w c e k w w w e w θ π =  ⋅ − ⋅ − ∈₌ 

where the decision to set w= is the firm’s decision not to produce, i.e. reject a permit.0 12 _This

decision is the firm’s so-called outside opportunity. The firm’s reservation profit is thus equal to 0 .

In the absence of regulation the firm will choose w w= and e_{= . The permit implies a} 0 possible surplus for the firm of max _{m w k}

π = ⋅ − . Figure 2.1 displays the firm’s iso-profit curves, i.e. the combinations of output and reduction effort that yield the same profit level β . The graph shows reduction effort ( e ) on the horizontal axis and output ( w ) on the vertical axis.13 _{Expressed in more compact format an iso-profit curve is}

{( , ) :w e m w⋅ − ⋅θ c e( )− =k β}. From concavity of the profit function it can be established that the upper contour set {( , ) :w e m w⋅ − ⋅θ c e( )− ≥k β}associated with any iso-profit curve is a convex set. Total differentiation of the expression m w⋅ − ⋅θ c e( )− = , and rearranging k β

gives the slope of an iso-profit curve, dw ce 0

de m

θ⋅

= > . It can easily be seen that the second derivate is also positive. The iso-profit curve slopes upward and at an increasing rate. Recalling the capacity constraint w w≤ the firm’s profit is increasing moving leftward towards the point ( ,0)w in the interior of the graph.

Figure 2.1. Iso-profit curves.

The vertical axis shows output, w, and the horizontal axis shows reduction effort, e. The graph displays iso-profit curves defined by { ( , )_π w e _=β} {( , ) : ( , )_≡ w e _π w e _{= ⋅ − ⋅}m w _θ c e( )_{− =}k _β} for _β<0, _β=0, _β>0, and max ₀

β π= > . The latter is the maximum profit attainable for the firm given the output capacity constraint w, i.e. _πmax _{= ⋅ −m w k. The graph also indicates the slope of the} iso-profit curves and the direction of increasing profit.

The efficient firm’s and the inefficient firm’s iso-profit curves cross only once, i.e. for a given output level, both firms may have the same profit only when reduction effort is zero. To see this, differentiate the slope of the iso-profit curve with respects to the parameter θ gives

2 0 e c w e θ m ∂ _{= >}

∂ ∂ . The slope of the inefficient firm’s iso-profit curve is thus larger than the efficient firm’s for all e> . This is known as the single-crossing, or Spence-Mirrlees, 0 condition.

w

e

( , ) 0w e π < ( , ) 0w e π = ( , ) 0w e π > max ( , )w e π =π w 0 Direction of increasing profit Slope: dw ce de m θ⋅ =

2.2.2 Harm

Harm from the facility is described by the convex function ( , )z w e with 0zw> , 0zww> ,

0

e

z < , 0zee> , and zwe= . These assumptions are fairly common for various harms, e.g. 0

pollution, arguably with the exception of the last one. The cross partial z_{we= implies that} 0 the effect of reduction effort is uncorrelated to the scale of output. This is restrictive, since the scale of output probably does affect the efficiency of reductions in some cases.

The “harm production function” is ( , )z w e , with output of w and reduction effort e as “inputs”. To ease the presentation, the vector of harm production inputs ( , )w e is denoted a precaution.

Figure 2.2 show a graph similar to the one in Figure 2.1, but the former displays instead iso-harm curves, i.e. different precautions ( , )w e that yield the same harm χ. More explicitly an iso-harm curve is expressed as{( , ) : ( , )w e z w e =χ}. The function ( , )z w e is convex, and the lower contour set {( , ) : ( , )w e z w e ≤χ}of an iso-harm curve is convex. Total differentiation and rearranging gives the slope of the iso-harm curves, e 0

w

z dw

de z

−

= > . The second derivate is

negative. The iso-harm curves slope upwards but at a decreasing rate. Harm is decreasing, moving to the right and towards the horizontal axis in the graph.

The iso-harm curve associated with zero harm would imply that most reasonable legal goals are fulfilled. It is simply assumed possible precautions with positive output do not fully eliminate harm.

