Environmental Policy in the Presence of an Informal Sector

Transcription

1 Environmental Policy in the Presence of an Informal Sector (Preliminary draft) Soham Baksi Department of Economics, University of Winnipeg Winnipeg, R3B 2E9, Canada Tel: ; Pinaki Bose Department of Economics, University of Memphis Memphis, TN 38152, USA Abstract We 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 producing the same good (the informal sector ). Firms in the formal and informal sectors produce a polluting intermediate good. The intermediate good is used as an input by the formal sector rms to produce a nal good. The formal sector sets the price of the intermediate good, which the informal sector rms take as given. The environmental policy requires only formal rms to abate a part of their own pollution. We show that a stricter environmental policy initially reduces total 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 dominates the former). Total pollution is, therefore, non-monotonic and convex in the environmental 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

2 1 Introduction A growing global concern about the health of the ecosystem has led to increasing pressures on developing countries to undertake policies that seek to protect the environment. Many developing country governments have responded, in part, by mandating environmental taxes and standards on their producers. However, given the relatively weaker institutions and greater corruption that characterize most developing countries, the question remains as to how broadly the environmental policies can be applied to polluting producers in such countries. From an administrative standpoint, while it is easier to implement the environmental policies on the (fewer) larger rms operating in the formal sector of the economy, enforcing the same policies on smaller (and more numerous) rms operating in the informal sector can be much more di cult. 1 A large part of the informal sector in developing countries is concentrated in manufacturing, servicing and retailing activities such as bleaching and dyeing of garments, leather tanning, brick manufacturing, automotive repair, metalworking, and hawking. Most of these activities have considerable negative environmental impacts. 2 E uents from bleaching, dyeing and tanning contain hazardous chemicals which, when disposed of improperly, can pollute rivers and groundwater. Brick kilns in the informal sector are often red using cheap fuel such as used tires, plastic refuse, and used motor oil which create air pollution. Street vending in many developing countries cause littering and congestion (Perera & Amin, 1996). Although, the informal sector is a signi cant source of detrimental externalities (pollution) in developing countries, very little attention has been paid to this problem by either researchers or policymakers. Blackman and Bannister (1998) identify four reasons why policymakers in developing coun- 1 The informal sector (also known as shadow economy) is commonly de ned as consisting of economic activities that contribute to the o cially calculated GDP but are unregistered by 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 or o cial sector of the economy (Portes, et al., 1989). The relevance of the shadow economy has 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 for OECD countries to 23% for transition countries and 39% for developing countries. 2 Collecting and sorting scrap for recycling is, in contrast, an informal sector activity that is environmentally bene cial. 2

3 tries have found tackling informal sector pollution an exceptionally challenging task: (i) the minimal ties that informal rms have with the state; (ii) di culty in monitoring informal rms which are small, numerous and widelydispersed; (iii) tendency of informal rms to be intensely competitive which makes them susceptible to cost-cutting even at the expense of harming the environment; and (iv) the large amount of employment (mostly for the poor) generated by the informal sector. Given these constraints, policymakers in developing countries have tended to focus on their formal sector for pollution control. 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 informal sector pollution are discussed in Blackman (2000). Blackman (2006) provides various case studies with respect to polluting informal sector in developing countries. In a theoretical work, Chaudhuri (2005) constructs a three-sector general equilibrium model with a polluting informal sector, a clean formal sector, and a clean agricultural sector. All sectors operate under perfectly competitive markets. The informal sector produces an intermediate good, while the formal sector produces a nal good using the intermediate good (as well as labour and capital) as input. Pollution is harmful as it reduces labour productivity. Since enforcing environmental policy measures on informal sector rms is di cult, Chaudhuri (2005) analyzes a situation where a tax is instead imposed on the formal sector, with the tax rate depending on the level of pollution generated by the informal sector. We consider a situation where both the formal and informal sectors produce a polluting intermediate good (for e.g., leather), but the environmental policy requires only the formal sector rms to abate their own emissions. Informal rms, however, do not undertake any abatement activity (perhaps because the policymaker does not wish to impose additional costs on informal rms which are a large source of employment for poorer people, or because the informal rms are able to evade an existing environmental regulation that applies to them). 3 The formal sector is imperfectly competitive, and uses the 3 In 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- 3

