Competitively-Issued Convertible Bank Notes in a Theory of Finance: Earl Thompson Meets Fischer Black

Abstract

In this paper, I show the validity of and the relationship between two previously unrelated claims in monetary theory. The first claim, made by Earl Thompson, is that privately-issued bank notes pay a positive rate of return in a competitive equilibrium. The second claim, made by Fischer Black, is that it is possible to have a gold standard in which the gold reserves of the central bank are near zero. I first show the validity of Thompson's claim. I then show that a corollary of my result is that Black's claim is correct in a competitive market. The link between these claims is the Black-Scholes equation applied to bank notes. In commodity-based monetary systems, bank notes are perpetual American options. I extend the model to consider the implications of a lack of commitment on the part of the bank and incomplete markets. I show that both arguments break down when banks lack commitment or markets are incomplete. I conclude with implications for macroeconomic theory.

Keywords: bank notes, competitive money supply, commodity money

JEL Classification: E42, E50