Efficient Pollution Management Through CETP: The Case of Calcutta Leather Complex

Abstract

India’s leather industry occupies a prominent place in the export market, generating scope for foreign exchange earning as well as large-scale employment. The export potential of this industry was recognized by the Government of India in the mid-1970s when it evolved a policy package consisting of a ban on export of raw hides and skins and providing fiscal and other incentives to stimulate the export of finished leather and leather products. Much of the economic benefits derived from leather production and trade; however, have come at a considerable cost to the environment and human health, which should be attended simultaneously to enjoy sustainable benefits from the industry. This poses a serious challenge before the sector and a number of strategies have been contemplated since early the 1990s to give the industry a cleaner shape.

Keywords

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Introduction

India’s leather industry occupies a prominent place in the export market, generating scope for foreign exchange earning as well as large-scale employment. The export potential of this industry was recognized by the Government of India in the mid-1970s when it evolved a policy package consisting of a ban on export of raw hides and skins and providing fiscal and other incentives to stimulate the export of finished leather and leather products. Much of the economic benefits derived from leather production and trade; however, have come at a considerable cost to the environment and human health, which should be attended simultaneously to enjoy sustainable benefits from the industry. This poses a serious challenge before the sector and a number of strategies have been contemplated since the early 1990s to give the industry a cleaner shape.

The leather industry may be regarded as a bridge between the production of the hide as by-product of the food industry and its manufacture into shoes and wearing apparel for which it provides the basic raw material. The production of leather is a long and complicated process which requires specialized skills. The first step is the removal of unwanted components leaving a network of fibers of hide and skin, through a series of pretanning operations. The second step is dealing with tanning materials to produce a stabilized fiber structure. This ensures the permanent preservation. The third step is to build into the tanned fibers characteristics of fullness, color, softness, and lubrication and to finish the fiber surface, to produce a useful product (Thorstensen 1969). As the leather industry, particularly the tanning segment is a pollution-intensive process it has been put under Red category by the Central Pollution Control Board of India. Tannery effluents contaminate air, surface and subsoil water, and undermine the fertility of the soil. The continuous discharge of untreated tannery effluents on land, rivers, and other water bodies has adversely affected the quality of water and agricultural land in the regions in which tanneries are located. Moreover, this industry is characterized by small-scale units which are technologically and financially incapable of undertaking pollution abatement at the individual level. Hence, what is required is a pollution management joint action. The Common Effluent Treatment Plant is a way by which the small tanneries can comply with the norms laid down by the regulatory authority.

With increasing public awareness about environmental damage caused by tanneries, many NGOs in different parts of the country began to protest loudly. In a landmark judgment delivered by the Supreme Court of India in 1996 against a petition filed by the Vellore Citizen’s Forum, more than 400 tanneries of Tamil Nadu were closed for their failure to treat generated waste. Similar public-interest litigation cases in Uttar Pradesh and West Bengal have culminated in Supreme Court Orders for relocation of tanneries or closure of tanneries which do not have their own individual effluent treatment plants(IETPs) or which are not connected to common effluent treatment plants (CETPs) .

Although the industry began to tackle environmental pollution rather slowly in the early 1990s, by the turn of the century, its achievements have been acknowledged by many as truly remarkable. The concept of Common Effluent Treatment Plants has taken deep roots in this industry. In an industry dominated by small-scale units, this has been recognized as an effective strategy. The CETP is found to work efficiently in Tamil Nadu; however, the case of Calcutta Leather Complex in Bantala is far from satisfactory. Though the industry is only too well aware that its ability to overcome environmental challenges is a prerequisite for its continued growth, the management of CETP has started posing some special problems. Because of the public good nature of the plant, here the members generally have an intrinsic tendency to free ride. Therefore, designing of incentive compatible cost sharing rules to ensure voluntary participation of all concerned stakeholders is an analytical challenge.