4 intermediate good for producing a nal good (e.g. leather shoes). 4 The informal sector, in contrast, consists of small price-taking rms. Smallness of size is a characteristic feature of informal rms that helps them operate below the regulatory radar. The e ective size of the informal sector is endogenously determined in our model. We nd that, in the presence of an informal sector, a stricter environmental policy (higher abatement level or lower emission intensity) that applies only to the formal sector initially reduces total pollution before increasing it. Of course, if the informal sector were absent, then total pollution would always decrease with more abatement by the formal sector. This result is shown 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 regulator) can change the e cient environmental policy and social welfare in either direction, depending on parameter values. Further, as the number of formal sector rms increases, the e cient environmental policy becomes stricter, but social welfare may get reduced. Policy implications and concluding comments are 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 intermediate good is needed to produce one unit of the nal good ( xed proportions production function). Hence, both the intermediate good as well as the nal good can be denoted by the variable X. The nal good is produced in the formal 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 less aware 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 pollution a ects more people directly (Blackman, 2000). 4 For example, leather tanning in India is done by Bata at its tanneries in Batanagar and 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. 4

5 in the formal sector thus produces both intermediate good and nal good, while each informal sector rm produces only intermediate good. The price of the intermediate good is set by the formal sector. The informal sector consists 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 (an intensity standard) requires each formal sector rm (or formal rm ) to abate part of its own pollution. Fringe rms, however, do not undertake any abatement (either because they are not required to do so, or because they are able to evade abatement regulations). Demand for the nal good is linear and given by p = a X, where a > 0 is the choke price and X is the market quantity. Sequence of moves is as follows. The regulator moves rst and chooses the emission intensity level that the formal rms must achieve. In the second stage, each formal rm chooses how much intermediate good to produce itself and how much to purchase from the informal sector (the total amount of intermediate good used determines the quantity of nal good produced). Finally, in stage three, fringe rms enter the informal sector and produce the intermediate 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 and undertake production. For simplicity, we assume that each fringe rm inelastically 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 is assumed to be uniformly distributed over support [c 2 ; c 2 +!]. Total number of rms that can potentially enter the informal sector is N 1. The probability density function is thus N 1 =! N. Suppose price of the intermediate good, as determined by the formal sector, is. Pro t of an informal sector (sector 2) rm then is 2 = The 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 c 5

6 last entrant is thus given by c =. The number of rms operating in the informal sector, as well as the total output of the informal sector, X 2, is X 2 = ( c 2 ) N (1) Combined pro t of all rms in the informal sector, 2, is 2 Z c 2 ( c) Ndc = 1 2 N ( c 2) 2 (2) The m rms in the formal sector are assumed to be identical to each other (symmetric case). In the second stage, each formal rm chooses the amount of the intermediate good it produces itself (denoted by x 1 ) and the amount of the intermediate good it purchases from the informal sector (de ned as x 2 ) to maximize 1 = (a x) x c 1 x 1 x 2 In the above pro t function, (a x) x is the representative formal rm s total revenue (T R), with x = x 1 + x 2 being the output produced by the rm and being the output produced by all other (m 1) formal rms. The formal rm s total cost of producing x 1 units of the intermediate good is T C 1 = c 1 x 1, and its total cost of purchasing x 2 units of the intermediate good from the informal sector is T C 2 = x 2. The formal rm s marginal cost of producing the intermediate good is thus MC 1 = c 1. Here 1 is the abatement level chosen by the government in the rst stage. 5 One unit of intermediate good produced by a formal rm leads to 1= units of net emission after abatement; 1= is thus the emission intensity of intermediate good output. A higher abatement level (lower emission intensity) involves increased operating cost, as c 1 > 0. 6 The total revenue described above gives the representative formal rm s marginal revenue as MR = a 2x. Moreover, using (1), we can rewrite 5 Kennedy (1994) uses a similar formulation for modeling abatement, in an article that deals with a di erent issue. 6 Although, for expositional ease we call the abatement level, abatement undertaken per unit of intermediate good produced by a formal rm is. When no abatement 1 1 is required (i.e. = 1), then a formal rm s operating cost consists only of production cost (its abatement cost is zero) and equals c 1. 6

