Environmental Policy in the Presenceof an Informal Sector

(Preliminary draft)

Soham BaksiDepartment of Economics, University of Winnipeg

Winnipeg, R3B 2E9, CanadaTel: 1-204-258-2945; Email: s.baksi@uwinnipeg.ca

Pinaki BoseDepartment of Economics, University of Memphis

Memphis, TN 38152, USAEmail: psbose@memphis.edu

AbstractWe analyze environmental policy when it applies to only a few large producers

of a polluting good (the �formal sector�) but not to many other smaller �rms pro-ducing the same good (the �informal sector�). Firms in the formal and informalsectors produce a polluting intermediate good. The intermediate good is used asan input by the formal sector �rms to produce a �nal good. The formal sectorsets the price of the intermediate good, which the informal sector �rms take asgiven. The environmental policy requires only formal �rms to abate a part oftheir own pollution. We show that a stricter environmental policy initially reducestotal pollution generated by both sectors (when the �scale e¤ect�dominates the�composition e¤ect�) but later on increases it (when the latter e¤ect dominatesthe former). Total pollution is, therefore, non-monotonic and convex in the en-vironmental policy variable. When the environmental policy is chosen e¢ ciently,an increase in the informal �rms�operating cost, or an increase in the number of�rms in the formal sector, may decrease social welfare.

JEL classi�cation: Q58, O17, L13

1

1 Introduction

A growing global concern about the health of the ecosystem has led to in-creasing pressures on developing countries to undertake policies that seekto protect the environment. Many developing country governments have re-sponded, in part, by mandating environmental taxes and standards on theirproducers. However, given the relatively weaker institutions and greater cor-ruption that characterize most developing countries, the question remainsas to how broadly the environmental policies can be applied to pollutingproducers in such countries. From an administrative standpoint, while it iseasier to implement the environmental policies on the (fewer) larger �rmsoperating in the formal sector of the economy, enforcing the same policies onsmaller (and more numerous) �rms operating in the informal sector can bemuch more di¢ cult.1

A large part of the informal sector in developing countries is concen-trated in manufacturing, servicing and retailing activities such as bleachingand dyeing of garments, leather tanning, brick manufacturing, automotiverepair, metalworking, and hawking. Most of these activities have consider-able negative environmental impacts.2 E­ uents from bleaching, dyeing andtanning contain hazardous chemicals which, when disposed of improperly,can pollute rivers and groundwater. Brick kilns in the informal sector areoften �red using cheap fuel such as used tires, plastic refuse, and used motoroil which create air pollution. Street vending in many developing countriescause littering and congestion (Perera & Amin, 1996).Although, the informal sector is a signi�cant source of detrimental ex-

ternalities (pollution) in developing countries, very little attention has beenpaid to this problem by either researchers or policymakers. Blackman andBannister (1998) identify four reasons why policymakers in developing coun-

1The informal sector (also known as shadow economy) is commonly de�ned as consistingof economic activities that contribute to the o¢ cially calculated GDP but are unregisteredby government. The central characteristic of informal �rms is that they are not regulated,or they are in violation of the legal requirements that society imposes on the formal oro¢ cial sector of the economy (Portes, et al., 1989). The relevance of the shadow economyhas been well documented and approximately measured in the economic literature (see,for examples, de Soto, 1989; Tanzi, 1999; and Friedman et al., 2000). Schneider and Enste(2000) �nd that the average size of the shadow economy varied from 12% of GDP forOECD countries to 23% for transition countries and 39% for developing countries.

2Collecting and sorting scrap for recycling is, in contrast, an informal sector activitythat is environmentally bene�cial.

