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Gatekeeping, Selection, and Welfare

Francesco Del Prato, Paolo Zacchia

Abstract

We study staged entry with costly gatekeeping in a differentiated-products economy: entrepreneurs observe noisy signals before paying a resource-intensive activation cost. Precision improves selection but requires more resources, reducing entry and variety: welfare need not rise with precision. Under CES preferences, the activation cutoff is efficient as profit displacement offsets the consumer-surplus gain from variety. Welfare losses arise from verification costs shrinking the feasible set of varieties, not from misaligned incentives. Because the market responds efficiently to any given regime, these losses cannot be corrected via Pigouvian taxes.

Gatekeeping, Selection, and Welfare

Abstract

We study staged entry with costly gatekeeping in a differentiated-products economy: entrepreneurs observe noisy signals before paying a resource-intensive activation cost. Precision improves selection but requires more resources, reducing entry and variety: welfare need not rise with precision. Under CES preferences, the activation cutoff is efficient as profit displacement offsets the consumer-surplus gain from variety. Welfare losses arise from verification costs shrinking the feasible set of varieties, not from misaligned incentives. Because the market responds efficiently to any given regime, these losses cannot be corrected via Pigouvian taxes.

Paper Structure

This paper contains 34 sections, 11 theorems, 51 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Results
  3. Contributions
  4. Policy implications
  5. Literature
  6. Outline
  7. The model
  8. Setup
  9. Analysis
  10. Operating fixed-cost shocks
  11. Limit cases
  12. Welfare
  13. Welfare building blocks
  14. Across-regime comparison: the cost of precision
  15. Within-regime efficiency: the planner's problem
  16. ...and 19 more sections

Key Result

proposition A1

Maintain Assumptions ass:signal-informativeness--ass:lognormality. Then an equilibrium pair $\left(\theta^{\ast},\varphi^{\ast}\right)$ exists and is unique. In the log-normal benchmark, the equilibrium is characterized by the intersection of the AC curve, $\varphi^{\ast}=A\left(\theta^{\ast}\right)

Figures (3)

  • Figure A1: Equilibrium of the model and comparative statics
  • Figure A2: Limit cases and fixed-cost intuition
  • Figure A3: Gatekeeping and welfare.

Theorems & Definitions (22)

  • proposition A1
  • proposition A2: Welfare continuity
  • proposition A3: Welfare can decline with bounded verification costs
  • corollary A1: Local welfare condition
  • remark A1: Unbounded cost schedules
  • proposition A4: Cutoff optimality under single-crossing
  • corollary A2: CES makes single-crossing redundant
  • lemma A1: Activation-cutoff efficiency
  • corollary A3: No Pigouvian correction at the activation margin
  • lemma A2: Single-peakedness
  • ...and 12 more