In this backdrop we have concentrated on the design and management practices adopted in the CETP of Calcutta Leather Complex where the system is technically feasible but still not economically viable. An attempt has been made to assess the existing level of efficiency and to recommend measures to improve it to make the project self sufficient in near future. “Calcutta Leather Complex” will briefly present the site planning, design, and location map of the Calcutta Leather Complex (CLC), “ The Prevailing State” will describe the present situation, “CETP as a Cooperative Game” will vouch the case for cooperative institution-based mechanism design, “Efficient Cost Allocation for CETP in CLC” will assess the economic prospect of CLC, and finally, “Concluding Observations” will conclude the chapter.

Calcutta Leather Complex

In 1985 a public-interest petition (No/3727/1985, M.C Mehta versus Union of India and others) was lodged in the Supreme Court of India directed against the tanneries located in the city of Kanpur for discharging untreated effluent into the river Ganga. Subsequently, the scope of the petition was enlarged and the industries located in various cities on the bank of the river were called upon to stop polluting the river. In this process, about 550 tanneries located at Tangra, Tiljola, Topsia, and Pagladanga, the four adjoining areas in the eastern fringe of Kolkata (the Old Tannery Complex) were identified. Because of dearth of space for establishment of waste-treatment plant in the old tannery complex, the Supreme Court of India instructed the Government of West Bengal to make space available for the relocation of tanneries with modern facilities for effluent treatment. The Government of West Bengal, so directed by the Supreme Court, acquired 1100 acres of land in Bantala,¹ 24-Parganas (South) by July 1992 and the Central Leather Research Institute (CLRI) of Chennai prepared the blueprint of the proposed Calcutta Leather Complex in May 1993. It was agreed that the installation cost of this CETP would be shared by the Central and the State Government on a 50–50 basis where the Ministry of Environment and Forest of the Government of India would include this project in the second phase of the Ganga Action Plan. Accordingly, the Calcutta Leather Complex (CLC) was developed in Bantala and the common effluent treatment plant (CETP) was activated in July 2005. The CLC was supposed to accommodate not only nearly 550 existing tanneries (CLRI estimate) from the old complex, but it was designed to set up new tanneries with state-of -the-art technology and an integrated leather hub to support all types of units connected with leather trade.

Design of CETP

Keeping in mind the requirements of both relocated tanneries with dated technology with a possibility of gradual infusion of upgraded process as well as newly established tanneries with state-of-the-art technology the Government of West Bengal instructed its joint venture partner M.L.Dalmiya & Company Limited to set up a CETP with 30 MLD installed capacity. The CETP has been planned in six modules each of 5 MLD capacity level. The effluent from various tanneries would be pretreated in-house within the individual tanneries through processes like coarse screening to remove large floating matters like flesh, hair etc., and grease traps for removal of grease. This pretreatment would prevent clogging the Effluent Conveying System (ECS) to ensure its smooth functioning.

The individual tanning units would be connected with CETP through two sets of underground pipeline networks. The treatment will pass through three stages: (i) Physical: removal of physical impurities through physical treatments like screening, de-gritting, settling, etc.; (ii) Chemical: removal of chemical impurities by chemical treatment such as pH correction by alkali/acid addition or nutrient/alum/poly-electrolyte addition; (iii) Biological: removal of organic matter and biological impurities by biological process like Aerobic Activated Sludge Treatment System and like. The sludge formed during the physical, chemical, and biological treatment can be further thickened and dewatered to be used as soil conditioner. It is proposed further that after treatment the CETP will make the final discharged water to pass through a microbiological treatment to get back the required purity to be allowed to flow into the water bodies that supply process water for the system.

The Prevailing State

For a more detailed discussion confer Bagchi (Majumdar) and Banerjee (2012).

In-House Treatment

This section reports the findings of a primary survey conducted on 201 tanneries in CLC during the winter of 2008–2009. The existing regulation has made it mandatory on the part of each tannery of the new complex to install in-house water meters (though we have encountered a few units without any such meter) at the inlet point. Even the tanneries that have taken water connection from Dalmiya & Co. have expressed serious reservation regarding the water quality. Nearly 68 % of the units interviewed consider this piped water unfit for tanning purposes due to excessive iron content, bad odor, and erratic supply. The CLC Complex is facing additional problems due to frequent power cuts. Since the process of leather production calls for continuous supply of water, to meet such emergency situations each unit was allowed to bore one in-house pump. Only 47 % of the tanneries visited were found to depend exclusively on Dalmiya’s supply, whereas the rest depend on bore wells either solely or partly. There is no way to measure the volume of water used in the production process from the bore wells and here the tanneries are not paying any tax for using the effluent treatment facilities. In fact, inside the premise of some of the units the interviewers have found even dug-wells. So, in the absence of any appropriate monitoring mechanism the initial idea of collecting pollution charges through installation of water meter at the inlet point (by applying the polluter’s pay principle) appears to be ineffective.² In presence of multiple sources of water supply, water meters at the outlet point would be more effective than at the inlet point.

Treatment Through CETP

In the CLC, out of the proposed six modules of CETP only four have been completed so far. The CETP has been set up to treat mainly Suspended Solids (SS), Biological Oxygen demand (BOD), Chemical Oxygen Demand (COD), Sulphide and Chromium. In 2010–2011 only 288 tanneries had started operation. The already constructed four modules have a capacity of 20 MLD. The tanneries operating in CLC were discharging around 18.83 MLD. Since the cost of running a CETP is quite high each tannery has to pay Rs.14.50 per KLD effluent generated. The effectiveness of CETP depends on the coordination among all the proposed treatment arrangements. If some of them are absent and some others are improperly done then very little can be expected from the final outcome. Proper in-house physical treatment through screening, settling, etc., of the liquid effluents by the individual tanneries before sending it to the CETP is a necessary prerequisite. However, our primary survey revealed that in many cases the effluents were being discharged directly in the rainwater channels. Moreover, since the presettler units are not used properly and adequately in many individual tanneries solid wastes are entering the underground High Density Polyethylene (HDPE) pipeline directly, leading to clogging, cracking, and chocking of the network.

From a number of press release and media reports on the miserably poor performance of the Calcutta Leather Complex there is not much doubt left about the acute coordination problem among the stakeholders since the inception of the project. There is no incentive to make the effluent treatment process effective and efficient. In the following section we briefly state the requirements for economic efficiency in the context of a common facility. The subsequent section will apply this theory for the CETP in CLC.

CETP as a Cooperative Game

For proper functioning of a CETP one needs to derive conditions under which the players of the game, namely the tanners, are likely to cooperate to minimize the total cost of pollution abatement. For each player the share of cost to be borne under coalition should be less than his/her stand-alone cost (this is the participation constraint, where every player would have the interest to participate) and there should be no incentive in terms of incremental cost to defect from the grand coalition by forming any sub-coalition (this is the incentive constraint). The solutions for which both these conditions are satisfied are said to form the CORE of the game. If the core is nonempty then CETP would be considered economically viable in terms of individual rationality, group rationality, and social desirability (in the sense of Pareto efficiency).

Definition and Existence of the CORE

For an N player game, let S be any coalition of n members where n ε [1, N] and $x^{i}$is the share of cost borne by the ith player. Core is a set of feasible payoff vectors X such that it satisfies

• (a) Stand-alone cost test: $x^{i} \le C^{i} \forall i;\sum\limits_{i \in S} {x^{i} } \le C\{ S\}$where $C^{i}$ is the stand-alone cost and C{S} is the total cost borne by all members of the coalition by trying to operate individually or collectively through any sub-coalition indicating it is always better to join the coalition than to operate individually and

• (b) Incremental cost test: $\sum\limits_{i} {x^{i} } \ge \{C(N) - C(N - S)\} \forall S \subseteq N$ where C(N)-C(N−S) is the incremental or marginal cost of any coalition S. The core condition eliminates all outcomes that any set of players can improve upon. It would seem reasonable to assume that if core exists then the imputation chosen should be in the core, since all (2^N−1) coalitions are accounted for. If the cost saving of a joint project increases with the increase in the size of the coalition then the core exists. So, the cost function has to be sub-additive, monotonic and consistent. However, the core may be empty. So, to apply this technique, one should check for the existence of core first, and then, go for the optimizing sharing rule for common cost within the core.

