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.

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