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tries have found tackling informal sector pollution an exceptionally challeng-ing task: (i) the minimal ties that informal �rms have with the state; (ii)di¢ culty in monitoring informal �rms which are small, numerous and widely-dispersed; (iii) tendency of informal �rms to be intensely competitive whichmakes them susceptible to cost-cutting even at the expense of harming theenvironment; and (iv) the large amount of employment (mostly for the poor)generated by the informal sector. Given these constraints, policymakers indeveloping countries have tended to focus on their formal sector for pollutioncontrol.Barring a few exceptions, the existing literature on the informal sector

has largely ignored analyzing this sector from an environmental standpoint.Blackman and Bannister (1998) empirically examine the adoption of propane(a cleaner fuel) by informal brick manufacturers in Cd. Juarez in Mexico,and �nd that community pressure can play an e¤ective role in such adoption.Besides peer monitoring, some other policy options for controlling informalsector pollution are discussed in Blackman (2000). Blackman (2006) providesvarious case studies with respect to polluting informal sector in developingcountries. In a theoretical work, Chaudhuri (2005) constructs a three-sectorgeneral equilibrium model with a polluting informal sector, a clean formalsector, and a clean agricultural sector. All sectors operate under perfectlycompetitive markets. The informal sector produces an intermediate good,while the formal sector produces a �nal good using the intermediate good (aswell as labour and capital) as input. Pollution is harmful as it reduces labourproductivity. Since enforcing environmental policy measures on informalsector �rms is di¢ cult, Chaudhuri (2005) analyzes a situation where a taxis instead imposed on the formal sector, with the tax rate depending on thelevel of pollution generated by the informal sector.We consider a situation where both the formal and informal sectors pro-

duce a polluting intermediate good (for e.g., leather), but the environmentalpolicy requires only the formal sector �rms to abate their own emissions.Informal �rms, however, do not undertake any abatement activity (perhapsbecause the policymaker does not wish to impose additional costs on informal�rms which are a large source of employment for poorer people, or becausethe informal �rms are able to evade an existing environmental regulation thatapplies to them).3 The formal sector is imperfectly competitive, and uses the

3In general, the informal sector is more pollution-intensive than its formal counterpart.Informal �rms usually lack the incentive and ability to use cleaner (and costlier) technolo-

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intermediate good for producing a �nal good (e.g. leather shoes).4 The infor-mal sector, in contrast, consists of small price-taking �rms. Smallness of sizeis a characteristic feature of informal �rms that helps them operate below theregulatory radar. The e¤ective size of the informal sector is endogenouslydetermined in our model.We �nd that, in the presence of an informal sector, a stricter environmen-

tal policy (higher abatement level or lower emission intensity) that appliesonly to the formal sector initially reduces total pollution before increasingit. Of course, if the informal sector were absent, then total pollution wouldalways decrease with more abatement by the formal sector. This result isshown in section 2.1 of the paper. In section 2.2, we consider social welfare.Here we �nd that an increase in the cost of operating in the informal sector(for instance, due to better monitoring of the informal sector by the regula-tor) can change the e¢ cient environmental policy and social welfare in eitherdirection, depending on parameter values. Further, as the number of formalsector �rms increases, the e¢ cient environmental policy becomes stricter, butsocial welfare may get reduced. Policy implications and concluding commentsare o¤ered in the last section of the paper.

2 The model

Consider a vertical production structure, where a downstream �nal good (e.g.a leather bag) is produced using a polluting upstream/intermediate good (e.g.leather). With appropriate de�nition of units, one unit of the intermediategood is needed to produce one unit of the �nal good (�xed proportions pro-duction function). Hence, both the intermediate good as well as the �nalgood can be denoted by the variable X. The �nal good is produced in theformal sector (denoted as sector 1), which is an m-�rm oligopoly (m � 1).The intermediate good, on the other hand, is produced both by formal sector�rms as well as by �rms in the informal sector (called sector 2). Each �rm

gies and inputs. As well, informal sector workers are more likely to be less trained and lessaware of the detrimental e¤ects of pollution on health and the environment (Kent, 1991).Moreover, informal �rms are often located near poor residential areas, and their pollutiona¤ects more people directly (Blackman, 2000).

4For example, leather tanning in India is done by Bata at its tanneries in Batanagarand Mokamehghat, as well as by numerous small and informal �rms. Bata is a dominant�rm in the formal sector, which produces shoes and other leather products.