Uniqueness of the Solution

To arrive at a unique solution one may have to encounter either the problem of nonexistence of core or its nonuniqueness. In case of the former, one has to relax the constraints in defining the core and for the latter one has to strengthen the constraints to eliminate the relatively less desirable solutions in terms of some additional requirements. Here the Nucleolus of the core needs to be identified.

(a) Nucleolus: The idea of the nucleolus is to find a solution in the core that is central in the sense of being as far away from the boundaries as possible. It can be shown that this allocation makes the least well-off coalition as well-off as possible by choosing that imputation which minimizes the maximum complaint that any coalition could have against any imputation. Coalition S is better off than T relative to an allocation x, if $c(S) - \sum\limits_{S} {x_{i} } > c(T) - \sum\limits_{T} {x_{i} }$. The quantity $e(x,S) = c(S) - \sum\limits_{S} {x_{i} }$ is called the excess of S relative to x, which measures the amount (the size of inequity) by which coalition $S$ falls short of its potential $c(S)$ in the allocation of x. Since the core is the set of imputations such that $\sum\limits_{S} {x_{i} } \ge c(S)$for all coalitions $S$, the imputation x is in the core, if and only if, all its excesses are negative or zero. So, one has to find out an allocation x that minimizes the maximum excess e(x, S) over all proper subsets $\phi \subset S \subset N$ is a problem in linear programming:

Max$\varepsilon$, subject to $e(x,S) \ge \varepsilon \forall S \ne \phi ,N;$ and $\sum\limits_{N} {x_{i} } = c(N).$

(b) Shapley Value: By solving a cost-minimizing type programming problem, Shapley Value technique suggests apportionment rule of the common cost among all players by satisfying both stand-alone cost and incremental cost constraints. This is one of the earliest methods of allocation to be based on a consistent set of postulates about how an allocation should be made. All players are assumed to sign up in some particular order. If a group S has already signed up and i was the last member of the group to arrive, his marginal cost contribution to S is [c(S)−c(S-i)]. The Shapley Value is i’s average marginal contribution if all orders for signing up are assumed to be equally likely. It is defined as $x_{i} = \sum\limits_{\begin{subarray}{l} S \subset N \\ i \in N \end{subarray} } {\frac{{\left| {S - i} \right|!\left| {N - S} \right|!}}{N!}} C^{i} (S),$ where $C^{i} (S) = C(S) - C(S - \{ i\} )$is the marginal cost of i relative to S, and the sum is over all subsets of S containing i, and x _i is the share of i in the total cost. Shapley value allocation is fair in the sense that it is order free, symmetric, and it gives the dummy player his own worth only and not a share of the saving/cost to which he has not contributed. It includes all possible intermediate coalitions while calculating the share of a particular project and, therefore, is a combinatorial version of marginal analysis by protecting additivity, monotonicity, and consistency properties of cost allocation (Shubik 1984). If the core exists the Shapley allocation belongs to core.

Illustration

To illustrate the technique let us derive the characteristic function of a 3-player cost-minimizing game as follows:

Minimize any variable c(1), c(2) or c(3), subject to:

$$ c(1) \le 81.7;c(2) \le 46.1;\;c(3) \le 12.5; $$

$$ c(1,2) \le 111.0;\;c(1,3) \le 89.1;\;c(2,3) \le 54.0;\;c(1,2,3) \le 118.1;\;c_{i} \ge 0\forall i = 1,2,3. $$

The values of the characteristic function can be plotted to show whether the core is empty or not. In Fig. 22.1, an equilateral triangle ΔXYZ is representing this 3-player cooperative game. The length of each arm is 118.1, which is the cost of the grand coalition and each point in or on the triangle is giving a solution to the cost sharing problem. All these solutions may not be feasible and the concept of core will help one to identify the feasible set, provided it is non-empty.

