Resumen
In a world where the means of exchange is convertible into the numeraire consumption good at a fixed rate, no one wants to hold money over time ? and due to convertibility there is no means by which the Friedman rule can generate deflation. This is the environment we study in this paper in order to demonstrate that there is still a way to reach the first-best: institutionalize the naked shorting of the unit of account, or in other words establish a banking system.To motivate the benefits of a banking system, the environment has real productivity shocks that are constantly changing the optimal level of economic activity, so the optimal quantity of money is inherently stochastic. Efficiency in such an environment requires the capacity to expand the money supply on an ?as needed? basis. We show how a debt-based payments system that relies on banks to certify the individual debtors? IOUs addresses the monetary problem.This model explains (i) central bank monetary policy as a means of stabilizing the banking system and (ii) usury laws as means of promoting equilibria that favor non-banks over those that favor banks. Furthermore, by modeling a commercial bank-based monetary system as an efficient solution to a payments problem this paper develops a theoretic framework that may be used to evaluate central bank digital currency proposals.