• E42;
  • E58;
  • G21
  • overlapping generations;
  • spatial separation;
  • competitive banks;
  • monopoly bank;
  • Friedman rule;
  • discount window

In this paper, I examine the differences in optimal monetary policy in various banking systems. In particular, I compare two monetary economies: one with a competitive banking system and the other with a monopolistic one. In addition, the optimality of the discount window policy is considered. It is shown that the Friedman rule is the optimal monetary policy in a monopolistic banking economy, and the zero-inflation policy is optimal in a competitive banking economy under appropriate parameters. In addition, the combination of the Friedman rule and the discount window policy can achieve efficient allocation in both banking systems.