Speculative runs on interest rate pegs the frictionless case

In this paper we show that interest rate rules lead to multiple equilibria when the central bank faces a limit to its ability to print money, or when private agents are limited in the amount of bonds that can be pledged to the central bank in exchange for money. Some of the equilibria are familiar and common to the environments where limits to money growth are not considered. However, new equilibria emerge, where money growth and inflation are higher. These equilibria involve a run on the central bank's interest target: households borrow as much as possible from the central bank, and the shadow interest rate in the private market is different from the policy target.