Polluting tanneries and small farmers in Kanpur, India: a theoretical analysis

We focus on the interaction between a representative polluting tannery and a negatively impacted small farmer in Kanpur, India. The tannery produces leather and toxic chemical waste that ends up in wastewater used by the small farmer to irrigate agricultural land and grow vegetables. The waste generated by the tannery is functionally related to its output of leather. The small farmer faces a capacity constraint that describes the maximum amount of vegetables he can grow. In this setting, we perform three tasks. First, we determine the optimal production of leather when the tannery does not account for the negative effect it has on the small farmer. Second, on the assumption that the tannery compensates the small farmer per unit of waste it generates, we ascertain the optimal compensation amount, the optimal output of leather, and the profit levels of the tannery and the small farmer. Finally, we compare the solutions in the preceding two cases and explain what accounts for the differences between them.