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in the formal sector thus produces both intermediate good and �nal good,while each informal sector �rm produces only intermediate good. The priceof the intermediate good is set by the formal sector. The informal sectorconsists of price-taking fringe �rms.Without abatement, production of one unit of the intermediate good

generates one unit of pollution. The government�s environmental policy (anintensity standard) requires each formal sector �rm (or �formal �rm�) toabate part of its own pollution. Fringe �rms, however, do not undertake anyabatement (either because they are not required to do so, or because theyare able to evade abatement regulations). Demand for the �nal good is linearand given by p = a�X, where a > 0 is the �choke price�and X is the marketquantity.Sequence of moves is as follows. The regulator moves �rst and chooses the

emission intensity level that the formal �rms must achieve. In the secondstage, each formal �rm chooses how much intermediate good to produceitself and how much to purchase from the informal sector (the total amountof intermediate good used determines the quantity of �nal good produced).Finally, in stage three, fringe �rms enter the informal sector and produce theintermediate good. The above game is solved using backward induction.

2.1 Market equilibrium for given environmental policy

In the third stage, price-taking fringe �rms enter the informal sector andundertake production. For simplicity, we assume that each fringe �rm in-elastically produces one unit of the intermediate good (recall that informal�rms are usually small). Let c denote the per-unit production cost of a fringe�rm. These �rms are heterogeneous in terms of their production cost, and c isassumed to be uniformly distributed over support [c2; c2 + !]. Total numberof �rms that can potentially enter the informal sector is N1. The probabilitydensity function is thus N1=! � N . Suppose price of the intermediate good,as determined by the formal sector, is �. Pro�t of an informal sector (sector2) �rm then is

�2 = �� cThe fringe �rms take price � as given, and entry into the informal sector

goes on until the last entrant makes zero pro�t. The marginal cost of the

5

last entrant is thus given by c = �. The number of �rms operating in theinformal sector, as well as the total output of the informal sector, X2, is

X2 = (�� c2)N (1)

Combined pro�t of all �rms in the informal sector, �2, is

�2 �Z �

c2

(�� c)Ndc = 1

2N (�� c2)2 (2)

Them �rms in the formal sector are assumed to be identical to each other(symmetric case). In the second stage, each formal �rm chooses the amountof the intermediate good it produces itself (denoted by x1) and the amountof the intermediate good it purchases from the informal sector (de�ned asx2) to maximize

�1 = (a� �� x)x� c1 x1 � �x2In the above pro�t function, (a� �� x)x is the representative formal �rm�stotal revenue (TR), with x = x1+ x2 being the output produced by the �rmand � being the output produced by all other (m� 1) formal �rms. Theformal �rm�s total cost of producing x1 units of the intermediate good isTC1 = c1 x1, and its total cost of purchasing x2 units of the intermediategood from the informal sector is TC2 = �x2. The formal �rm�s marginal costof producing the intermediate good is thus MC1 = c1 . Here � 1 is the�abatement level� chosen by the government in the �rst stage.5 One unitof intermediate good produced by a formal �rm leads to 1= units of netemission after abatement; 1= is thus the emission intensity of intermediategood output. A higher abatement level (lower emission intensity) involvesincreased operating cost, as c1 > 0.6

The total revenue described above gives the representative formal �rm�smarginal revenue as MR = a� �� 2x. Moreover, using (1), we can rewrite

5Kennedy (1994) uses a similar formulation for modeling abatement, in an article thatdeals with a di¤erent issue.

6Although, for expositional ease we call the �abatement level�, abatement undertaken

per unit of intermediate good produced by a formal �rm is�1� 1

�. When no abatement

is required (i.e. = 1), then a formal �rm�s operating cost consists only of productioncost (its abatement cost is zero) and equals c1.

