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Setting a carbon tax using Lagrange's duality

Ce projet a été attribué.

Encadrants

  • Olivier Fercoq (IDS) ; Iyad Walwil (IDS)
  • Emails: olivier.fercoq@telecom-paris.fr
  • Bureaux: 5C48

Nombre d'étudiant par instance du projet:

  • Minimum: 2
  • Maximum: 4

Nombre d'instances du projet :

2

Sigles des UE couvertes et/ou Mots-clés :

carbon tax, optimization, disciplined convex programming, micro-economics, utility function

Image

project image

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

Références bibliographiques: