Beyond Pigouvian Taxes: A Worst Case Analysis

TL;DR

This paper analyzes the limitations of Pigouvian taxes in achieving socially optimal outcomes, showing that no tax scheme guarantees bounded inefficiency in the worst case, but some schemes outperform the traditional Pigouvian approach.

Contribution

It demonstrates that all tax structures can lead to unbounded social inefficiency in the worst case and identifies a tax scheme with a lower price of anarchy than Pigouvian taxes.

Findings

No tax structure bounds worst-case inefficiency.

A specific tax scheme improves over Pigouvian taxes in worst-case scenarios.

Results extend to alternative transportation scenarios.

Abstract

In the early $20^{th}$ century, Pigou observed that imposing a marginal cost tax on the usage of a public good induces a socially efficient level of use as an equilibrium. Unfortunately, such a "Pigouvian" tax may also induce other, socially inefficient, equilibria. We observe that this social inefficiency may be unbounded, and study whether alternative tax structures may lead to milder losses in the worst case, i.e. to a lower price of anarchy. We show that no tax structure leads to bounded losses in the worst case. However, we do find a tax scheme that has a lower price of anarchy than the Pigouvian tax, obtaining tight lower and upper bounds in terms of a crucial parameter that we identify. We generalize our results to various scenarios that each offers an alternative to the use of a public road by private cars, such as ride sharing, or using a bus or a train.