Fig. 22.1

CORE of the game in terms of characteristic functions

For the first player: stand-alone cost [c(1) = 81.7], represented by the straight line AA; incremental costs of coalition with the second and third players, one at a time, are [c(1,2) − c(2) = 111.0−46.1 = 64.9] and [c(1,3) − c(3) = 89.1 − 12.5 = 76.6] where both 64.9 and 76.6 < 81.7. So, it will be cost-saving option for the first player to form and stay in the two-person coalition. Similarly, if a grand coalition is formed by all three players then the incremental cost for the first player would be [c(1,2,3) − c(2,3) = 118.1 − 54.0 = 64.1] which is even smaller than what he could achieve through two-person coalition. So, the maximum cost saving through coalition that could be attained by player I is 64.1 and it is represented by the straight line A’A’ in the diagram. The area in between the two lines AA and A’A’ is giving the interest zone for player I. and as the magnitude of cost saving is increasing in the size of the coalition, player I has no incentive to defect.

Following the same logic for player II, the straight line BB represents his stand-alone cost c(2) = 46.1 and he will not be interested in any coalition where his share of cost will exceed BB. Incremental costs of coalition with the first and third players, one at a time, are [c(1,2)−c(1) = 111.0−81.7 = 29.3] and [c(2,3)−c(3) = 54.0−12.5 = 41.5] where both 29.3 and 41.5 < 46.1. Similarly, the incremental cost of the second player from joining a grand coalition would be [c(1,2,3)–c(1,3) = 118.1–89.1 = 29.0] which is even smaller than what could be achieved by joining 2-person coalition This maximum cost saving by player II is represented by B’B’ in Fig. 22.1. For player III, the straight line CC represents her stand-alone cost c(3) = 12.5. Incremental costs of coalition with first and second players, one at a time, are 7.4 and 7.9, respectively, and that for the 3-person coalition is 7.1. All these values are less than the stand-alone cost and the maximum possible cost saving is represented by the line C’C’.

Thus, the bargaining zone where each player will have incentive to participate is identified first in terms of stand- alone constraints AA, BB, and CC as the area DEFG. When the incremental cost constraint of player I, viz., A’A’ is superimposed triangle ΔA” got eliminated. Similarly, B’B’ eliminated the triangle ΔB” and C’C’ eliminated the shaded area C”. Finally, the dotted area Q represents the core of the game.³ Since the core is nonempty, two alternative solutions⁴ to this cost sharing game have been reported in Table 22.1.

Table 22.1 Comparison of alternative solutions

In the following section we will try to estimate the component-wise cost and total cost of running a CETP and the pumping stations in CLC and will try to find out the share of common costs to be borne by each pumping station by following both Nucleolus as well as Shapley principles. Since these allocations are efficient, it is expected that if introduced, they will create incentive for better in-house pollution management through effective and adequate pretreatment.

Efficient Cost Allocation for CETP in CLC

There are at present 288⁵ tanneries operating at Calcutta Leather Complex spread over nine zones. There are six pumping stations. Each tannery is connected with some effluent pumping station (EPS) through HDPE pipelines of proper gradient whereby the pretreated effluent is supposed to reach the EPS without any external pressure. The effluents accumulated at the pumping stations are sent to CETP for further treatment. If from any zone effluent is sent to more than one EPS then a proportional allocation rule is applied to estimate the total volume of effluent at those EPSs.⁶ The primary data on the design of the treatment plant, location map of zones and the position of the EPS, and operation and maintenance cost have been gathered from the West Bengal Pollution Board and the officials of the Calcutta Leather Tanners Association.

Table 22.2 shows the number of tanneries attached to each EPS and the volume of effluent sent to the CETP by each EPS. The first problem encountered in defining the cost function is related to the identification of independent actors in the system. We could have taken either the zones or the Effluent Pumping Stations (EPS) as the actors. If the former is taken, we have to deal with (2⁹−1) = 511 possible coalitions and for the latter the number would be reduced to (2⁶−1) = 63 possible coalitions. The second option is more manageable. Moreover, from individual tanneries the pretreated effluent reaches the EPS through underground gradient pipelines by gravitational forces and from there the pumping and treatment process starts. Hence, we have considered the six EPS as the players and the 288 operating tanneries have been grouped accordingly.

Table 22.2 Zone and EPS-wise distribution of effluent in CLC

The Game Setup

Players:

The EPSs are taken as the players in our cooperative game

Common knowledge:

All the players have all the information regarding CETP

Negotiation set:

The negotiation set is obtained by pre play agreements and it defines the minimum and maximum points (stand-alone and incremental costs) for all the players

Outcomes:

Determination of fair and equitable cost allocation to member units and the optimal size of coalition.