7 2 + x 2 T C 2 = x 2 = N + c 2 x 2 ; where 2 is the amount of intermediate good purchased from the informal sector by all other (m 1) formal rms (so that 2 + x 2 = X 2 ). Thus, the representative formal rm s marginal cost of procuring the intermediate good from the informal sector is MC 2 = 2x c 2 N N Notice that MC 1 = c 1 MC 2 for all x 2 1 (c 2 1N 2 c 2 N), or using the fact that 2 = (m 1) x 2 due to symmetry, MC 1 MC 2 for all x 2 less than (or equal to) c 1 c 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 sector rather than produce it. The pro t-maximizing output of nal good is given by MR = MC 1, or x = 1 (a c 2 1). Using the symmetry condition, = (m 1) x, we have x = a c 1 (4) 1 + m Consequently, the optimal amount of intermediate good for the formal rm to produce is x 1 = x x 2 = a + c 2N c 1 (1 + N) (5) 1 + m To focus on the situation where both the sectors produce the intermediate good, 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 abatement level : c 2 c 1 min < < a + c 2N c 1 (1 + N) max Note that the total amount of inputs used (and output produced), x, is independent of the informal sector parameters (c 2 and N). Instead, what the informal sector in uences is the manner in which the total input is obtained 7

8 by the formal rms (self-production vs. sourcing from the informal sector). The outsourcing ratio, de ned as the proportion of total inputs procured from the informal sector, equals x 2 x = c 1 c 2 a c 1 N A more stringent environmental policy (a higher ) increases the formal rms cost of producing the intermediate good. This decreases the total amount of intermediate good used, and nal good produced, x by these rms ( scale e ect ). The higher additionally leads to less self-production (x 1) and more outsourcing (x 2) by each formal rm ( composition e ect ). The combined impact 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 and = mx 2 N + c 2 = mc 1 + c m p = a mx = a + mc m (6) (7) Remark: The equilibrium price a formal rm pays for intermediate goods outsourced from the informal sector ( ) is less than the formal rm s own marginal cost of producing the intermediate good ( c 1 ). Proof: From (6), MC 1 = c 1 mc 1 +c 2 1+m = c 1 c 2 1+m > 0 The above result is a re ection of the market (monopsony) power enjoyed by formal rms when they buy the intermediate good from the informal sector. As m increases, and the formal sector becomes more competitive, the di erence MC 1 decreases, until! MC 1 as m! 1. The equilibrium amount of pollution generated from production of the dirty 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 + c 2N c 1 (1 + N) + N (c 1 c 2 )) (8) 8

9 < 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+c 2 N c 1 N 1), and later on increases (when > 1 ), the level of total pollution; (ii) an increase in the cost of operating in the informal sector ( c 2 ) leads to a decrease in the level of total pollution, in the presence of an abatement policy (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 and only if q a+c 2 N c 1 = a+c 2N c 1 (1+N)+N(c 1 c 2 (1+m) = m (1+m) 2 ( 2 Nc 1 a c 2 N) 0 if 1; (ii) = mn 1 (1+m) > 0. 0; and (iii) Proposition 1(i) implies that total pollution is non-monotonic and convex in the abatement level. A stricter environmental policy (higher ) that applies only to the formal sector has two counteracting e ects on combined pollution that emerges from both the sectors. On one hand, the abovementioned 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 outsourcing from the higher polluting informal sector. When < 1, the former e ect dominates, and pollution generated by the formal and informal sectors together decreases as environmental policy become tighter. The converse is true when > 1. 7 Consequently, total pollution is U-shaped in the abatement level imposed on the formal sector. Of course, had the informal sector been altogether absent (if it is successfully banned, for instance) the composition e ect would be absent, and a more stringent policy would always reduce total pollution (i.e., if N = < 0 for all Recall that c 2 denotes the lower bound of the informal rms heterogeneous cost of operating in the informal sector (the upper bound is c 2 +!). Some possible reasons for a change in c 2 are as follows. If the government 7 Note that 1, as de ned above, is greater than min if and only if ac 1 +c 2 N (c 1 c 2 ) > 0. As well, 1 is less than max if and only if an > c 1 (1 + 2N) + N 2 (c 1 c 2 ). We later provide numerical examples where these conditions are satis ed. 9