Figure 2.2. Iso-harm curves.

The vertical axis shows output, w, and the horizontal axis shows reduction effort, e. The graph displays the iso-harm curves defined by { ( , )z w e _=χ} {( , ) : ( , )_≡ w e z w e _=χ}, for _χ<0, _χ=0, and _zmax ₀

χ= > . The latter is the maximum harm the firm can incur, given the output capacity constraint w. The assumption of non-negative harm implies that iso-harm curves associated with

0

χ< are not applicable, as shown in the graph. The graph also indicates the slope of the iso-harm curves, and the direction of decreasing harm.

2.2.3 The regulator

The regulator is assumed to implement the objective of law. The law stipulates that the permit should be denied if harm exceeds some critical level, B . The law also stipulates that if harm is less than this critical level, then the permit should be granted. For example, environmental permits should typically not be granted if environmental quality standards are violated as a consequence (see OECD (1999a), Defra (2005)). If the permit is granted, then the law stipulates that permit conditions should minimize harm, given that the firm is entitled to a

w

e

max ( , ) z w e =z ( , ) 0 z w e > ( , ) 0 z w e = Not applicable Slope: e w z dw de z − = 0 Direction of decreasing harm w

normal profit. This objective is roughly similar to the technology-based approach, appearing under a number of acronyms, e.g. BAT, BACT, RACT, and ALARA.14 The technology-based approach typically implies that environmental harms should be minimized (e.g. Michanek (1993)). However, the law also restrains the regulator that harm should be affordable for a “well-managed” firm. Affordable regulation is equivalent to an entitlement to a normal, or non-negative, profit (Førsund (1992), Brisson & Pearce (1993), Pearce (2000), and Sorrell (2002)). Here, the entitlement to a normal profit comes down to all precautions

( , )w e restricted by:

w w≥ (capacity constraint), and

( ) 0

i

m w_{⋅ − ⋅θ} c e _{− ≥ (normal profit constraint)} k

Putting it all together, gives what might be called the “affordability constraint”, i.e.

Affordable

Ω ≡ {( , ) :w e w w m w≥ , ⋅ − ⋅θi c e( )− ≥ . The affordability constraint is simply the k 0} upper contour set of the iso-profit curve associated with zero profit (i.e.β = ) limited by the 0 capacity constraint. The affordability constraint is displayed graphically in Figure 2.3.15

To summarize, law then instruct the regulator to implement the level of harm induced by the precaution which solve the following constrained minimization problem:

, min ( , ) w e z w e s.t. w w≥ m w⋅ − ⋅θi c e( )− ≥ k 0 ( , ) B z w e≥

where the affordability constraint ( , )_{w e ∈Ω}Affordability _{has again been separated into the two}

constraints w w≥ , and m w⋅ − ⋅_θi c e( )− ≥ . If the constraint k 0 B z w e≥ ( , ) is binding, then this means that the regulator in order to grant a permit requires a precaution, which violates the normal profit entitlement. This resembles legal practice. For example, the EU’s Integrated Pollution Prevention and Control (IPPC) directive mandates that permit conditions should be stricter than BAT when required by an environmental quality standard, (Article 10).

Figure 2.3. Affordability constraint.

The vertical axis shows output, w, and the horizontal axis shows reduction effort, e. The set of affordable precautions are defined by Affordability {( , ) : , ( , ) 0}

w e w wπ w e

Ω ≡ ≥ ≥ , and is in the graph

encircled by the bold lines. The affordable precautions are thus bounded by w∈[ , ]w w along the vertical axis, and a reduction effort on the horizontal axis between e∈[0, ]e . The output level w is the one that just covers the fixed costs. The maximum reduction effort e solves _θ⋅c e( )_{= ⋅ −}m w k. The water permits (NPDES) in the U.S. contain uniform technology-based discharge limits (the “Effluent Guidelines”). Again, if these technology-based limits are not enough for an acceptable water quality, then the regulator may impose more stringent individual discharge limits, so called WQBEL (Water Quality Based Effluent Limit). Finally, the following tie-breaking condition is imposed:

