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Prices vs. Quantities: Robust Regulation

Zi Yang Kang

Abstract

This paper revisits the classic instrument choice problem in a setting with consumption externalities, through the lens of robust mechanism design. A regulator can implement any incentive-compatible policy but is uncertain about how individual demand is correlated with marginal externalities, and evaluates policies by worst-case welfare. The optimal policy is a quantity control: a floor for positive externalities and a ceiling for negative externalities. If the sign of the correlation is known, a uniform tax or subsidy can be optimal. The framework also applies to regulatory uncertainty and costly screening, providing a welfare-based explanation for the prevalence of non-price policies.

Prices vs. Quantities: Robust Regulation

Abstract

This paper revisits the classic instrument choice problem in a setting with consumption externalities, through the lens of robust mechanism design. A regulator can implement any incentive-compatible policy but is uncertain about how individual demand is correlated with marginal externalities, and evaluates policies by worst-case welfare. The optimal policy is a quantity control: a floor for positive externalities and a ceiling for negative externalities. If the sign of the correlation is known, a uniform tax or subsidy can be optimal. The framework also applies to regulatory uncertainty and costly screening, providing a welfare-based explanation for the prevalence of non-price policies.
Paper Structure (24 sections, 8 theorems, 49 equations)

This paper contains 24 sections, 8 theorems, 49 equations.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Framework
  4. Model
  5. Discussion of Assumptions
  6. Information about the externality.
  7. Information about demand.
  8. Demand and supply specifications.
  9. Main Results
  10. Unknown Correlation
  11. Positive vs. Negative Correlation
  12. Applications
  13. Vaccines
  14. Negative Externalities
  15. Regulatory Uncertainty
  16. ...and 9 more sections

Key Result

Lemma 1

Define Then an allocation function $q:\Theta\times\mathbb{R}_+\to[0,A]$ is implementable only if there exists $\hat{q}\in\mathcal{Q}$ such that $q(\theta,\xi)=\hat{q}(\theta)$ for almost every $(\theta,\xi)\in\Theta\times\mathbb{R}_+$.

Theorems & Definitions (10)

  • Lemma 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Proposition 1
  • Theorem 1
  • Theorem 2
  • Proposition 2
  • Proposition 3