10 randomly monitored the informal sector in order to discourage fringe rms from operating, and imposed higher penalties on detected violators, it could lead to an increase in c 2. Alternatively, c 2 could also rise if, due to economic development, the fringe rms outside option (alternative to joining the informal sector) became more pro table (e.g. if their opportunity cost of labour increased). In any event, Proposition 1(ii) shows that an increase in c 2 will lead 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. total pollution. > 0), and raises 2.2 E cient environmental policy In the rst stage of the game, a government regulatory body sets the abatement level. Suppose the regulator chooses so as to maximize social welfare, W, de ned as the sum of consumer surplus plus pro t of both formal and informal rms minus pollution damage: 9 1 W 2 (mx 1 + mx 2 ) 2 mx1 +m (p (x 1 + x 2 ) c 1 x 1 x 2 )+ 2 + mx 2 ; (9) where 0 is the marginal pollution damage. Making use of (2), (3), (5), (6) and (7), the FOC for maximum W = m c (1 + N) (m + 2) + (1 + m) (a + c 2 N) 2 (1 + m) 2 c 1 2 (N (1 + m) + (m + 2) (a + c 2 N)) = 0 (10) Notice that there are three roots of that satisfy the FOC. As well, the second derivative of W with respect to 2 2 = m (2 (1 + m) (a + c 2N) c (2 + m) (1 + N)) (1 + m) 2 3 ; (11) 8 If, in an alternative scenario, the formal and informal rms produced the same polluting good for a market, total pollution may fall when m increases. This is shown in the Appendix, which analyses the alternative scenario. 9 Alternatively, the government could choose on considerations such as those involving political factors or lobbying. 10

11 which is negative for all such that 0 < < 1 2 (1 + m) (a + c2 N) 3 2 c 2 1 (2 + m) (1 + N) To focus on the interior solution, we assume parameter values are such that welfare W is maximized at, where is the value of the abatement level that satis es the FOC (10), and 2 (1; 2 ). 10 This implies that the 2 W < 0 is satis ed at. In the next section we provide numerical 2 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 of welfare W (): Proposition 2: An increase in the cost of operating in the informal sector d (i) makes the e cient environmental policy more stringent, i.e. dc 2 > 0, if and only if (1 + m) c 1 2 (2 + m) > 0; dw (ii) increases social welfare, i.e. dc 2 > 0, if and only if c 1 2 (2 + m) ( (1 + m) + c 2 (2 + m)) + (1 + m) < 0. Proof: (i) The sign of d dc 2 can be derived using the methodology of comparative statics with respect to the FOC (10). Subject to satisfaction of the 2 W < 0, we 2 sign = sign dc 2 From (10), we = mn (1 + m) 2 (1 + m) c 1 2 (2 + m) 2 (ii) Using the envelope theorem, we have dw dc 2 ( = ). From = mn (c 1 2 (2 + m) ( (1 + m) + c 2 (2 + m)) + (1 + m)) (1 + m) 2 10 In contrast, a corner solution would involve = 1 or = max. 11

