carbon tax, optimization, disciplined convex programming, micro-economics, utility function
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Description du projet :
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.
Objectifs du projet :
Build a dataset of products (price and carbon footprint) and
agents (utility function). The goal is that they consume too much
when not constrained.
Learn how to use CVXPY, recognise convex and concave
functions
Write a software that computes the dual function and
maximizes it.
Economical interpretation
Design a Lagrange multiplier method in order to emulate the
behaviour of a government
Study an alternative model: maximize the utility under budget
constraint instead of minimize cost under utility constraint