6

TC2 = �x2 =

��2 + x2N

+ c2

�x2;

where �2 is the amount of intermediate good purchased from the informalsector by all other (m� 1) formal �rms (so that �2 + x2 = X2). Thus, therepresentative formal �rm�s marginal cost of procuring the intermediate goodfrom the informal sector is

MC2 =2x2 + �2 + c2N

N

Notice that MC1 = c1 � MC2 for all x2 � 12(c1 N � �2 � c2N), or

using the fact that �2 = (m� 1)x2 due to symmetry, MC1 � MC2 for allx2 less than (or equal to)

c1 � c21 +m

N � x�2 (3)

As long as the pro�t-maximizing output of the �nal good is less than x�2,the formal �rm will buy the intermediate good from the informal sectorrather than produce it. The pro�t-maximizing output of �nal good is givenby MR = MC1, or x = 1

2(a� �� c1 ). Using the symmetry condition,

� = (m� 1)x, we have

x� =a� c1 1 +m

(4)

Consequently, the optimal amount of intermediate good for the formal �rmto produce is

x�1 = x� � x�2 =

a+ c2N � c1 (1 +N)1 +m

(5)

To focus on the situation where both the sectors produce the intermediategood, we assume that parameter values are such that x�1 and x

�2, as given by

(3) and (5), are positive. This imposes the following limits on the abatementlevel :

c2c1� min < <

a+ c2N

c1 (1 +N)� max

Note that the total amount of inputs used (and output produced), x�, isindependent of the informal sector parameters (c2 and N). Instead, what theinformal sector in�uences is the manner in which the total input is obtained

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by the formal �rms (self-production vs. sourcing from the informal sector).The �outsourcing ratio�, de�ned as the proportion of total inputs procuredfrom the informal sector, equals

x�2x�=c1 � c2a� c1

N

Amore stringent environmental policy (a higher ) increases the formal �rms�cost of producing the intermediate good. This decreases the total amount ofintermediate good used, and �nal good produced, x� by these �rms (�scalee¤ect�). The higher additionally leads to less self-production (x�1) and moreoutsourcing (x�2) by each formal �rm (�composition e¤ect�). The combinedimpact of these two e¤ects is to increase the outsourcing ratio x�2=x

�, as increases.Using (1), (3) and (4), we get the equilibrium prices of the intermediate

and �nal goods as

�� =mx�2N

+ c2 =mc1 + c21 +m

(6)

andp� = a�mx� = a+mc1

1 +m(7)

Remark: The equilibrium price a formal �rm pays for intermediate goodsoutsourced from the informal sector ( ��) is less than the formal �rm�s ownmarginal cost of producing the intermediate good ( c1 ).

Proof: From (6), MC1 � �� = c1 � mc1 +c21+m

= c1 �c21+m

> 0

The above result is a re�ection of the market (monopsony) power enjoyedby formal �rms when they buy the intermediate good from the informalsector. As m increases, and the formal sector becomes more competitive, thedi¤erence MC1 � �� decreases, until �� !MC1 as m!1.

The equilibrium amount of pollution generated from production of thedirty intermediate good by both formal and informal �rms, Z, is given by(using (3) and (5))

Z � mx�1

+mx�2 =m

(1 +m)(a+ c2N � c1 (1 +N) + N (c1 � c2)) (8)

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The following proposition holds.

Proposition 1: In the presence of an informal sector,(i) increased abatement by the formal sector initially reduces (when

<q

a+c2Nc1N

� 1), and later on increases (when > 1), the level of totalpollution;(ii) an increase in the cost of operating in the informal sector ( c2) leads

to a decrease in the level of total pollution, in the presence of an abatementpolicy (i.e. when > 1);(iii) an increase in the number of formal �rms (m) leads to an increase

in the level of total pollution.

Proof: From (8), we have (i) @Z@ = m

(1+m) 2( 2Nc1 � a� c2N) � 0 if

and only if �q

a+c2Nc1N

� 1; (ii) and@Z@c2

= �mN �1(1+m)

� 0; and (iii)@Z@m= a+c2N�c1 (1+N)+ N( c1�c2)

(1+m)2 > 0.