Tie-breaking condition 2.1: If π =0,w> the firm will start producing in the locality.0 16

w

e

( , ) 0π w e = m ax ( , )w e π =π w 0 {( , ) : , ( , ) 0} Affordability _{w e w w w e} π Ω ≡ ≥ ≥ k w m = e

2.2.4 Sequence of events

The following sequence of events, within one time-period, is assumed:

s = 0: The firm’s type is determined. s = 1: The firm applies for a permit.

s = 2: The regulator offers a permit or a menu of permits.

s = 3: The firm accepts a permit or withdraws its application (i.e. rejects offered permits). s = 4: The facility is constructed and production takes place.

2.2.5 First best level of harm

The first best level of harm is the level the law stipulates. Implementation of the first best is then “perfect” legal goal fulfilment. Assume an interior equilibrium in the decision variables (i.e w w_{> ), and that the first best level of harm is less than the critical level, i.e. B z> . The} Lagrange-function denoted by ℜ , is then:

,

min_{w e} ℜ( , )w e =z w e( , )− ⋅λ (m w⋅ − ⋅θi c e( )− k)

where _λis the Kuhn-Tucker multiplier. The necessary and sufficient conditions17 _are:

0 w z m w λ ∂ℜ = − ⋅ = ∂ 0 e i e z c e λ θ ∂ℜ = + ⋅ ⋅ = ∂ (m w θi c e( ) k) 0 λ ∂ℜ = − ⋅ − ⋅ − = ∂

Solving w ∂ℜ ∂ for λgives 0 w z m

λ= > . The affordability constraint binds. Inserting this expression into

e ∂ℜ

∂ , and rearranging gives the optimal reduction effort, denoted by superscript FB_: FB i e such that e i e w z c z m θ − ₌ ⋅ _[2.FB.1]

and from the entitlement to a normal profit, i.e. the affordability constraint:

( FB) FB i i c e k w m θ ⋅ + = [2.FB.2]

Finally, inserting the optimal output and reduction effort into the harm function result in the first best level of harm:

( , )

FB FB FB i i i

z =z w e [2.FB.3]

The LHS of [2.FB.1] is the slope of the harm curve, and the RHS is the slope of the iso-profit curve.The first best level of harm is thus found where an iso-harm curve is tangential to the iso-profit curve with profit level zero, i.e. the affordability constraint. This result is shown graphically in Figure 2.4.

The conflict of interest between the firm and the regulator is now evident. The firm wants to move to the left and up in the graph of Figure 2.4, and the regulator to the right and down, at least down to where the firm earns a normal profit. The permit thus both grants a valuable right to the firm, i.e. access to the location rent, and at the same time impose duties, which fully transform the surplus of the permit into harm reduction demands. Millimet & List (2004) found in an econometric analysis that firm’s rationally trade off higher pollution precaution costs against local public goods, e.g. agglomeration economics, cheap labour and so on. This result seems to lend support to the conflict of interest as modelled here. Some further useful results are:

Figure 2.4. First best harm.

The vertical axis shows output, w, and the horizontal axis shows reduction effort, e. The first best precaution

(

_wFB,_eFB

)

_{is found where the slope of the iso-harm curve is tangential to the affordability}

constraint _ΩAffordability_{. The induced first best harm is z w(} FB_,eFB_{), and with the associated iso-harm}

curve{( , ) : ( , )_{w e z w e =z w}( FB,_eFB)}_{. The graph also indicates the set of unacceptable harm, i.e. the} upper contour set of the iso-harm curve z w e( , )=B.

Result 2.1: To implement the first best harm level, the regulator should reap the entire surplus from the firm, and use this to impose reduction effort. To reap the entire surplus the regulator needs to have all of the bargaining power.

