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Regulating a Monopolist without Subsidy

Jiaming Wei, Dihan Zou

TL;DR

This paper studies monopoly regulation under asymmetric information about costs when subsidies are infeasible, using a unit-tax instrument within a Baron–Myerson style framework. It derives a necessary and sufficient condition for laissez-faire to be optimal and, when intervention is warranted, shows that a progressive price cap—featuring delegation at low prices and increasing taxes at high prices—can implement an optimal mix of pricing incentives. It clarifies the role of taxes as substitutes or complements to subsidies and analyzes how policy feasibility shapes regulator design, including special cases with linear and constant-elastic demand and a uniform-cost environment. The results provide a tractable, policy-relevant blueprint for balancing access, affordability, and profitability when subsidies are unavailable, offering insights into the design of price-based regulatory instruments under information frictions.

Abstract

We study monopoly regulation under asymmetric information about costs when subsidies are infeasible. A monopolist with privately known marginal cost serves a single product market and sets a price. The regulator maximizes a weighted welfare function using unit taxes as sole policy instrument. We identify a sufficient and necessary condition for when laissez-faire is optimal. When intervention is desired, we provide simple sufficient conditions under which the optimal policy is a progressive price cap: prices below a benchmark face no tax, while higher prices are taxed at increasing and potentially prohibitive rates. This policy combines delegation at low prices with taxation at high prices, balancing access, affordability, and profitability. Our results clarify when taxes act as complements to subsidies and when they serve only as imperfect substitutes, illuminating how feasible policy instruments shape optimal regulatory design.

Regulating a Monopolist without Subsidy

TL;DR

This paper studies monopoly regulation under asymmetric information about costs when subsidies are infeasible, using a unit-tax instrument within a Baron–Myerson style framework. It derives a necessary and sufficient condition for laissez-faire to be optimal and, when intervention is warranted, shows that a progressive price cap—featuring delegation at low prices and increasing taxes at high prices—can implement an optimal mix of pricing incentives. It clarifies the role of taxes as substitutes or complements to subsidies and analyzes how policy feasibility shapes regulator design, including special cases with linear and constant-elastic demand and a uniform-cost environment. The results provide a tractable, policy-relevant blueprint for balancing access, affordability, and profitability when subsidies are unavailable, offering insights into the design of price-based regulatory instruments under information frictions.

Abstract

We study monopoly regulation under asymmetric information about costs when subsidies are infeasible. A monopolist with privately known marginal cost serves a single product market and sets a price. The regulator maximizes a weighted welfare function using unit taxes as sole policy instrument. We identify a sufficient and necessary condition for when laissez-faire is optimal. When intervention is desired, we provide simple sufficient conditions under which the optimal policy is a progressive price cap: prices below a benchmark face no tax, while higher prices are taxed at increasing and potentially prohibitive rates. This policy combines delegation at low prices with taxation at high prices, balancing access, affordability, and profitability. Our results clarify when taxes act as complements to subsidies and when they serve only as imperfect substitutes, illuminating how feasible policy instruments shape optimal regulatory design.

Paper Structure

This paper contains 28 sections, 11 theorems, 61 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Environment
  4. Example
  5. Timing
  6. Regulator's Objective
  7. Preliminary analysis
  8. Discussion
  9. Optimal Regulation
  10. Laissez-faire as the optimal regulation
  11. Economic Interpretation
  12. Relation to Alternative Regulatory Environments
  13. Taxes and Subsidies: Substitute and Complementary Instruments
  14. Linear Demand
  15. Constant-Elastic Demand
  16. ...and 13 more sections

Key Result

Lemma 2.1

There is a unique laissez-faire production strategy for some cutoff $\overline{c}_{LF} \in (0, 1]$, where $\hat{q}(c)$ solves $P(q) = c - qP'(q)$ for each $c$. Furthermore, $q_{LF}(c)$ strictly decreases in $c$ for $[0, \overline{c}_{LF})$.

Figures (4)

  • Figure 1: Examples of regulated inverse demand curves. The left panel compares the regulated inverse demand under $\tau_1$ (red solid line) against the unregulated one (black dotted line); the right panel compares the regulated inverse demand under $\tau_2$ (blue solid line) against the unregulated one (black dotted line)
  • Figure 2: Firm's inverse demand function $P_\tau(q)$ (left) and the induced pricing strategy $p^*(c)$ (right). $P(q) = 1 - q$, $c \sim U[0,1]$, $\alpha = 1$.
  • Figure 3: Firm's inverse demand function $P_\tau(q)$ (left) and the induced pricing strategy $p^*(c)$ (right) with flexible transfers according to BaronMyerson82. $P(q) = 1 - q$, $c \sim U[0,1]$, $\alpha = 1$.
  • Figure 4: Firm's inverse demand function $P_\tau(q)$ (left) and the induced pricing strategy $p^*(c)$ (right). $P(q) = 1 - q$, $c \sim N(0.5, 0.01)$, $\alpha = 0.1$.

Theorems & Definitions (12)

  • Lemma 2.1: Laissez-Faire Baseline
  • Proposition 3.1
  • Definition 1: Progressive Price Cap
  • Proposition 3.2
  • Lemma B.1
  • Lemma B.2: AmadorBagwell22Regulation
  • Lemma B.3
  • Lemma B.4
  • Lemma B.5
  • Lemma B.6
  • ...and 2 more