Proposition 1(i) implies that total pollution is non-monotonic and convexin the abatement level . A stricter environmental policy (higher ) thatapplies only to the formal sector has two counteracting e¤ects on combinedpollution that emerges from both the sectors. On one hand, the above-mentioned scale e¤ect (lower x� and x�1= ) tends to reduce total pollution.On the other hand, the composition e¤ect tends to increase total pollution,as it leads to less self-production by the formal �rms and more outsourcingfrom the higher polluting informal sector. When < 1, the former e¤ectdominates, and pollution generated by the formal and informal sectors to-gether decreases as environmental policy become tighter. The converse istrue when > 1.

7 Consequently, total pollution is U-shaped in the abate-ment level imposed on the formal sector. Of course, had the informal sectorbeen altogether absent (if it is successfully banned, for instance) the com-position e¤ect would be absent, and a more stringent policy would alwaysreduce total pollution (i.e., if N = 0, @Z

@ < 0 for all ).

Recall that c2 denotes the lower bound of the informal �rms�heteroge-neous cost of operating in the informal sector (the upper bound is c2 + !).Some possible reasons for a change in c2 are as follows. If the government

7Note that 1, as de�ned above, is greater than min if and only if ac1+c2N (c1 � c2) >0. As well, 1 is less than max if and only if aN > c1 (1 + 2N) +N

2 (c1 � c2). We laterprovide numerical examples where these conditions are satis�ed.

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randomly monitored the informal sector in order to discourage fringe �rmsfrom operating, and imposed higher penalties on detected violators, it couldlead to an increase in c2. Alternatively, c2 could also rise if, due to economicdevelopment, the fringe �rms�outside option (alternative to joining the infor-mal sector) became more pro�table (e.g. if their opportunity cost of labourincreased). In any event, Proposition 1(ii) shows that an increase in c2 willlead to reduced pollution as long as > 1.Finally, an increase in the number of formal �rms leads to an increase

in the total output produced by informal �rms (i.e.@(mx�2)@m

> 0), and raisestotal pollution.8

2.2 E¢ cient environmental policy

In the �rst stage of the game, a government regulatory body sets the abate-ment level . Suppose the regulator chooses so as to maximize social wel-fare, W , de�ned as the sum of consumer surplus plus pro�t of both formaland informal �rms minus pollution damage:9

W ��1

2(mx1 +mx2)

2

�+m (p (x1 + x2)� c1 x1 � �x2)+�2��

�mx1

+mx2

�;

(9)where � � 0 is the marginal pollution damage. Making use of (2), (3), (5),(6) and (7), the FOC for maximum W is

F � @W

@ =

m

2 (1 +m)2

�c21

3 (1 +N) (m+ 2) + � (1 +m) (a+ c2N)�c1 2 (�N (1 +m) + (m+ 2) (a+ c2N))

�= 0

(10)Notice that there are three roots of that satisfy the FOC. As well, thesecond derivative of W with respect to is

@2W

@ 2= �m (2� (1 +m) (a+ c2N)� c

21 3 (2 +m) (1 +N))

(1 +m)2 3; (11)

8If, in an alternative scenario, the formal and informal �rms produced the same pol-luting good for a market, total pollution may fall when m increases. This is shown in theAppendix, which analyses the alternative scenario.

9Alternatively, the government could choose on considerations such as those involvingpolitical factors or lobbying.

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which is negative for all such that

0 < <

�2� (1 +m) (a+ c2N)

c21 (2 +m) (1 +N)

� 13

� 2

To focus on the interior solution, we assume parameter values are suchthat welfareW is maximized at , where is the value of the abatement levelthat satis�es the FOC (10), and 2 (1; 2).10 This implies that the SOC@2W@ 2

< 0 is satis�ed at . In the next section we provide numerical examples,which identify su¢ cient conditions for such interior welfare maximization.Given an interior solution, Propositions 2 and 3 delineate how changes in

each sector a¤ect the e¢ cient abatement level and the maximized level ofwelfare W ( ):

Proposition 2:An increase in the cost of operating in the informal sector(i) makes the e¢ cient environmental policy more stringent, i.e. d

dc2> 0,

if and only if � (1 +m)� c1 2 (2 +m) > 0;(ii) increases social welfare, i.e. dW

dc2> 0, if and only if c1 2 (2 +m) �

(� (1 +m) + c2 (2 +m)) + � (1 +m) < 0.