Result 2.2: The first best harm level implies cost efficiency, i.e. the first best output and reduction levels are the least cost method to achieve the first best harm level.

w

e

w 0 ( , ) 0w e π = w e ( , ) z w e = B ( , ) 0 z w e = ( , ) FB z w e ₌z

First best harm:

( , ) FB FB FB z =z w e FB w FB e Unacceptable harm Affordability Ω

The condition for a least cost allocation, for any given level of harm, is simply that the slope of the iso-harm curve is tangent to the slope of the iso-profit curve, i.e. condition [2.FB.1]. Formally, this is shown by solving the firm’s profit maximizing problem constrained by harm being less than or equal to some given level, see Appendix A2.1. Furthermore by doing some comparative statics (see Appendix A2.1), a trajectory of cost efficient allocations in ( , )w e -space can be drawn as in Figure 2.5.

2.2.6 Comparative statics

This section will discuss comparative statics results; the derivation of these results is however given in Appendix A2.2.

If the fixed cost k increases, then 0

FB w k ∂ _> ∂ , and 0 FB e k ∂ _<

∂ , which of course implies that the first best level of harm increases. Note that a change in the fixed cost can also be interpreted as change (in the same direction) in what is considered a reasonable rate of return, or normal profit level.

An increase in the effort cost parameter,θ, has the effect that 0

FB

e

θ

∂ _<

∂ , but the effect on output is ambiguous. Nevertheless, first best harm increases. The ambiguity of the change in output depends on the altered slope of the iso-profit curve, i.e. the slope is increased in case of an increase. Hence, the trade-off between increasing output and reduction effort differs.

An increase in the location rent, m , is qualitatively similar to that of an increase in the reduction cost parameter. Again, this implies a change in the slope of the iso-profit curves, this time the slope is decreased (for an increase in m ), and the effect on output is ambiguous. The effect on reduction effort is definite, 0

FB

e m ∂ _>

Figure 2.5. The Trajectory of Affordable Cost Efficient Precautions.

The vertical axis shows output, w, and the horizontal axis shows reduction effort, e. The broken line shows the trajectory of least cost precautions, which also satisfy the affordability constraint. The condition for a cost efficient precaution is that an iso-profit curve is tangent to an iso-harm curve. The affordable cost efficient precautions are the trajectory of such tangency points.

Table 2.1 Different types of permits used in the analysis.

Specification permit Performance permit Individual

₍

_{w e} _{i, i}

₎

_{∀ ∈i { , }l h}

( )

zi ∀ ∈i { , }l h Uniform

_{( )}

w e  ,

( )

z

e

w 0 (_wFB,_eFB) e

w

2.2.7 Design of permit conditions

Permit conditions may limit the level of harm, i.e. a constraint ( , )z w e ≤  , where a tilde (~) z denotes regulated levels. In the case that the permit contains a limit on harm, the permit is denoted a performance permit. Permit conditions may instead specify the necessary harm precaution, i.e. the vector of harm production input ( , )w e . Formally, firm output must satisfy the constraint w w≤  , and reduction effort must satisfy the constraint e e≥  . The permit is thus the pair ( , )w e  . Such a permit is called a specification permit. The economic literature on “standards” (i.e. permit conditions) does not usually include output limits, and if so, not in combination with a mandate on reduction effort, e.g. Besanko (1987), Helfand (1991), Førsund (1992), and Marino (1998). It is often claimed that output is not regulated, for instance Helfand (1991) reports a review of U.S. regulations that found no example of output limits (although input limits which amount to the same thing in this model). This is likely true for central regulation, but on a source level, which is in the permits, output limits are common (see Førsund (1992), Dwyer et al (2000), Gustafsson & Hellberg (2002)). Moreover, even if no output limit is set, output may still be regulated by the requirement to obtain a new permit for increasing output. The claim is that in conditional permits regulators may typically mandate a certain precaution rather than a certain reduction effort.

