Chapter 14 — Institutions and the Design of Gates
Part V · The Designer’s Desk · Week 13
K→𝒢→Q→Ξ
The rule-writers. Institutions are gate-writers, and the whole apparatus of the book becomes a design problem: where to place a gate, whether to toll the interior, how to price the last resort.
Learning objectives
- LOS 14.3 — Compute the regulator’s sufficient statistic: aggregate gate pressure.
- LOS 14.4 — State and prove the Neutrality Theorem and its three failure clauses.
- LOS 14.6 — Derive the Bagehot band for last-resort pricing.
The laboratory module
Module 14 — The Designer’s Desk. A gate optimizer, a neutrality sandbox, a certification designer, and a facility desk.
The optimal gate. A gate at level \(\theta\) governs a population; welfare balances the marginal screening benefit against aggregate gate pressure. The bench computes the welfare-optimal \(\theta^*\) for the default population and shows how it shifts for a fat-tailed one.
The Neutrality Theorem (14.5): optimal burdens sit at the boundary — an interior toll is pure deadweight absent congestion, and becomes Pigouvian only when congestion is present. The Bagehot band prices the last resort: lend freely against good collateral at a penalty rate within a band above the base rate.
Guided experiments
- Find \(\theta^*\) for the default population and then for a fat-tailed one, and explain the shift.
- Construct a case where an interior toll beats every boundary scheme, and name its clause.
- Empty the Bagehot band by raising the penalty rate, and report the facility’s concentration at the new equilibrium.
ch14 · 8/8 PASS