12 Proposition 3: In the presence of an informal sector, an increase in the number of formal rms d (i) makes the e cient environmental policy more stringent, i.e. > 0; dm (ii) increases social welfare, i.e. dw > 0, if and only if the expression in dm eq. (12), when evaluated at =, is positive. Proof: Similar to proof of Proposition 2. (i) From (10), = 2c2 1 3 (1 + N) c 1 2 (2 (a + c 2 N) + N (1 + m)) + (1 + m) (a + c 2 N) (1 + m) 3 ; 2 which is positive when evaluated at = (note F () = 0 by de nition of ). (ii) From (9), = c (1 + N) c 1 2 (N (1 + m) + 2 (a + c 2 N)) (1 + m) (a + c 2 N) + (a 2 + Nc (1 + m) (c 2 N + c 1 (1 + N))) (1 + m) 3 (12) The scenario analyzed in our model involves three sources of market failure, which the environmental policy variable has to address. First, there is the negative externality of pollution, which is generated through production of the intermediate good. Correcting the overproduction associated with this externality calls for an abatement level > 1. Second, due to imperfect competition in the formal sector, there is underproduction of the nal output. Correcting this market failure requires a production subsidy, which exerts a downward pressure (implying a less stringent environmental policy) on costly abatement activities. Third, an increase in the abatement level increases the formal rms operating cost and makes sourcing the intermediate good from the informal sector more pro table for them. However, this exacerbates the negative externality problem as, unlike the formal rms, the informal rms do not undertake any abatement. These three considerations have to be incorporated 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

13 enables the regulator to relax the e cient environmental policy, when the pollution damage parameter is su ciently small. An increase in the number of formal rms, on the other hand, lessens the underproduction e ect and enables 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; c 1 = 2; c 2 = 0, N = 3 Numerical Example 1: Suppose the number of formal rms is m = 1, and the pollution damage parameter is = 5. Then the previouslyde 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. As well, from W ( = 1: 29) = 219: 19. With an e cient 2 policy, equilibrium values of the other variables are x 1 = 44:83, x 2 = 3:88, = 1:29, p = 51:29 and Z = 38:54. Moreover, evaluated at = 1: = 4: 119, = 1092: 3. Thus, from Proposition an increase in the cost of operating in the informal sector (c 2 ) decreases both the e cient level of abatement (signifying a weaker environmental policy) and also social welfare. An increase in the number of formal rms, on the other hand, increases social welfare (following Proposition 3). Numerical Example 2: Alternatively, suppose m = 1 and = 15. As before, max = 12:5 and 1 = 4: 08. The three roots of that satisfy the FOC (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 W ( = 2: 1) = 149: 55. With abatement set 2 its e cient level, values of the other variables are x 1 = 41: 59, x 2 = 6: 31, = 2: 1, p = 52: 1 and Z = 26: 1. = 0: = 2: 34, = 958: 04. Therefore, an increase in the cost of operating in the sector c 2 now increases both e cient abatement level (signifying a stricter environmental policy) as well as social welfare. An increase in the number of formal rms also increases social welfare. 13

14 Numerical Example 3: Suppose instead m = 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 W ( = 1: 54) = 249: 35. With e cient 2 policy, equilibrium values of the other variables are x 1 = 2: 83, x 2 = 0: 3, = 2: 98, p = 6: 21, and Z = 64: 06. = 0: = 4: 14, = 2: Therefore, an increase in the cost of operating the informal sector c 2 increases e cient abatement level but decreases social welfare. Unlike examples 1 and 2, an increase in the number of formal rms now decreases social welfare. 3 Conclusion This paper considers a situation where an environmental policy targets a few dominant producers of a polluting good but leaves many smaller polluters outside its scope. 11 The speci c context modeled is one where imperfectly competitive formal rms and price-taking informal rms produce a polluting intermediate good. The formal sector rms also produce the downstream nal good. We nd that imposition of an environmental policy, which requires only the formal sector rms to abate their own emissions, reduces the total amount of intermediate good used by the formal rms but increases the amount of intermediate good outsourced from the informal sector. These counteracting e ects are shown in the paper to imply that more stringent abatement requirements on the formal sector initially reduces total pollution before increasing it. 12 When the abatement level is chosen by the regulator to maximize social welfare, we nd that an increase in the cost of operating in the informal 11 Although our model is motivated in terms of a formal vs. informal sector example, the model and the results are also applicable to any situation where a few dominant polluters are 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 is considering an environmental policy that targets a few large polluters of greenhouse gases but leaves smaller polluters unregulated. 12 The 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 the market (see Appendix). 14

