Competitive and Revenue-Optimal Pricing with Budgets

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. Firstly, we show that competitive equilibrium outcomes, and only those, are constrained utilitarian efficient, a notion of utilitarian efficiency that respects buyers' demands and budgets. Secondly, we establish that, when buyers have linear valuations, competitive equilibrium prices are unique and revenue-optimal for a zero-cost seller.