Cost Calculation

To estimate cost for each EPS, information is required on the following items:

• The capital cost of the grand coalition;

• The operation and maintenance cost of each coalition and the grand coalition.

Estimation of Capital Cost

Table 22.3 gives the cost of the CLC project. To estimate the current cost figures the available dated figures have been transformed into equivalent current price values.⁷ The total cost (TC) of the CETP is given by the summation of capital cost (CC) and the operation and maintenance cost (O&M cost). CC has three components: (a) engineering cost like civil, mechanical, and the cost of other technical services, called the capacity cost (b) the conveyance cost (which depends on the length of pipeline of the effluent transmission system [ETS]) and (c) the pumping cost (which is dependent on the cost of pump station).

Table 22.3 Cost of CLC project (Rupees in lakhs)

Capacity cost has been estimated by applying the following formulae CC(a) = A*(capacity)^α, where A is a constant and α is assumed to be equal to 0.75 (to keep in line with the falling fixed cost per unit of production.) ⁸ The capacity cost excludes the costs related to conveyance, and pumping. Here the capacity cost CC(a) is: [15784.28−(3215.84 + 868.6)] = 11699.84 and current capacity is 18833⁹ KLD. Hence, from the cost equation for CC (a), A can be solved as 7.27. Given this value of A for each player, i.e., for each EPS, the CC (a) can be estimated corresponding to the volume of effluent pumped.

To estimate the cost of conveyance CC (b), information on the length of pipeline from each effluent pumping station (EPS) to the CETP is required. The total length of pipeline is 24.98 km¹⁰ and the total cost of conveyance is Rs. 3215.84 lakhs, making the cost of conveyance per kilometer equal to Rs. 128.736 lakhs. This total length of pipeline is basically the summation of all pipelines connecting all tanneries to different EPS (18.0 km) and from six different EPSs to the CETP (6.98 km). So, for each EPS, the conveyance cost has been calculated as (specific distance * unit cost).

Finally, the third component of capital cost, viz., the pumping cost CC(c) has been obtained as [868.6/18833]*(volume of effluent per EPS).

Now, [CC (a) + CC (b) + CC(c)] gives the total capital cost for each EPS. To obtain the corresponding annualized value assumptions need to be made regarding the length of the project life and the social discount rate. Following the standard practice applied in case of VANITEC CETP of Tamil Nadu (Anuradha 2005), we have taken the span of project life as 20 years and the social discount rate as 15 %. Then the present value factor would be $PVF = \sum\limits_{t = 1}^{20} {\left( {\frac{1}{1.15}} \right)}^{t} = [6.2613]^{ - 1} .$

Multiplying the Total Capital Cost (TCC) for each coalition by this PVF the annualized capital cost is obtained.

Finally, the operation and maintenance cost is added to this TCC to get the total cost of treatment incurred by each coalition. According to CLCTA, the total O&M cost per month for 18833 KLD is Rs. 81.67 lakhs at CETP and another Rs. 25 lakhs (ETS + EPS) for all pumping stations taken together. So the total operation and maintenance cost is Rs. 106.67 lakhs per month. Hence the variable cost per KLD of effluent turned out to be Rs. 566.4. As the annualized average cost is an annual cost, we represent the operation maintenance cost on a yearly basis by multiplying it by 12.

Ultimately, the total capital cost and the operation and maintenance cost has been added to arrive at the total cost. Since the effluent entering the CETP is measured as Kiloliters per day the total cost (CC + O & M) has been divided by 365 to generate an estimate of daily cost. Tables 22.4 and 22.5 present the break ups of cost.

Table 22.4 Components of capital cost for each EPS (Rs. in lakhs)

Table 22.5 Total cost per EPS (Rs. in lakhs)

Table 22.5 gives the total cost of for the six players. With six players we will have [2⁶ −1] = 63 number of possible coalitions (including the grand coalition). Given these cost information we want to explore the possibility of cost saving through economically viable cooperation and for that we want to apply the Shapley Value criterion and Nucleolus criterion of cost sharing. Since for each player the stand-alone cost C _i is greater than the incremental cost of joining any coalition and the incremental cost is consistently falling with an increase in the size of the coalition, hence everyone has the interest to participate in the coalition and once joined, no one would have the incentive to defect. Hence the CORE will exist and the cooperation will be stable.