Proof:(i) The sign of d

dc2can be derived using the methodology of comparative

statics with respect to the FOC (10). Subject to satisfaction of the SOC@2W@ 2

< 0, we have

sign

�d

dc2

�= sign

�@F

@c2

�From (10), we get

@F

@c2=

mN

(1 +m)2 2

�� (1 +m)� c1 2 (2 +m)

�(ii) Using the envelope theorem, we have dW

dc2= @W

@c2( = ). From (9),

@W

@c2= �mN (c1

2 (2 +m)� (� (1 +m) + c2 (2 +m)) + � (1 +m))(1 +m)2

10In contrast, a corner solution would involve = 1 or = max.

11

Proposition 3: In the presence of an informal sector, an increase in thenumber of formal �rms(i) makes the e¢ cient environmental policy more stringent, i.e. d

dm> 0;

(ii) increases social welfare, i.e. dWdm> 0, if and only if the expression in

eq. (12), when evaluated at = , is positive.

Proof: Similar to proof of Proposition 2.(i) From (10), we get

@F

@m=2c21

3 (1 +N)� c1 2 (2 (a+ c2N) + �N (1 +m)) + � (1 +m) (a+ c2N)(1 +m)3 2

;

which is positive when evaluated at = (note F ( ) = 0 by de�nition of ).(ii) From (9), we have

@W

@m=

c21 3 (1 +N)� c1 2 (�N (1 +m) + 2 (a+ c2N))� � (1 +m) (a+ c2N)

+ (a2 +Nc22 + � (1 +m) (c2N + c1 (1 +N)))

(1 +m)3 (12)

The scenario analyzed in our model involves three sources of market fail-ure, which the environmental policy variable has to address. First, there isthe negative externality of pollution, which is generated through productionof the intermediate good. Correcting the overproduction associated with thisexternality calls for an abatement level > 1. Second, due to imperfect com-petition in the formal sector, there is underproduction of the �nal output.Correcting this market failure requires a production subsidy, which exerts adownward pressure (implying a less stringent environmental policy) on costlyabatement activities. Third, an increase in the abatement level increases theformal �rms�operating cost and makes sourcing the intermediate good fromthe informal sector more pro�table for them. However, this exacerbates thenegative externality problem as, unlike the formal �rms, the informal �rmsdo not undertake any abatement. These three considerations have to be in-corporated by the regulator when she sets the e¢ cient environmental policy.An increase in the operating cost of the informal �rms implies fewer �rms

can survive in that sector, for any given price of the intermediate good. This

12

enables the regulator to relax the e¢ cient environmental policy, when thepollution damage parameter is su¢ ciently small. An increase in the numberof formal �rms, on the other hand, lessens the underproduction e¤ect andenables the regulator to strengthen the environmental policy.

2.3 Numerical analyses

Here we provide three numerical examples to support of our analytical results.Suppose the various parameters in our model take the following values:

a = 100; c1 = 2; c2 = 0, N = 3

Numerical Example 1: Suppose the number of formal �rms is m =1, and the pollution damage parameter is � = 5. Then the previously-de�ned threshold values of abatement level are max = 12:5 and 1 = 4: 08(de�ned in Proposition 1). The three roots of that satisfy the FOC (10)are = �1: 18 , = 1: 29, and = 17: 22. Since W ( = 1: 29) = 3373:3 > W ( = max) = 2625, the e¢ cient level of abatement is = 1: 29. Aswell, from (11), @

2W@ 2

( = 1: 29) = �219: 19. With an e¢ cient environmentalpolicy, equilibrium values of the other variables are x1 = 44:83, x2 = 3:88,� = 1:29, p = 51:29 and Z = 38:54. Moreover, evaluated at = , @F

@c2=

�1: 53� 10�2, @W@c2

= �4: 119, and @W@m

= 1092: 3. Thus, from Proposition 2,an increase in the cost of operating in the informal sector (c2) decreases boththe e¢ cient level of abatement (signifying a weaker environmental policy)and also social welfare. An increase in the number of formal �rms, on theother hand, increases social welfare (following Proposition 3).

