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

Joshua Hendrickson

The B.E. Journal of Theoretical Economics, 2022, vol. 22, issue 1, 311-328

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 show that both of these claims are correct under the assumption of complete markets and perfect commitment. The link between these claims is the Black-Scholes equation applied to convertible 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 to redemption or markets are incomplete. I conclude with implications for macroeconomic theory.

Keywords: bank notes; competitive money supply; commodity money (search for similar items in EconPapers)
JEL-codes: E42 E50 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1515/bejte-2020-0021

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