It is apparent from Table 22.6 that the present cost of running the CETP is Rs. 11.954 lakh and the least cost in core is Rs. 8.244 lakhs. We can now apply the Shapley Value allocation and Nucleolus method to find out the efficient cost allocation over the six players (Table 22.7). Both these allocations belong to core, both are individually rational, group rational, and Pareto efficient. However, the least cost combination in core (i.e., Rs. 8.244 lakhs) is not attainable. The maximum possible cost saving would be (Rs. 11.9540−9.4000) = Rs. 2.5540 lakhs per day, which means a 21.365 % cost saving. Comparison of Shapley allocation for each of the six players¹¹ indicates that players 1 and 2 (the biggest players) are subsidizing others.

Table 22.6 Coalition cost combinations and existence of core (Rs. in lakhs)

Table 22.7 Alternative cost allocation options for CETP

At present, the rate charged per KLD is Rs. 14.50. Given the volume of effluent at 18.833 MLD, the total collection is Rs. 2.73 lakhs per day. This creates a deficit of Rs. 0.83 lakhs per day, even when one is inclined to cover only the operation and maintenance cost. However, the Shapley allocation would save Rs. 2.554 lakhs per day; and thereby not only the running cost but a part of the capital cost will also be covered, and eventually the CETP would come out as a self-financed project.

Concluding Observations

Thus we see that to be successful, a CETP institution needs to be organized by following the structure of a cooperative game where all the parties will have incentive to participate and no one will have the scope to violate the rules of participation. If such conditions can be created, the game is said to have a stable core solution. Here the rate structure should be so designed that it would be less costly for each agent to participate in the coalition in the sense that the part of the shared cost borne by her would definitely be less than the stand-alone cost. Moreover, the cost share in this grand coalition would be less than her share of cost in every possible sub-coalition.

The pollution management issue is mostly approached in India on a case-by-case basis from the perspective of social cost benefit analysis. Here, technical feasibility enjoys greater weight compared to economic efficiency. However, this practice imposes huge fiscal burden on the regulatory authority and the success of the project becomes more contingent on the quality of monitoring, allowing incentive designing no significant role to play. Given the rapid expansion of environmental awareness, more proactive role of the civil society in protecting public interest, time has become ripe enough to incorporate pollution management in the greater agenda of fiscal reform.

Appendices

Appendix A

1. The Nucleolus allocation for three players:

Solving LPP for Nucleolus

min$\varepsilon$

subject to $x_{A} \ge - \varepsilon ,\;x_{B} \ge - \varepsilon ,x_{C} \; \ge - \varepsilon$

$$ x_{A} + x_{B} \ge 16.8 - \varepsilon ,x_{A} + x_{C} \ge 5.1 - \varepsilon ,x_{B} + x_{C} \ge 4.6 - \varepsilon , $$

$$ x_{A} + x_{C} + x_{B} = 2 2. 2 $$

The solution is $\varepsilon = - 2. 7,\;x_{A} = 1 4. 9,x_{B} = 4. 6,\;x_{C} = 2.7$

The corresponding unique cost allocation, the Nucleolus allocation is ($y_{A} = 6 6. 8,\;y_{B} = 4 1. 5,\;y_{C} = { 9}. 8$);

2. The Shapley allocation for three players:

$X_{i} = \sum\limits_{\begin{subarray}{l} S \subset N \\ i \in N \end{subarray} } {\frac{{\left| {S - i} \right|!\left| {N - S} \right|!}}{N!}} C^{i} (S),$ where i = 1, 2, …,n and $C^{i} (S) = C(S) - C(S - \{ i\} )$