Numerical Example 2: Alternatively, suppose m = 1 and � = 15. Asbefore, max = 12:5 and 1 = 4: 08. The three roots of that satisfy theFOC (10) now are = �1: 86; = 2: 1 and = 16: 01. Since W ( = 2: 1) =3069: 8 > W ( = max) = 2250, the e¢ cient level of abatement is = 2:1. Moreover, from (11), @

2W@ 2

( = 2: 1) = �149: 55. With abatement set atits e¢ cient level, values of the other variables are x1 = 41: 59, x2 = 6: 31,� = 2: 1, p = 52: 1 and Z = 26: 1. Moreover, @F

@c2= 0: 59, @W

@c2= 2: 34, and

@W@m= 958: 04. Therefore, an increase in the cost of operating in the informal

sector c2 now increases both e¢ cient abatement level (signifying a stricterenvironmental policy) as well as social welfare. An increase in the numberof formal �rms also increases social welfare.

13

Numerical Example 3: Suppose insteadm = 30 and � = 5. As before, max = 12:5 and 1 = 4: 08. The three roots of that satisfy the FOC (10)now are = �1: 39; = 1: 54 and = 14: 17. Since W ( = 1: 54) = 4385:9 > W ( = max) = 3383: 2, the e¢ cient level of abatement is = 1: 54.Moreover, from (11), @

2W@ 2

( = 1: 54) = �249: 35. With e¢ cient abatementpolicy, equilibrium values of the other variables are x1 = 2: 83, x2 = 0: 3,� = 2: 98, p = 6: 21, and Z = 64: 06. Moreover, @F

@c2= 0: 13, @W

@c2= �4: 14,

and @W@m

= �2: 82 � 10�2. Therefore, an increase in the cost of operating inthe informal sector c2 increases e¢ cient abatement level but decreases socialwelfare. Unlike examples 1 and 2, an increase in the number of formal �rmsnow decreases social welfare.

3 Conclusion

This paper considers a situation where an environmental policy targets a fewdominant producers of a polluting good but leaves many smaller pollutersoutside its scope.11 The speci�c context modeled is one where imperfectlycompetitive formal �rms and price-taking informal �rms produce a pollutingintermediate good. The formal sector �rms also produce the downstream�nal good. We �nd that imposition of an environmental policy, which re-quires only the formal sector �rms to abate their own emissions, reduces thetotal amount of intermediate good used by the formal �rms but increasesthe amount of intermediate good outsourced from the informal sector. Thesecounteracting e¤ects are shown in the paper to imply that more stringentabatement requirements on the formal sector initially reduces total pollutionbefore increasing it.12

When the abatement level is chosen by the regulator to maximize socialwelfare, we �nd that an increase in the cost of operating in the informal

11Although our model is motivated in terms of a formal vs. informal sector example, themodel and the results are also applicable to any situation where a few dominant pollutersare targeted by an environmental policy whilst smaller producers are exempted from it.Such a situation, for instance, may arise in Canada, where the current government isconsidering an environmental policy that targets a few large polluters of greenhouse gasesbut leaves smaller polluters unregulated.12The non-monotonicity of total pollution is robust to an alternative speci�cation of the

model, where formal and informal �rms produce and sell a polluting (�nal) good in themarket (see Appendix).

14

sector may reduce social welfare. Welfare may also get reduced if the numberof formal sector �rms increases. These results have important implicationsfor both development policy and competition policy. In particular, theysuggest that, under certain conditions, discouraging the informal sector, orpromoting entry into the formal sector, may not be desirable from a socialwelfare perspective.