15 sector may reduce social welfare. Welfare may also get reduced if the number of formal sector rms increases. These results have important implications for both development policy and competition policy. In particular, they suggest that, under certain conditions, discouraging the informal sector, or promoting entry into the formal sector, may not be desirable from a social welfare perspective. 15

16 Appendix Consider an alternative (to that in the main text) scenario where there is a polluting good Q (e.g. bricks), which is produced by both the formal and 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 there is no abatement, production of one unit of the good generates one unit of pollution (or some other negative externality such as littering or congestion). Formal rms are required by the government to undertake abatement, such that 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 the same as before (in the main text), in order to facilitate comparison. The only di erence is that the production structure in this appendix does not involve a vertical (upstream/downstream) relation between the formal and informal sectors. 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 earns zero pro t. The number of informal rms, and total output produced by the informal sector (sector 2), is Q 2 = (p c 2 ) N (13) In the second stage, the formal sector (sector 1) rms now face a residual demand given by p = a Q 1 Q 2 or, using (13), p = a Q 1 + c 2 N ; (14) 1 + N where Q 1 is the total output of the formal sector. The representative formal rm chooses its own production q 1 in order to maximize its pro t! 1 = a Q1 f q 1 + c 2 N q 1 c 1 q 1 ; 1 + N where Q f 1 is the output of all other (m 1) formal rms. The formal rm s unit cost is c 1 as before. The FOC for pro t maximization, along with the symmetric condition Q f 1 = (m 1) q 1, yields 16

17 q1 A = a + c 2N c 1 (1 + N) ; m + 1 where we use superscript A to denote the equilibrium values of the variables in the alternative scenario considered in this appendix. To ensure positive production by the formal rms (q1 A > 0), we assume < a + c 2N c 1 (1 + N) = max Equilibrium price of the good, using (14), is p A = a + c 2N + mc 1 (1 + N) (m + 1) (1 + N) (15) From (13) and (15), total output of the informal sector is Q A 2 = N (a c 2 + m (c 1 c 2 ) (1 + N)) (m + 1) (1 + N) Equilibrium pollution from the formal and informal sectors rms together now is Z A mqa 1 + Q A 2 = (N (a c2 ) m (1 + N) (c 1 (1 + N) + c 2 N)) +mc 1 N 2 (1 + N) + m (1 + N) (c 2 N + 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+c 2 N c 1 N < = 1), and later on increases (when > 1 ), the level of total pollution; (ii) an increase in the cost of operating in the informal sector ( c 2 ) leads to a decrease in the level of total pollution, < 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+N N 3. 17

18 Proof: From (16), we have m = ( 2 (1+m) 2 1 a c 2 N) 0 if q a+c and only if 2 N = c 1 N 1; +m( 1)(1+N) = N < 0; and (iii) A = (1 + N N) a+c 2N c 1 (1+N) 0 if and only if (m+1) 2 (1+N) N 3. Note that total pollution now may fall with an increase in the number of formal rms, unlike Proposition 1(iii) in the main text. The key reason behind the di erential impact of an increase in m on total pollution in the two models is as follows. Whereas an increase in m leads to an increase in total output produced by informal rms (i.e. 2) > 0) in the main (where informal rms produced an input for the formal rms), an increase in m leads to a reduction in total output produced by the informal sector < 0) in the appendix (where informal and formal rms sell the same good). This creates the potential for total pollution to decrease in the latter scenario but not in the former. The welfare implications of the two models, nevertheless, remain qualitatively similar. 18

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