Competitive and Revenue-Optimal Pricing with Budgets

TL;DR

This paper explores how in markets with budget-constrained buyers and divisible goods, competitive equilibrium prices are unique and maximize revenue for sellers with zero costs, under linear valuations.

Contribution

It proves that with linear valuations, competitive equilibrium prices are both unique and revenue-maximizing in such markets.

Findings

Competitive equilibrium prices are unique with linear valuations.

These prices are revenue-optimal for zero-cost sellers.

Competitive equilibria are constrained utilitarian efficient.

Abstract

In markets with budget-constrained buyers, competitive equilibria need not be efficient in the utilitarian sense, or maximise the seller's revenue. We consider a setting with multiple divisible goods. Competitive equilibrium outcomes, and only those, are constrained utilitarian efficient, a notion of utilitarian efficiency that respects buyers' demands and budgets. Our main contribution establishes that, when buyers have linear valuations, competitive equilibrium prices are unique and revenue-optimal for a zero-cost seller.