Using the above equation, the Shapley allocation for the game is calculated as follows

$$ \begin{aligned} {\text{X}}_{ 1} & = \, \left( { 1/ 3} \right) \, \left[ {{\text{C}}_{ 1} - {\text{C}}_{0} } \right] \, + \, \left( { 1/ 6} \right)\left[ {\left( {{\text{C}}_{ 1 2} - {\text{C}}_{ 2} } \right) + \left( {{\text{C}}_{ 1 3} - {\text{C}}_{ 3} } \right)} \right] \, + \left( { 1/ 3} \right) \, )\left[ {{\text{C}}_{ 1 2 3} - {\text{C}}_{ 2 3} } \right] \\ {\text{X}}_{ 2} & = \, \left( { 1/ 3} \right)\left[ {{\text{C}}_{ 2} - {\text{C}}_{0} } \right] + \left( { 1/ 6} \right)\left[ {\left( {{\text{C}}_{ 1 2} - {\text{C}}_{ 1} } \right) +_{ } } \right)\left[ {\left( {{\text{C}}_{ 2 3} - {\text{C}}_{ 3} } \right)} \right] \, + \left( { 1/ 3} \right) \, )\left[ {{\text{C}}_{ 1 2 3} - {\text{C}}_{ 1 3} } \right] \\ {\text{X}}_{ 3} & = \, \left( { 1/ 3} \right)\left[ {{\text{C}}_{ 3} - {\text{C}}_{0} } \right] + \left( { 1/ 6} \right)\left[ {\left( {{\text{C}}_{ 1 3} - {\text{C}}_{ 1} } \right) +_{ } } \right)\left[ {\left( {{\text{C}}_{ 2 3} - {\text{C}}_{ 2} } \right)} \right] \, + \left( { 1/ 3} \right) \, )\left[ {{\text{ C}}_{ 1 2 3} - {\text{C}}_{ 1 2} } \right] \\ \end{aligned} $$

Which gives

$$ \begin{aligned} {\mathbf{X}}_{{\mathbf{1}}} & = 1/ 3\left( { 8 1. 7} \right) \, + 1/ 6\left( { 1 4 1. 4} \right) \, + 1/ 3\left( { 6 4. 1} \right) \, = { 72}. 1 8\\ {\mathbf{X}}_{{\mathbf{2}}} & = 1/ 3\left( { 4 6. 2} \right) \, + 1/ 6\left( { 70. 3} \right) \, + 1/ 3\left( { 2 9} \right) \, = { 36}. 8 4\\ {\mathbf{X}}_{{\mathbf{3}}} & = 1/ 3\left( { 1 2. 5} \right) \, + 1/ 6\left( { 1 5. 2} \right) \, + 1/ 3\left( { 7. 1} \right) \, = 9.0 8\\ \end{aligned} $$

Also $\sum\limits_{i} {X_{i} } = { 118}. 1$

where X₁ = cost allocation of 1st player

X₂ = cost allocation of 2nd player

X₃ = cost allocation of 3rd player

The Shapley allocation satisfies the individual rationality, group rationality and Pareto optimality conditions.

Appendix B

Comparison of costs under different allocation schemes at CETP in CLC

Player	Volume of effluent (KLD)	Present cost (Rs. Lakhs)/day		Shapley cost allocation (Rs. Lakhs)/day		Cost saving (%)	Nucleolus cost allocation (Rs. Lakhs)/day		Cost saving (%)
		Total (Ci)	Unit	Total (Xi)	Unit		Total (Yi)	Unit
EPS-1	6108	3.509	0.00057	2.913	0.00048	17.007	2.889	0.00047	17.671
EPS-2	5046	3.023	0.00060	2.462	0.00049	18.581	2.562	0.00051	15.266
EPS-3	2822	1.868	0.00066	1.416	0.00050	24.174	1.406	0.00050	24.713
EPS-4	2394	1.681	0.00070	1.264	0.00053	24.819	1.220	0.00051	27.448
EPS-5	2144	1.460	0.00068	1.070	0.00050	26.694	0.999	0.00047	31.606
EPS-6	319	0.412	0.00129	0.275	0.00086	33.199	0.324	0.00102	21.270
Total	18833	11.954	0.00063	9.400	0.00050	21.365	9.400	0.00050	21.365

1. Source Calculated from information given by WBPCB and CLCTA