15

Appendix

Consider an alternative (to that in the main text) scenario where thereis a polluting good Q (e.g. bricks), which is produced by both the formaland informal sector �rms. The good is sold by each (formal or informal)�rm in the market, where the demand is given by p = a � Q. If thereis no abatement, production of one unit of the good generates one unit ofpollution (or some other negative externality such as littering or congestion).Formal �rms are required by the government to undertake abatement, suchthat their emission is 1

units per unit output. The agents in this game, their

sequence of moves, and the nature of the �rms�costs are assumed to be thesame as before (in the main text), in order to facilitate comparison. The onlydi¤erence is that the production structure in this appendix does not involvea vertical (upstream/downstream) relation between the formal and informalsectors.Price p of the good is determined by the formal sector. In the third stage,

price-taking fringe �rms enter the informal sector until the last entrant earnszero pro�t. The number of informal �rms, and total output produced by theinformal sector (sector 2), is

Q2 = (p� c2)N (13)

In the second stage, the formal sector (sector 1) �rms now face a residualdemand given by

p = a�Q1 �Q2or, using (13),

p =a�Q1 + c2N

1 +N; (14)

where Q1 is the total output of the formal sector. The representative formal�rm chooses its own production q1 in order to maximize its pro�t

�1 =

a� fQ1 � q1 + c2N

1 +N

!q1 � c1 q1;

where fQ1 is the output of all other (m� 1) formal �rms. The formal �rm�sunit cost is c1 as before. The FOC for pro�t maximization, along with thesymmetric condition fQ1 = (m� 1) q1, yields

16

qA1 =a+ c2N � c1 (1 +N)

m+ 1;

where we use superscript A to denote the equilibrium values of the variablesin the alternative scenario considered in this appendix. To ensure positiveproduction by the formal �rms (qA1 > 0), we assume

<a+ c2N

c1 (1 +N)= max

Equilibrium price of the good, using (14), is

pA =a+ c2N +mc1 (1 +N)

(m+ 1) (1 +N)(15)

From (13) and (15), total output of the informal sector is

QA2 =N (a� c2 +m (c1 � c2) (1 +N))

(m+ 1) (1 +N)

Equilibrium pollution from the formal and informal sectors �rms togethernow is

ZA � mqA1

+QA2 =

� (N (a� c2)�m (1 +N) (c1 (1 +N) + c2N))+mc1N

2 (1 +N) +m (1 +N) (c2N + a)

� (m+ 1) (1 +N)

(16)

Proposition A1: In the presence of an informal sector,(i) increased abatement by the formal sector initially reduces (when

<q

a+c2Nc1N

= 1), and later on increases (when > 1), the level of totalpollution;(ii) an increase in the cost of operating in the informal sector ( c2) leads

to a decrease in the level of total pollution, i.e. @ZA

@c2< 0, even in the absence

of an abatement policy (i.e. even when = 1);(iii) an increase in the number of formal �rms (m) leads to an increase

in the level of total pollution if and only if < 1+NN� 3.

17

Proof: From (16), we have (i) @ZA

@ = m

(1+m) 2( 2Nc1 � a� c2N) � 0 if

and only if �q

a+c2Nc1N

= 1; (ii)@ZA

@c2= �N +m( �1)(1+N)

(m+1)(1+N)< 0; and (iii)

@ZA

@m= (1 +N �N ) a+c2N�c1 (1+N)

(m+1)2(1+N)� 0 if and only if � 1+N

N� 3.

Note that total pollution now may fall with an increase in the numberof formal �rms, unlike Proposition 1(iii) in the main text. The key reasonbehind the di¤erential impact of an increase in m on total pollution in thetwo models is as follows. Whereas an increase inm leads to an increase in thetotal output produced by informal �rms (i.e.

@(mx�2)@m

> 0) in the main text(where informal �rms produced an input for the formal �rms), an increasein m leads to a reduction in total output produced by the informal sector(@Q

A2

@m< 0) in the appendix (where informal and formal �rms sell the same

good). This creates the potential for total pollution to decrease in the latterscenario but not in the former. The welfare implications of the two models,nevertheless, remain qualitatively similar.

18

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