In addition, a permit condition may be either uniform or individual. A uniform permit condition applies equally to all firms within an industry. An individual permit condition is firm specific. The law stipulates that both the efficient and inefficient firm is entitled to a normal profit. This implies that a uniform permit must satisfy the inefficient firms affordability constraint, while individual permits can be conditioned to each firm’s ability to reduce harm, i.e. the permits are based on each type of firm’s affordability constraint. Clearly, a uniform permit results in greater aggregated harm than individual permits. Yet, increasing the use of uniform permits, on the behalf of individual permits is often advocated (Sunding & Zilberman (2002), Davies (2001)). The rationale is based on the lower transaction costs with uniform permits. For this reason is a comparison between individual and uniform permits interesting. The theoretical results derived in 2.3 and 2.4 on this topic are compared with some empirical facts, and information on transaction costs in 2.5. In summary, the main analysis compares the permits in Table 2.1.

Figure 2.6. Specification permit as constraint.

The graph has reduction effort on the horizontal axis and output on the vertical axis. The first best precaution is displayed, the affordability constraint, and the iso-harm curve associated with first best level of harm. For labels see the graph in Figure 2.5. Bold broken lines show the constraint associated with the specification permit, i.e. to comply the firm must choose output and reduction effort that belong to the broken lines.

w

e

w 0 w e FB w FB e

Figure 2.7. Performance permit as constraint.

The graph has reduction effort on the horizontal axis and output on the vertical axis. The first best precaution is displayed, the affordability constraint, and the iso-harm curve associated with first best level of harm. For labels see the graph in Figure 2.5. The bold broken curve show the constraint associated with the performance permit, which is equivalent to the iso-harm curve associated with the first best level of harm. Any precaution satisfying this level of harm implies compliance with the permit.

w

e

w 0 w e FB w FB e

2.3 Implementation under symmetric information

In this section it is assumed that there is no private information. The regulator and the firm both know the model settings described in the previous section, and the outcome in stage s = 0. An interpretation is that the regulator can without cost learn about the firm’s ability to afford harm precaution. More precisely, the regulator learns, or knows, about the location rent, and the harm reduction costs in the permitting process. First individual permits are analysed, and then uniform permits.

2.3.1 Individual permits

The individual specification permit ( , )w e  i i

To implement the first best level of harm the regulator simply offers the permit

( FB, FB)

i i i i

w =w e =e for a firm i . The firm can choose any w w≤  and e e≥  . Figure 2.6 shows the firm’s possible choices given the permit conditions. From the graph it is immediate that the only choice with non-negative profit is (_wFB,_eFB)_{. The firm will accept the permit and} implement the first best precaution.

The individual performance permit ( )z i

The regulator can implement the first best harm level by the performance permit ( FB, FB)

i i i

z ₌z w e . The permit constraint curve is simply the iso-harm curve associated with the first best level. The constraint curve is shown in Figure 2.7. With this permit the firm is allowed to choose any precaution ( , )w e that satisfies the harm constraint. It is evident from Figure 2.7 that the firm cannot increase (or equal) the profit by choosing another precaution than

(

FB, FB

)

i i

w e , which accordingly the firm will implement.

Both a specification permit and a performance permit implement the first best level of harm, and result in the same precaution, i.e. the first best level of output and reduction effort. Generally, economists favour performance regulation. The reason is a performance requirement gives the regulated more flexibility to choose the precaution, which minimize compliance costs (see Besanko (1987), Marino (1998) and Helfand (1991)). If information is symmetric, and the regulator wants to implement a cost efficient allocation, then the

flexibility is irrelevant. As mentioned, much of the literature compares a performance regulation with a mandate on reduction effort, with unregulated output. In such a case, the firm would produce w . Given that the firm is entitled to a normal profit, the regulator would require reduction effort of e , which solves θ⋅c e( )= ⋅ − . It can easily be shown that the m w k precaution ( , )w e results both in a larger harm, and cost inefficiency.

2.3.2 Uniform permits

As mentioned a uniform permit must be available to both types of firm. This implies that the affordability constraint of the inefficient firm is the only that will bind. For all permits the optimal uniform permit is simply the inefficient firm’s individual permit. Letting superscript

U _{denote optimal uniform permit, then}

(

U_, U

) (

FB_, FB

)

h h

w e  = w e , and

( ) ( )

U FB h

z = z .

