Setting a carbon tax using Lagrange's duality

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The goal of this project is to study the problem of setting the level of a carbon tax. We consider a model where several economical agents want to minimize the price of the products they buy so that they reach a given satisfaction level and at the same time satisfy jointly a total carbon footprint constraint. We propose to solve this problem using Lagrange duality, where the Lagrange multiplier models the tax level. The goal is to show that by setting a carbon tax appropriately, the consumers can jointly satisfy the constraint while they continue to act selfishly in a day to day basis.

We shall use the optimization software CVXPY for this project that combines mathematics and modelization in micro-economics.