Float on a note

From 1863-1914, banks in the U.S. could issue notes subject to full collateral, a tax on outstanding notes, redemption of notes on demand, and a clearing fee per issued note cleared through the Treasury. The system failed to satisfy a purported arbitrage condition: the yield on collateral exceeded the tax rate plus the product of the clearing fee and the average clearing rate of notes. The failure is explained by a model in which note issuers choose to issue notes only in trades that produce a low clearing rate (high float), but in which there are diminishing returns to additional note issue.