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, the interest charged on overnight liquidity affects output, while the cost of intraday liquidity only affects the distribution of resources between money holders and non–money holders. The low cost of intraday liquidity follows from the Friedman rule, but with respect to overnight liquidity, it is optimal to deviate from the Friedman rule. The cost differential simultaneously reduces the incentive to overuse money and encourages risk sharing.