Why does overnight liquidity cost more than intraday liquidity?

In this paper, we argue that the observed difference in the cost of intraday and overnight liquidity is part of an optimal payments system design. In our environment, overnight liquidity affects output while intraday liquidity affects only the distribution of resources between money holders and non-money holders. The low cost of intraday liquidity is explained by the Friedman rule. The optimal cost differential achieves the twin objective of reducing the incentive to overuse money at night and encouraging payment-risk sharing during the day.