The uniform specification permit (_{w e}U, U)

The situation is displayed in Figure 2.8. Recall that the uniform permit is equal to the inefficient firm’s individual permit. The firm can choose any output level as long as

U

w w≤ and reduction effort satisfy _{e e≥} U_{. For the reasons given in Figure 2.6 the inefficient}

firm will implement

(

_{w e . In this case, over-complying with one condition does not allow} U, U

)

the firm to exceed the other. The firms thus treat the two conditions separately. It is obvious

that U

i

w =w , since profit is increasing in output. Exactly satisfying the reduction condition, i.e. U

i

e =e , minimizes the reduction cost. Both firms implement the precaution, or allocation, in the permit. However, the efficient firm will make a positive profit consisting of the cost differential ( ) (φ eh ≡ θ θh− l) ( )⋅c eh .

Figure 2.8. Uniform specification permit

(

_{w e}U, U

)

_.

The uniform permit

(

_{w e}U, U

)

_{is marked with a filled circle in the graph. For comparison purposes the}

efficient firm’s optimal individual permit is also shown (the empty circle). The firm can choose any output level as long as _{w w≤} U_{and reduction effort that satisfies e e≥} U_{, which the broken lines along}

the vertical axis and horizontal axis show respectively. The uniform permit is equal to the inefficient firm’s individual permit displayed by the black circle in the graph. Both firms implement

(

_{w e}U, U

)

_.

The efficient firm’s profit is equal to the cost differential ( )_eU

φ , which is the difference between the efficient and inefficient firm’s iso-profit curves (or affordability constraints) at

(

_{w e}U, U

)

_.

( )_eU φ w e w ACh ACl FB h z FB l z U e U w

The uniform performance permit ( )_zU

A firm can choose any precaution ( , )w e as long as the uniform harm condition is satisfied. For the same reason as with the individual permit the inefficient firm implements the precaution (_{w e}U, U)_{, see Figure 2.7. But, the efficient firm can increase its profit by choosing} a different precaution. This is shown graphically in Figure 2.9. The reason is that the efficient firm’s iso-profit curve at profit level ( )_φ e_h is not tangential to the uniform harm constraint curve, i.e. the iso-harm curve associated with the inefficient firm’s first best harm. This is expressed algebraically by using [2.FB.1]:

, , ,

Slope of the inefficient firm's iso-profit curve Slope of t Slope of the harm constraint curve =

iso-harm curve yielding the inefficient firm's level of harm

U U U U U U e h e l e w e w e w e w z c c z m m θ θ − ₌ ⋅ _> ⋅    

he efficient firm's iso-profit curve 

The efficient firm can improve profit by increasing reduction effort and thus output until its iso-profit curve is tangent to the uniform harm constraint curve. More formally, the efficient firm maximizes profit subject to the harm constraint _zU _{≥z w e}( , )_{. However, this type of} problem has already been solved in Appendix A2.1 (simply exchange _zU_{for B ). Denote the}

firm’s profit maximizing precaution with a superscript FirmUz_{. It is immediate from Appendix}

A2.1 that FirmUz FB l l

e <e and FirmUz FB l l

w >w . From the perspective of the efficient firm the uniform permit is simply an increase in allowable harm. The optimal precaution is then the one on the least cost trajectory, which results in pollution _zU_.

A uniform performance permit give the efficient firm a higher profit than a uniform specification permit, despite the fact that harm is equal with both permits, highlighting a potential inefficiency of using specification permits. Thus, the economists’ general preference for the flexibility inherent in performance regulation holds here only for uniform regulation.

Figure 2.9. Optimal uniform performance permit ( )_zU _.

The constraint curve associated with the uniform permit

( )

_zU _{is marked with a broken curve in the}

graph. This curve is the iso-harm curve at the inefficient firm’s first best level of harm

( , )

FB FB FB h h h

z =z w e . For comparison purposes the efficient firm’s optimal individual permit is also shown (the empty circle). Note the inefficient firm’s optimal individual permit is naturally on the constraint curve. The firm can choose any output and reduction effort as long as the harm constraint

U

z is satisfied. For the reasons given in Figure 2.7 the inefficient firm implements

(

_{w e}U, U

)

_{, the}

black filled circle in the graph. The efficient firm can however increase its profit. The efficient firm’s optimal precaution is

(

FirmUz, FirmUz

)

l l

w e , see the text, as shown with the grey filled circle in the graph. This is on a higher iso-profit curve than the one corresponding with the precaution

(

_{w e}U, U

)

_yielding

a profit equal to the cost-differential ( )U

e φ . ( )_eU φ e w ACh ACl FB l z U e U w ( ) FirmUz FirmUz l m wl l c el k π = ⋅ − ⋅θ − _{( )}U l e π φ= U FB h z =z w

2.4 Implementation under asymmetric information

The firm obviously has incentives to claim that θ is larger than it is and that the location rent, m, is smaller. In this chapter it is assumed that only the reduction possibilities (θ) may be private information. However the regulator knows the values of θl and θh and the

probabilities αand (1−α) respectively. The regulator cannot tell for a given firm if it has high or low costs, i.e. the outcome in stage s = 0 is only known to the firm. The assumption is made that the regulator can only find out about θi if the firm reveals this information. The

presumption is that the regulator will use the permits, or the conditions contained in them, as a direct revelation mechanism. A direct revelation mechanism must satisfy the incentive compatibility constraints defined as:

( ) ( )

i i i j i j

m w_{⋅ − ⋅θ} c e _{≥ ⋅}m w _{− ⋅θ} c e _{∀ ∈}i j, { , }l h and i_≠ j [ICi]

The tie-breaking condition is imposed that in the case of indifference (equality) the firm would choose the permit intended for its type. It is clear that uniform permits do not utilize information on _θi so asymmetric information does not change the optimal uniform permits. Moreover, it is not possible to have the efficient firm accept a permit with a more stringent harm limit, i.e. individual performance permits cannot be incentive compatible. The analysis needs only to be made for individual specification permits.

The individual specification permit

(

w e  i, i

)

The regulator’s problem under asymmetric information is to minimize expected harm subject to the affordability and incentive compatible constraints:

, , , min l h l h w w e e [ ( , )]E z w e = ⋅α z w e( , ) (1l l + − ⋅α) ( , )z w eh h s.t. m w⋅ − ⋅l θl c e( )l − ≥ k 0 [ACl] m w⋅ h− ⋅θh c e( )h − ≥ k 0 [ACh] m w⋅ − ⋅_{l θl} c e( )_l ≥ ⋅m w_h− ⋅_θl c e( )_h [ICl] m w⋅ h− ⋅θh c e( )h ≥ ⋅ − ⋅m wl θh c e( )l [ICh]

where E denotes the expectation operator. A common approach to simplify the problems like the above is to “guess” that the following two results are true in equilibrium:

Result 2.3: [ACh] holds with equality and [ACl] hold with strict inequality. The proof is

given in Appendix A2.3.

Result 2.4: [ICl] holds with equality and [ICh] holds with strict inequality. The proof is

given in Appendix A2.3.

Using the claims wh and wl can be solved from the inefficient types affordability constraint

[ACh], and the efficient types incentive compatibility constraint [ICl] respectively. This gives

( ) h h c e k w m θ ⋅ + = and l ( )l ( )h l c e k e w m θ ⋅ + +φ

= . In the latter the previous definition of the cost

differential φ( )eh ≡

(

θ θh− l

)

⋅c e( )h is used. This cost differential is what in principal-agent

theory is called the information rent, since it is the rent necessary to give up to the efficient firm in order to have it truthfully reveal its type. Here it will however be called the cost differential since it also appears with the uniform permit. Substituting these expressions into the objective function turns the problem into an unconstrained maximization. Assuming an interior solution the first order conditions are:

( ) ( ) , [ ] 0 ( ) ( ) , l l l l e l l h w l l l l h e l c c e k e z e m m E z e c e k e z e m θ θ φ α θ φ ⋅   _{⋅ + +} _{⋅ +}     ∂ _{= ⋅}   ₌   ∂ _  ⋅ + +  _ +    _{ }    ( ) ( ) [ ] , ( ) ( ) (1 ) , , 0 h l h h h e l l h w l h h e h h h h w h e h c e k e E z z e e m m c c e k c e k z e z e m m m φ θ φ α θ θ θ α  _{⋅ + +}  ∂ _{= ⋅}  _⋅     ∂     ⋅   _{⋅ +}   _{⋅ +}  + − ⋅ _ _⋅ + _ _=  

Rearranging the first of these gives the optimal reduction effort for the efficient firm: Asy l e such that

( )

l ( )l ( )h , l e( )l e w l c e k e c e z z e m m m θ ⋅ + φ θ ⋅   − = _ + _⋅ [2.Asy.1]

where superscript Asy_{denotes the optimal level. Rearranging the second condition gives the}

optimal reduction effort for the inefficient firm:

Asy h e such that

( )

( ) , ( ) ( ), ( ) 1 h h h e l l h e h e w h w l c e k c c e k e e z z e z e m m m m θ θ α θ φ φ α ⋅ + ⋅ + +     − = _ _⋅ + ₋ ⋅ _ _⋅ [2.Asy.2]

From the constraints it is straightforward to solve for the optimal output levels for the efficient and inefficient firm respectively:

Asy l w such that ( ) ( ) Asy Asy Asy l l h l c e k e w m m θ ⋅ + φ = + [2.Asy.3] Asy h w such that ( ) Asy Asy h h h c e k w m θ ⋅ + = [2.Asy.4]

The efficient firm’s second best precaution is ( Asy, Asy)

l l

w e . To have the efficient firm reveal its type, it must be given a positive profit. From [2.Asy.1] and [2.Asy.3] it follows that the efficient firm makes a profit equal to the cost differential ( Asy)

h

e

φ . Compared with the first best permit, which implies a zero profit, the positive second best profit is equivalent to an increase in the fixed cost k . From the comparative statics it follows that second best output is larger than the first best, i.e. Asy FB

l l

w _>w , and second best reduction effort is smaller than the first best effort, i.e. Asy FB

l l

e <e . To reveal information the efficient firm is allowed to incur more harm. Asymmetric information thus results in slippage in the efficient firm’s permit.

However, the condition [2.Asy.1] is the same as the symmetric information counterpart [2.FB.1], which assures that the efficient firms precaution is cost efficient, that is, the

allocation ( Asy, Asy)

l l

w e is on the efficient firm’s least cost trajectory, (cf. Figure 2.5). Note that if harm increased linearly with output, then the regulator would maintain reduction effort at first best, and compensate the efficient firm solely through output. This is the typical result in the literature when a monetary transfer is used as payment.

As mentioned, the regulator must give the efficient firm a profit equal to the cost differential. The cost differential is a function of the inefficient firm’s reduction effort. The regulator can thus decrease the cost differential, and the efficient firm’s surplus, by reducing the inefficient firm’s reduction effort. Decreasing the cost differential implies that the efficient firm’s permitted harm approaches the first best. Naturally, it also implies that the harm caused by the inefficient firm (by optimality) increases. Even though the inefficient firm makes zero profit, there is slippage in its permit. The optimal trade-off between these two effects is given in condition [2.Asy.2].

The LHS and the first term of the RHS of condition [2.Asy.2] are the same as the symmetric information condition [2.FB.1]. The second term of the RHS is a downward distortion in the inefficient firm’s reduction effort to decrease the cost differential. The distortion term is simply the marginal cost of the efficient firm’s compensation from increasing e_h. The distortion increases in α, the probability that a given firm is efficient, which is not surprising. A higher α implies that the probability of having to pay compensation to the efficient firm is relatively larger than the probability to endure the inefficiency created by distorting the inefficient type’s precaution. The latter is true since the inefficient type’s affordability constraint [ACh] binds, and then ehAsy <ehFBimplies that

Asy FB h h

w <w . Note that the inefficient firm’s second best precaution is not cost efficient. This is the well-known rent extraction-efficiency trade-off in the principal-agent models. The graphical solution to the regulator’s problem under asymmetric information is given in Figure 2.10.